From 63edb63f85ed3a2c88cd413d1eb038a7e2fdb690 Mon Sep 17 00:00:00 2001 From: Neil Smith Date: Fri, 16 Feb 2018 14:33:32 +0000 Subject: [PATCH] Added R markdown file --- accidents-regression.ipynb | 62 ++++-- section5.1.Rmd | 219 ++++++++++++++++++++ section5.1.html | 404 +++++++++++++++++++++++++++++++++++++ section5.1.ipynb | 158 +++++++++++++-- section5.1solutions.ipynb | 191 +++++++++++++----- 5 files changed, 952 insertions(+), 82 deletions(-) create mode 100644 section5.1.Rmd create mode 100644 section5.1.html diff --git a/accidents-regression.ipynb b/accidents-regression.ipynb index 56a78c4..a2cf506 100644 --- a/accidents-regression.ipynb +++ b/accidents-regression.ipynb @@ -2,9 +2,31 @@ "cells": [ { "cell_type": "code", - "execution_count": 25, + "execution_count": 1, "metadata": {}, - "outputs": [], + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "── Attaching packages ─────────────────────────────────────── tidyverse 1.2.1 ──\n", + "✔ ggplot2 2.2.1 ✔ purrr 0.2.4\n", + "✔ tibble 1.4.2 ✔ dplyr 0.7.4\n", + "✔ tidyr 0.8.0 ✔ stringr 1.2.0\n", + "✔ readr 1.1.1 ✔ forcats 0.2.0\n", + "── Conflicts ────────────────────────────────────────── tidyverse_conflicts() ──\n", + "✖ dplyr::filter() masks stats::filter()\n", + "✖ dplyr::lag() masks stats::lag()\n", + "\n", + "Attaching package: ‘lubridate’\n", + "\n", + "The following object is masked from ‘package:base’:\n", + "\n", + " date\n", + "\n" + ] + } + ], "source": [ "library(tidyverse)\n", "library(mongolite)\n", @@ -13,7 +35,7 @@ }, { "cell_type": "code", - "execution_count": 26, + "execution_count": 2, "metadata": {}, "outputs": [], "source": [ @@ -24,7 +46,7 @@ }, { "cell_type": "code", - "execution_count": 27, + "execution_count": 3, "metadata": {}, "outputs": [ { @@ -59,7 +81,7 @@ }, { "cell_type": "code", - "execution_count": 28, + "execution_count": 4, "metadata": {}, "outputs": [ { @@ -87,7 +109,7 @@ }, { "cell_type": "code", - "execution_count": 29, + "execution_count": 5, "metadata": {}, "outputs": [ { @@ -115,7 +137,7 @@ }, { "cell_type": "code", - "execution_count": 30, + "execution_count": 6, "metadata": {}, "outputs": [ { @@ -351,7 +373,7 @@ }, { "cell_type": "code", - "execution_count": 31, + "execution_count": 7, "metadata": { "scrolled": true }, @@ -636,7 +658,7 @@ }, { "cell_type": "code", - "execution_count": 32, + "execution_count": 8, "metadata": { "scrolled": true }, @@ -987,7 +1009,7 @@ }, { "cell_type": "code", - "execution_count": 33, + "execution_count": 9, "metadata": {}, "outputs": [ { @@ -1008,7 +1030,7 @@ }, { "cell_type": "code", - "execution_count": 34, + "execution_count": 10, "metadata": { "scrolled": true }, @@ -1020,7 +1042,7 @@ }, { "cell_type": "code", - "execution_count": 35, + "execution_count": 11, "metadata": { "scrolled": true }, @@ -1307,7 +1329,7 @@ }, { "cell_type": "code", - "execution_count": 42, + "execution_count": 12, "metadata": {}, "outputs": [ { @@ -1334,7 +1356,7 @@ }, { "cell_type": "code", - "execution_count": 44, + "execution_count": 13, "metadata": {}, "outputs": [ { @@ -1360,7 +1382,7 @@ }, { "cell_type": "code", - "execution_count": 43, + "execution_count": 14, "metadata": {}, "outputs": [ { @@ -1388,7 +1410,7 @@ }, { "cell_type": "code", - "execution_count": 39, + "execution_count": 15, "metadata": {}, "outputs": [ { @@ -1424,7 +1446,7 @@ }, { "cell_type": "code", - "execution_count": 40, + "execution_count": 16, "metadata": {}, "outputs": [ { @@ -1453,7 +1475,7 @@ }, { "cell_type": "code", - "execution_count": 45, + "execution_count": 17, "metadata": {}, "outputs": [ { @@ -1492,7 +1514,7 @@ }, { "cell_type": "code", - "execution_count": 47, + "execution_count": 18, "metadata": {}, "outputs": [], "source": [ @@ -1501,7 +1523,7 @@ }, { "cell_type": "code", - "execution_count": 48, + "execution_count": 19, "metadata": {}, "outputs": [ { diff --git a/section5.1.Rmd b/section5.1.Rmd new file mode 100644 index 0000000..4281f69 --- /dev/null +++ b/section5.1.Rmd @@ -0,0 +1,219 @@ +--- +title: "section5.1" +output: html_document +--- + +```{r setup, include=FALSE} +knitr::opts_chunk$set(echo = TRUE) + +library(tidyverse) +library(repr) +library(ggfortify) + +# Change plot size to 4 x 3 +# options(repr.plot.width=6, repr.plot.height=4) + +# Multiple plot function +# +# ggplot objects can be passed in ..., or to plotlist (as a list of ggplot objects) +# - cols: Number of columns in layout +# - layout: A matrix specifying the layout. If present, 'cols' is ignored. +# +# If the layout is something like matrix(c(1,2,3,3), nrow=2, byrow=TRUE), +# then plot 1 will go in the upper left, 2 will go in the upper right, and +# 3 will go all the way across the bottom. +# +multiplot <- function(..., plotlist=NULL, file, cols=1, layout=NULL) { + library(grid) + + # Make a list from the ... arguments and plotlist + plots <- c(list(...), plotlist) + + numPlots = length(plots) + + # If layout is NULL, then use 'cols' to determine layout + if (is.null(layout)) { + # Make the panel + # ncol: Number of columns of plots + # nrow: Number of rows needed, calculated from # of cols + layout <- matrix(seq(1, cols * ceiling(numPlots/cols)), + ncol = cols, nrow = ceiling(numPlots/cols)) + } + + if (numPlots==1) { + print(plots[[1]]) + + } else { + # Set up the page + grid.newpage() + pushViewport(viewport(layout = grid.layout(nrow(layout), ncol(layout)))) + + # Make each plot, in the correct location + for (i in 1:numPlots) { + # Get the i,j matrix positions of the regions that contain this subplot + matchidx <- as.data.frame(which(layout == i, arr.ind = TRUE)) + + print(plots[[i]], vp = viewport(layout.pos.row = matchidx$row, + layout.pos.col = matchidx$col)) + } + } +} +``` + +## Modelling abrasion loss + +This example concerns the dataset `rubber`, which you first met in Exercise 3.1. The experiment introduced in that exercise concerned an investigation of the resistance of rubber to abrasion (the abrasion loss) and how that resistance depended on various attributes of the rubber. In Exercise 3.1, the only explanatory variable we analysed was hardness; but in Exercise 3.19, a second explanatory variable, tensile strength, was taken into account too. There are 30 datapoints. + +```{r load_rubber} +rubber <- read.csv('rubber.csv') +rubber +``` + +The figures below show scatterplots of abrasion loss against hardness and of abrasion loss against strength. (A scatterplot of abrasion loss against hardness also appeared in Solution 3.1.) Figure (a) suggests a strong decreasing linear relationship of abrasion loss with hardness. Figure (b) is much less indicative of any strong dependence of abrasion loss on tensile strength. + +```{r rubber_plots} +hardloss <- ggplot(rubber, aes(x=hardness, y=loss)) + geom_point() +strloss <- ggplot(rubber, aes(x=strength, y=loss)) + geom_point() + +multiplot(hardloss, strloss, cols=2) +``` + +In exercise 3.5(a) you obtained the following output for the regression of abrasion loss on hardness. + +```{r hardness_fit} +fit <- lm(loss ~ hardness, data = rubber) +summary(fit) +anova(fit) +``` + +### Exercise 5.1 + +Now repeat the for the regression of abrasion loss on tensile strength. + +Enter your solution in the cell below. + +```{r ex5.1} +# Your solution here +``` + +### Solution 5.1 + +```{r ex5.1sol} +fit <- lm(loss ~ strength, data = rubber) +summary(fit) +anova(fit) +``` + +Individually, then, regression of abrasion loss on hardness seems satisfactory, albeit accounting for a disappointingly small percentage of the variance in the response; regression of abrasion loss on tensile strength, on the other hand, seems to have very little explanatory power. + + +### Multiple regression +However, back in Exercise 3.19 it was shown that the residuals from the former regression showed a clear relationship with the tensile strength values, and this suggested that a regression model involving both variables is necessary. + +Let us try it. The only change is to include `strength` in the equations being fitted in the `lm()` function. Instead of + +```{r, eval = FALSE} +lm(loss ~ hardness, data = rubber) +``` +use +```{r, eval = FALSE} +lm(loss ~ hardness + strength, data = rubber) +``` + +```{r hardness_str_fit} +fit <- lm(loss ~ hardness + strength, data = rubber) +summary(fit) +anova(fit) +``` + +Looking at the regression coefficient output next, the estimated model for the mean response is + +$$ \hat{y} = \hat{\alpha} + \hat{\beta}_1 x_1 + \hat{\beta}_2 x_2 = 885.2 − 6.571 x_1 − 1.374 x_2 $$ + +where $x_1$ and $x_2$ stand for values of hardness and tensile strength, respectively. + +Associated with each estimated parameter, GenStat gives a standard error (details of the calculation of which need not concern us now) and hence a _t_-statistic (estimate divided by standard error) to be compared with the distribution on `d.f. (Residual)`=27 degrees of freedom. GenStat makes the comparison and gives _p_ values, which in this case are all very small, suggesting strong evidence for the non-zeroness (and hence presence) of each parameter, $\alpha$, $\beta_1$ and $\beta_2$, individually. + +So, even though the single regression of abrasion loss on tensile strength did not suggest a close relationship, when taken in conjunction with the effect of hardness the effect of tensile strength is also a considerable one. A key idea here is that $\beta_1$ and $\beta_2$ (and more generally $\beta_1, \beta_2, \ldots , \beta_k$ in model (5.1)) are partial regression coefficients. That is, $\beta_1$ measures the effect of an increase of one unit in $x_1$ treating the value of the other variable $x_2$ as fixed. Contrast this with the single regression model $E(Y) = \alpha + \beta_1 x_1$ in which $\beta_1$ represents an increase of one unit in $x_1$ treating $x_2$ as zero. The meaning of $\beta_1$ in the regression models with one and two explanatory variables is not the same. + +You will notice that the percentage of variance accounted for has increased dramatically in the two-explanatory-variable model to a much more respectable 82.8%. This statistic has the same interpretation — or difficulty of interpretation — as for the case of one explanatory variable (see [Unit 3](unit3.ipynb)). + +Other items in the GenStat output are as for the case of one explanatory variable: the `Standard error of observations` is $\hat{\sigma}$, and is the square root of `m.s. (Residual)`; the message about standardised residuals will be clarified below; and the message about leverage will be ignored until [Unit 10](unit10.ipynb). + +The simple residuals are, again, defined as the differences between the observed and predicted responses: + +$$ r_i = y_i - \left( \hat{\alpha} + \sum_{j=1}^{k} \hat{\beta}_j x_{i, j} \right) ,\ i = 1, 2, \ldots, n. $$ + +GenStat can obtain these for you and produce a plot of residuals against fitted values. The fitted values are simply $\hat{Y}_i = \hat{\alpha} + \sum_{j=1}^{k} \hat{\beta}_j x_{i, j}$. As in the regression models in [Unit 3](unit3.ipynb), the default in GenStat is to use deviance residuals which, in this context, are equivalent to standardised residuals (simple residuals divided by their estimated standard errors). + +## Gratuitous example of more complex maths markup +If + +$$ \rho(z) = \rho_c \exp \left( - \frac{z^2}{2H^2} \right) $$ + +then + +\begin{eqnarray*} +\frac{\partial \rho(z)}{\partial z} & = & \rho_c \frac{\partial}{\partial z}\exp + \left( - \frac{z^2}{2H^2} \right) \\ + & = & \rho_c \exp \left( - \frac{z^2}{2H^2} \right) \cdot + \frac{\partial}{\partial z} \left( - \frac{z^2}{2H^2} \right) \\ + & = & \rho_c \exp \left( - \frac{z^2}{2H^2} \right) \cdot + - \frac{z}{H^2} \\ + & = & - \frac{z}{H^2} \rho(z) +\end{eqnarray*} + + +## Example 5.2 +Something about plots of residuals... + +```{r residual_plots} +fit <- lm(loss ~ hardness + strength, data = rubber) +autoplot(fit) +``` + +These plots are of just the same sort as those in [Unit 3](unit3.ipynb), and are interpreted in the same way. In this case, the normal plot and histogram show some slight suggestion of skewness in the residuals, but there is no obvious cause to doubt the model. In the regression output, GenStat flagged one of the points (number 19) as having a large standardised (i.e. deviance) residual. To decide which points to flag in this way, GenStat uses the same rules as described in [Units 3](unit3.ipynb) and [4](unit4.ipynb). In this case, it warned us about the most negative residual. However, the value of this standardised residual is not very large (at −2.38), and the plot of residuals against fitted values in Figure 5.2 makes it clear that this particular residual is not exceptionally large relative to some of the others, which are almost as large. + + +### Exercise 5.2 +The table below shows values for the first five datapoints, of 13, of a dataset concerned with predicting the heat evolved when cement sets via knowledge of its constituents. There are two explanatory variables, tricalcium aluminate (TA) and tricalcium silicate (TS), and the response variable is the heat generated in calories per gram (heat). + +heat | TA | TS +-----|----|----- +78.5 | 7 | 26 +74.3 | 1 | 29 +104.3 | 11 | 56 +87.6 | 11 | 31 +95.9 | 7 | 52 + $\vdots$ | $\vdots$ | $\vdots$ + +a. Load the `cemheat` dataset. + +b. Make scatterplots of heat against each of TA and TS in turn, and comment on what you see. + +c. Use GenStat to fit each individual regression equation (of heat on TA and of heat on TS) in turn, and then to fit the regression equation with two explanatory variables. Does the latter regression equation give you a better model than either of the individual ones? + +d. According to the regression equation with two explanatory variables fitted in part (b), what is the predicted value of heat when TA = 15 and TS = 55? + +e. By looking at the (default) composite residual plots, comment on the appropriateness of the fitted regression model. + +The solution is in the [Section 5.1 solutions](section5.1solutions.ipynb) notebook. + +### Exercise 5.3: Fitting a quadratic regression model +In Unit 3, the dataset `anaerob` was briefly considered (Example 3.1) and swiftly dismissed as a candidate for simple linear regression modelling. The reason is clear from the figure below, in which the response variable, expired ventilation ($y$), is plotted against the single explanatory variable, oxygen uptake ($x$). (The same plot appeared as Figure 3.1 in Example 3.1.) A model quadratic in $x$, i.e. $E(Y) = \alpha + \beta x + \gamma x^2$, was suggested instead. + +```{r anaerobic_plot} +anaerobic <- read.csv('anaerob.csv') +ggplot(anaerobic, aes(x=oxygen, y=ventil)) + geom_point() +``` + +Since this quadratic model is nonetheless linear in its parameters, we can fit it using multiple regression of $y$ on $x$ plus the new variable $x^2$. Even though $x_1 = x$ and $x_2 = x^2$ are closely related, there is no immediate impediment to forgetting this and regressing on them in the usual way. A variable such as $x_2$ is sometimes called a derived variable. + +a. Using GenStat, perform the regression of expired ventilation (`ventil`) on oxygen uptake (`oxygen`). Are you at all surprised by how good this regression model seems? + +b. Now form a new variable `oxy2`, say, by squaring oxygen. (Create a new column in the `anearobic` dataframe which is `anaerobic$oxygen ^ 2`.) Perform the regression of ventil on `oxygen` and `oxy2`. Comment on the fit of this model according to the printed output (and with recourse to Figure 3.2 in Example 3.1). + +c. Make the usual residual plots and comment on the fit of the model again. + +The solution is in the [Section 5.1 solutions](section5.1solutions.ipynb) notebook. + diff --git a/section5.1.html b/section5.1.html new file mode 100644 index 0000000..4b01163 --- /dev/null +++ b/section5.1.html @@ -0,0 +1,404 @@ + + + + + + + + + + + + + +section5.1 + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
+ + + + + + + + + + + + + + +
+

Modelling abrasion loss

+

This example concerns the dataset rubber, which you first met in Exercise 3.1. The experiment introduced in that exercise concerned an investigation of the resistance of rubber to abrasion (the abrasion loss) and how that resistance depended on various attributes of the rubber. In Exercise 3.1, the only explanatory variable we analysed was hardness; but in Exercise 3.19, a second explanatory variable, tensile strength, was taken into account too. There are 30 datapoints.

+
rubber <- read.csv('rubber.csv')
+rubber
+
##    loss hardness strength
+## 1   372       45      162
+## 2   206       55      233
+## 3   175       61      232
+## 4   154       66      231
+## 5   136       71      231
+## 6   112       71      237
+## 7    55       81      224
+## 8    45       86      219
+## 9   221       53      203
+## 10  166       60      189
+## 11  164       64      210
+## 12  113       68      210
+## 13   82       79      196
+## 14   32       81      180
+## 15  228       56      200
+## 16  196       68      173
+## 17  128       75      188
+## 18   97       83      161
+## 19   64       88      119
+## 20  249       59      161
+## 21  219       71      151
+## 22  186       80      165
+## 23  155       82      151
+## 24  114       89      128
+## 25  341       51      161
+## 26  340       59      146
+## 27  283       65      148
+## 28  267       74      144
+## 29  215       81      134
+## 30  148       86      127
+

The figures below show scatterplots of abrasion loss against hardness and of abrasion loss against strength. (A scatterplot of abrasion loss against hardness also appeared in Solution 3.1.) Figure (a) suggests a strong decreasing linear relationship of abrasion loss with hardness. Figure (b) is much less indicative of any strong dependence of abrasion loss on tensile strength.

+
hardloss <- ggplot(rubber, aes(x=hardness, y=loss)) + geom_point()
+strloss <-  ggplot(rubber, aes(x=strength, y=loss)) + geom_point()
+
+multiplot(hardloss, strloss, cols=2)
+

+

In exercise 3.5(a) you obtained the following output for the regression of abrasion loss on hardness.

+
fit <- lm(loss ~ hardness, data = rubber)
+summary(fit)
+
## 
+## Call:
+## lm(formula = loss ~ hardness, data = rubber)
+## 
+## Residuals:
+##    Min     1Q Median     3Q    Max 
+## -86.15 -46.77 -19.49  54.27 111.49 
+## 
+## Coefficients:
+##             Estimate Std. Error t value Pr(>|t|)    
+## (Intercept) 550.4151    65.7867   8.367 4.22e-09 ***
+## hardness     -5.3366     0.9229  -5.782 3.29e-06 ***
+## ---
+## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
+## 
+## Residual standard error: 60.52 on 28 degrees of freedom
+## Multiple R-squared:  0.5442, Adjusted R-squared:  0.5279 
+## F-statistic: 33.43 on 1 and 28 DF,  p-value: 3.294e-06
+
anova(fit)
+
## Analysis of Variance Table
+## 
+## Response: loss
+##           Df Sum Sq Mean Sq F value    Pr(>F)    
+## hardness   1 122455  122455  33.433 3.294e-06 ***
+## Residuals 28 102556    3663                      
+## ---
+## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
+
+

Exercise 5.1

+

Now repeat the for the regression of abrasion loss on tensile strength.

+

Enter your solution in the cell below.

+
# Your solution here
+
+
+

Solution 5.1

+
fit <- lm(loss ~ strength, data = rubber)
+summary(fit)
+
## 
+## Call:
+## lm(formula = loss ~ strength, data = rubber)
+## 
+## Residuals:
+##      Min       1Q   Median       3Q      Max 
+## -155.640  -59.919    2.795   61.221  183.285 
+## 
+## Coefficients:
+##             Estimate Std. Error t value Pr(>|t|)    
+## (Intercept) 305.2248    79.9962   3.815 0.000688 ***
+## strength     -0.7192     0.4347  -1.654 0.109232    
+## ---
+## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
+## 
+## Residual standard error: 85.56 on 28 degrees of freedom
+## Multiple R-squared:  0.08904,    Adjusted R-squared:  0.0565 
+## F-statistic: 2.737 on 1 and 28 DF,  p-value: 0.1092
+
anova(fit)
+
## Analysis of Variance Table
+## 
+## Response: loss
+##           Df Sum Sq Mean Sq F value Pr(>F)
+## strength   1  20035 20034.8  2.7368 0.1092
+## Residuals 28 204977  7320.6
+

Individually, then, regression of abrasion loss on hardness seems satisfactory, albeit accounting for a disappointingly small percentage of the variance in the response; regression of abrasion loss on tensile strength, on the other hand, seems to have very little explanatory power.

+
+
+

Multiple regression

+

However, back in Exercise 3.19 it was shown that the residuals from the former regression showed a clear relationship with the tensile strength values, and this suggested that a regression model involving both variables is necessary.

+

Let us try it. The only change is to include strength in the equations being fitted in the lm() function. Instead of

+
lm(loss ~ hardness, data = rubber)
+

use

+
lm(loss ~ hardness + strength, data = rubber)
+
fit <- lm(loss ~ hardness + strength, data = rubber)
+summary(fit)
+
## 
+## Call:
+## lm(formula = loss ~ hardness + strength, data = rubber)
+## 
+## Residuals:
+##     Min      1Q  Median      3Q     Max 
+## -79.385 -14.608   3.816  19.755  65.981 
+## 
+## Coefficients:
+##             Estimate Std. Error t value Pr(>|t|)    
+## (Intercept) 885.1611    61.7516  14.334 3.84e-14 ***
+## hardness     -6.5708     0.5832 -11.267 1.03e-11 ***
+## strength     -1.3743     0.1943  -7.073 1.32e-07 ***
+## ---
+## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
+## 
+## Residual standard error: 36.49 on 27 degrees of freedom
+## Multiple R-squared:  0.8402, Adjusted R-squared:  0.8284 
+## F-statistic:    71 on 2 and 27 DF,  p-value: 1.767e-11
+
anova(fit)
+
## Analysis of Variance Table
+## 
+## Response: loss
+##           Df Sum Sq Mean Sq F value    Pr(>F)    
+## hardness   1 122455  122455  91.970 3.458e-10 ***
+## strength   1  66607   66607  50.025 1.325e-07 ***
+## Residuals 27  35950    1331                      
+## ---
+## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
+

Looking at the regression coefficient output next, the estimated model for the mean response is

+

\[ \hat{y} = \hat{\alpha} + \hat{\beta}_1 x_1 + \hat{\beta}_2 x_2 = 885.2 − 6.571 x_1 − 1.374 x_2 \]

+

where \(x_1\) and \(x_2\) stand for values of hardness and tensile strength, respectively.

+

Associated with each estimated parameter, GenStat gives a standard error (details of the calculation of which need not concern us now) and hence a t-statistic (estimate divided by standard error) to be compared with the distribution on d.f. (Residual)=27 degrees of freedom. GenStat makes the comparison and gives p values, which in this case are all very small, suggesting strong evidence for the non-zeroness (and hence presence) of each parameter, \(\alpha\), \(\beta_1\) and \(\beta_2\), individually.

+

So, even though the single regression of abrasion loss on tensile strength did not suggest a close relationship, when taken in conjunction with the effect of hardness the effect of tensile strength is also a considerable one. A key idea here is that \(\beta_1\) and \(\beta_2\) (and more generally \(\beta_1, \beta_2, \ldots , \beta_k\) in model (5.1)) are partial regression coefficients. That is, \(\beta_1\) measures the effect of an increase of one unit in \(x_1\) treating the value of the other variable \(x_2\) as fixed. Contrast this with the single regression model \(E(Y) = \alpha + \beta_1 x_1\) in which \(\beta_1\) represents an increase of one unit in \(x_1\) treating \(x_2\) as zero. The meaning of \(\beta_1\) in the regression models with one and two explanatory variables is not the same.

+

You will notice that the percentage of variance accounted for has increased dramatically in the two-explanatory-variable model to a much more respectable 82.8%. This statistic has the same interpretation — or difficulty of interpretation — as for the case of one explanatory variable (see Unit 3).

+

Other items in the GenStat output are as for the case of one explanatory variable: the Standard error of observations is \(\hat{\sigma}\), and is the square root of m.s. (Residual); the message about standardised residuals will be clarified below; and the message about leverage will be ignored until Unit 10.

+

The simple residuals are, again, defined as the differences between the observed and predicted responses:

+

\[ r_i = y_i - \left( \hat{\alpha} + \sum_{j=1}^{k} \hat{\beta}_j x_{i, j} \right) ,\ i = 1, 2, \ldots, n. \]

+

GenStat can obtain these for you and produce a plot of residuals against fitted values. The fitted values are simply \(\hat{Y}_i = \hat{\alpha} + \sum_{j=1}^{k} \hat{\beta}_j x_{i, j}\). As in the regression models in Unit 3, the default in GenStat is to use deviance residuals which, in this context, are equivalent to standardised residuals (simple residuals divided by their estimated standard errors).

+
+
+
+

Gratuitous example of more complex maths markup

+

If

+

\[ \rho(z) = \rho_c \exp \left( - \frac{z^2}{2H^2} \right) \]

+

then

+\[\begin{eqnarray*} +\frac{\partial \rho(z)}{\partial z} & = & \rho_c \frac{\partial}{\partial z}\exp + \left( - \frac{z^2}{2H^2} \right) \\ + & = & \rho_c \exp \left( - \frac{z^2}{2H^2} \right) \cdot + \frac{\partial}{\partial z} \left( - \frac{z^2}{2H^2} \right) \\ + & = & \rho_c \exp \left( - \frac{z^2}{2H^2} \right) \cdot + - \frac{z}{H^2} \\ + & = & - \frac{z}{H^2} \rho(z) +\end{eqnarray*}\] +
+
+

Example 5.2

+

Something about plots of residuals…

+
fit <- lm(loss ~ hardness + strength, data = rubber)
+autoplot(fit)
+

+

These plots are of just the same sort as those in Unit 3, and are interpreted in the same way. In this case, the normal plot and histogram show some slight suggestion of skewness in the residuals, but there is no obvious cause to doubt the model. In the regression output, GenStat flagged one of the points (number 19) as having a large standardised (i.e. deviance) residual. To decide which points to flag in this way, GenStat uses the same rules as described in Units 3 and 4. In this case, it warned us about the most negative residual. However, the value of this standardised residual is not very large (at −2.38), and the plot of residuals against fitted values in Figure 5.2 makes it clear that this particular residual is not exceptionally large relative to some of the others, which are almost as large.

+
+

Exercise 5.2

+

The table below shows values for the first five datapoints, of 13, of a dataset concerned with predicting the heat evolved when cement sets via knowledge of its constituents. There are two explanatory variables, tricalcium aluminate (TA) and tricalcium silicate (TS), and the response variable is the heat generated in calories per gram (heat).

+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
heatTATS
78.5726
74.3129
104.31156
87.61131
95.9752
\(\vdots\)\(\vdots\)\(\vdots\)
+
    +
  1. Load the cemheat dataset.

  2. +
  3. Make scatterplots of heat against each of TA and TS in turn, and comment on what you see.

  4. +
  5. Use GenStat to fit each individual regression equation (of heat on TA and of heat on TS) in turn, and then to fit the regression equation with two explanatory variables. Does the latter regression equation give you a better model than either of the individual ones?

  6. +
  7. According to the regression equation with two explanatory variables fitted in part (b), what is the predicted value of heat when TA = 15 and TS = 55?

  8. +
  9. By looking at the (default) composite residual plots, comment on the appropriateness of the fitted regression model.

  10. +
+

The solution is in the Section 5.1 solutions notebook.

+
+
+

Exercise 5.3: Fitting a quadratic regression model

+

In Unit 3, the dataset anaerob was briefly considered (Example 3.1) and swiftly dismissed as a candidate for simple linear regression modelling. The reason is clear from the figure below, in which the response variable, expired ventilation (\(y\)), is plotted against the single explanatory variable, oxygen uptake (\(x\)). (The same plot appeared as Figure 3.1 in Example 3.1.) A model quadratic in \(x\), i.e. \(E(Y) = \alpha + \beta x + \gamma x^2\), was suggested instead.

+
anaerobic <- read.csv('anaerob.csv')
+ggplot(anaerobic, aes(x=oxygen, y=ventil)) + geom_point()
+

+

Since this quadratic model is nonetheless linear in its parameters, we can fit it using multiple regression of \(y\) on \(x\) plus the new variable \(x^2\). Even though \(x_1 = x\) and \(x_2 = x^2\) are closely related, there is no immediate impediment to forgetting this and regressing on them in the usual way. A variable such as \(x_2\) is sometimes called a derived variable.

+
    +
  1. Using GenStat, perform the regression of expired ventilation (ventil) on oxygen uptake (oxygen). Are you at all surprised by how good this regression model seems?

  2. +
  3. Now form a new variable oxy2, say, by squaring oxygen. (Create a new column in the anearobic dataframe which is anaerobic$oxygen ^ 2.) Perform the regression of ventil on oxygen and oxy2. Comment on the fit of this model according to the printed output (and with recourse to Figure 3.2 in Example 3.1).

  4. +
  5. Make the usual residual plots and comment on the fit of the model again.

  6. +
+

The solution is in the Section 5.1 solutions notebook.

+
+
+ + + + +
+ + + + + + + + diff --git a/section5.1.ipynb b/section5.1.ipynb index 5b433be..9a234b9 100644 --- a/section5.1.ipynb +++ b/section5.1.ipynb @@ -9,18 +9,16 @@ }, { "cell_type": "markdown", - "metadata": { - "heading_collapsed": true - }, + "metadata": {}, "source": [ "### Imports and defintions" ] }, { "cell_type": "code", - "execution_count": 35, + "execution_count": 25, "metadata": { - "hidden": true + "init_cell": true }, "outputs": [], "source": [ @@ -35,9 +33,9 @@ }, { "cell_type": "code", - "execution_count": 36, + "execution_count": 26, "metadata": { - "hidden": true + "init_cell": true }, "outputs": [], "source": [ @@ -88,6 +86,30 @@ "}" ] }, + { + "cell_type": "code", + "execution_count": 27, + "metadata": { + "init_cell": true + }, + "outputs": [], + "source": [ + "# From https://sejohnston.com/2012/08/09/a-quick-and-easy-function-to-plot-lm-results-in-r/\n", + "ggplotRegression <- function (fit) {\n", + "\n", + "require(ggplot2)\n", + "\n", + "ggplot(fit$model, aes_string(x = names(fit$model)[2], y = names(fit$model)[1])) + \n", + " geom_point() +\n", + " stat_smooth(method = \"lm\", col = \"red\") +\n", + " labs(title = paste(\"Adj R2 = \",signif(summary(fit)$adj.r.squared, 5),\n", + " \"Intercept =\",signif(fit$coef[[1]],5 ),\n", + " \" Slope =\",signif(fit$coef[[2]], 5),\n", + " \" P =\",signif(summary(fit)$coef[2,4], 5))) + \n", + " theme(plot.title = element_text(size=12))\n", + "}" + ] + }, { "cell_type": "markdown", "metadata": {}, @@ -99,7 +121,7 @@ }, { "cell_type": "code", - "execution_count": 37, + "execution_count": 28, "metadata": { "scrolled": true }, @@ -268,7 +290,7 @@ }, { "cell_type": "code", - "execution_count": 38, + "execution_count": 29, "metadata": { "scrolled": false }, @@ -300,7 +322,7 @@ }, { "cell_type": "code", - "execution_count": 39, + "execution_count": 30, "metadata": {}, "outputs": [ { @@ -376,6 +398,58 @@ "# print(cbind(af,PctExp=afss/sum(afss)*100))" ] }, + { + "cell_type": "code", + "execution_count": 31, + "metadata": {}, + "outputs": [ + { + "data": {}, + "metadata": {}, + "output_type": "display_data" + }, + { + "data": { + "image/png": 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MFKpfKLL76Ii4ubNGmSWCy22t7R/bla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+ "text/plain": [ + "plot without title" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "ggplot(rubber, aes(x=hardness, y=loss)) + \n", + " geom_point() +\n", + " stat_smooth(method = \"lm\", col = \"red\")" + ] + }, + { + "cell_type": "code", + "execution_count": 32, + "metadata": {}, + "outputs": [ + { + "data": {}, + "metadata": {}, + "output_type": "display_data" + }, + { + "data": { + "image/png": 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MEHZ8+e1X+GxcSJE2fPnu3GIgEAADdB4PAYThrGIhKJVqxYsWLFCsfutp2Ijo4u\nKCj46quvLly4IJVKExMTMzIyTN5nAQCAdg4Ch4dx+0RhwEBISMjbb7/t7lIAAADXQR8OjwTT\nogMAAPAsEDg8GMQOAAAAngICh8eD2AEAAID7IHB4CYgdAAAAuAwCh1eBzAEAAICbIHB4G2jq\nAAAAwEEQOLwTxA4AAACcAoHDm928ebOoqMjdpQAAAAAgcLQD169fh9YOAAAA7gWBo72AmywA\nAADcCAJH+wKZAwAAgFtA4Gh3oKkDAACA60HgaKcgdgAAAHAlCBztGsQOAAAArgGBA0DsAAAA\n4HQQOMBfIHYAAABwHggc4BEQOwAAADgDBA5gAmQOAAAAjgWBA5gGTR0AAAAcCAIHsARiBwAA\nAIeAwAGsg9gBAADAThA4AFsQOwAAANgMAgdoG4gdAAAAbACBA9gCYgcAAIA2gcBhVsgPP8j3\n7MFbW91dEO6CzAEAAIAlnrsLwFVNTWEbNxJNTdGffVaXmFg5d66yc2d3l4mL6MzRqVMndxcE\nAAAAp0ELh2nEjz8STU0IIaK5WZ6T02fevJ5PPhl4+DCm07m7aFwEd1gAAABYBi0cpmFVVaRA\ngKvVzBLZxYuyixfVoaHVqanVM2dqAgPdWDxugtYOAAAA5kALh2na11678vPP5StXqiIi9JcL\nKisjN2zoP2NG59WrZRcuuKt4XAatHQAAAIxBC4dZWn//ikWLKh57zPfcOXlOTsDRoxhJ0qsw\njSbowIGgAwdaO3asmT69KiVF5+Pj3tJyDbR2AAAA0AeBwxocb4iPb4iPF969K9+5U56by6uv\nZ1aKSkuj1q8P37Kldtq0qrQ0JXy+PgpiBwAAABrcUmFLFRlZvnLlhdzcm++/3xAfr7+KaG4O\n2bGjz9y5vTIygvftw7RadxWSm+AOCwAAAFe0cJSXl2/evLm4uJggiL59+/79738PDg5GCOl0\nuq1bt548eVKr1cbHxz/55JN8Pt/Cci6g+Py6CRPqJkyQXL0asnNn0M8/40ols1ZaXNxpzZqo\nr76qmTatKj1dHRbmxqJyCjR1AABAO0esWbPGqX9Ao9G88sorcrn8mWee6dev37lz5/Lz8xMT\nExFC33333YkTJ5YtW5aQkLB3796SkpKEhAQLy83tX6PROLzYAoGgpqaGfNhpw8TfDQ5WjBpV\nlZ6uCQoS3rvHe/CAWUUolT4XL4bu2CG5eVPr768KD0cY5vASsoHjOJ/PJ0lSx/jvfwcAACAA\nSURBVI3RvAqFQqFQBAQEtPWFGIaJRKJWz5+ETSgUEgShVCopinJ3WezC5/MpitJ6eGMejuNi\nsVin06n1xqN5KLFYrNT78uOhBAIBj8drbW21cO31CDweD8MwZ3w2uRKGYRKJhCRJlUrF/lUS\nicTcKqffUikpKbl///4zzzzTtWvX+Pj4hQsXXrt2rbW1ValUHjx4cMmSJfHx8QMHDly2bFl+\nfv6DBw/MLXd2OW2j8/GpnD//clZW0bff1k2YQBEEswrT6QIOH+7x9NN909PDt23jNTS4sZyc\nAsNYAACgHXL6LZWuXbvu2LGD/npaUVFx4sSJbt26iUSi4uLi1tbWuLg4erP+/fvrdLpbt26J\nxWKTywcMGEAvUavVubm5zP67devmjIZ6giAIgsBYt0yohgwpGzKkorIyODs7cOdOfm0ts0p0\n507U+vURmzfXJyXVzJmj7NbN4aU1B8dxhBCGYdy5J8UoLy9HCHXt2pXNxhiG0Y0cTi6U09E1\nIhQKPb2Fg8fjefpbQA+rgyAILzi0vOMEIQgCPWzncHdZ7MLn872gRuhPQBzH2b8Ry5cFp1cq\nU9Y1a9YUFhbKZLIPP/wQIVRfX8/j8aRS6V/l4PFkMlldXZ1EIjG5nNlhc3Pze++9x/y6dOnS\nvn37OqPktnxIx8TUPfdc/YoVPocOBfz4o+TcOWYN3tISlJUVlJWlHDiwbv78xsREylUhgMfj\ncfbsvXPnDkKoZ8+ebDaWyWROLo6LMIe3pxMKhe4uggPQFxl3l8IBvONdIItt8p5FIBC4uwgO\nQBAE+0PL8u17130Ovfbaa0ql8sCBA6tWrfrPf/5DUZRx+4FOpzO3nPlZKpW++uqrzK/dunVr\nampyeGmFQqFGo7H5PmLr+PHV48cLS0uD9uwJysoiGhuZVeLff4/8/Xft++/XzZxZk56ufnRi\nMcei+3BotVqO9OEw58KFC8hiaweGYWKxuKWlxYWFcgqRSMTj8Zqbmz29eUAgEFAU5em3qHEc\nl0gkWq3WC7oHSaXS5uZmd5fCXkKhkM/nt7S0eHofDrqFw9P7BmEYJpVKdTod++5BFEX5mJ+V\nyumB4/bt27W1tQMHDvTx8fHx8Xnsscd27959+fLlwMBAjUajVCrFYjFCSKfTNTU1BQcHSyQS\nk8uZHQoEgtTUVObXlpYWZ3wO8Xg8nU5nZ584TWRk0/Ll5RkZQfv2hWRlifU6LvDq6kK2bJFv\n3fpg1Kiq9PQH8fHO6FhKEATduc8jPhiKioqQmZEsXtNplP7Go1KpPP16iuM4SZKeXiMEQUgk\nEp1O5+lvBCEkkUi84F3weDw+n69Wqz29PzJCCMdxT68ROnC09Uy3EDhc0Wn0s88+Y75ht7S0\nqNVqHo8XExMjFAovX75MLy8sLMRxvFOnTuaWO7uczqOTSqtmz/7zp5+KN2yomzCB0ru7gZGk\n//Hj3Veu7JueHva//0HHUgSTdgAAgJdy+rDYwMDA3Nzc8vLy4ODgysrKjRs3YhiWkZEhFovr\n6+t//vnnnj17KhSKDRs2xMXFjRs3js/nm1xubv/uGhZrA3VERP3EidWzZmkDAkRlZYTenSBe\nQ4Pf6dNh27eLr1/XyOWOmsCDa8NiWTIePes1LRwwLJZTYFgs18CwWE5x+LBYzAUXvmvXrm3Z\nsqWkpEQoFPbp02fx4sUhISEIIZ1Ot3nz5lOnTpEkOXTo0CVLljATf5lcbpKTbqnIZLKioiLn\nXU8xnc7/+PGQrCzf8+eRURU09+pVlZ5el5hI2tfniCAIsVis0WjadLhwCt24hWGYv79/vd6k\n8h7K19dXIBDU1dV5+vWUvgx5egQkCCIgIEClUjXq9bLyUIGBgfqd6z2UTCYTiUQKhcLTs6xI\nJMJx3NO7nWEYFhQUpNFo2jQzhX4XCMMdevo3LQ8NHAxRaWlIVlbwvn2EUddXrZ9fzYwZVamp\nqqgo23buBYGD1rlzZwgcnAKBg2sgcHAKBA6T4FkqbtbasWPZiy9e+PnnkjVrWrp311/Fe/Ag\n7Pvv+6Wn91ixIvDwYcyjbos4VklJSXFxsbtLAQAAwHYcnZ6hvSEFgpqkpJqkJNmFCyHZ2YFH\njmDMzT+S9D1zxvfMGVV4eHVaWvWMGdq2Tw3uHeCBLAAA4LmghYNbmuLibr399sXc3PLlyw26\njgorKqLWr4+bMaPzm2/KHo7iaYdgZnQAAPBE0MLBRZqAgIrHH69YvNj33Dl5Tk7A0aPYw1v+\nmFodtH9/0P79yo4dq1NTq2fOJMVi95bWLaC1AwAAPAsEDg7D8Yb4+Ib4eGF5uXzXLvmePTyF\nglkpLi2N+fTTyI0b6xITK+fMUXbp4saSugvEDgAA8BRwS8UDqKKiylesuLh3b8nrrzf36qW/\nimhulufk9FmwoMeKFQHHjrXPjqVwhwUAALgPWjg8BikU1syYUTNjhrS4WJ6TE7R/P84MSqQo\numOpJji4JimpavZsdWioWwvratDUAQAAHAfzcJjmsnk4bMZraAjeuzdk507hnTsGqyg+v37s\n2Kr09JbBg71jHo42PbyNy7HDC+bhIEkyOzv7999/x3E8ISFh2rRpxk9b9BQwDwfXwDwcnAIT\nfxlqt4HjLyTp99tvIVlZfidOYEafYcouXR489ljNlClKrj6eniUbnhbLzdjh6YFDrVanp6ef\nOnWKWTJ16tT//ve/OO6RN2chcHANBA5OgYm/wKNw/EFCwvVPPrmUk1OxeLHBFB3imzfD1q7t\nOWlSh48+Erezjg4wetYZvvjiC/20gRDav3//li1b3FUeAIAHgcDhJdTh4eXPPHNh795bb73V\n1Lev/iqiuTkkM7PP3Lmxy5cHHjqEefhXhzaB2OFY+/btM164f/9+15cEAOBxPLulHRigBILa\nqVNrp04Vl5bKs7Ple/bgeg+Q9Dl/3uf8eU1QUM20aVVpaerwcDcW1ZWgS6mjmHweqae3GwMA\nXANaOLyTsmPHshdeuLx/f+WqVaqOHfVX8Wtrw7dt65ea2vWVV3zPnDF+Vq23gtYO+/Xr1894\nYf/+/V1fEgCAx4HA4c10Pj51ixZd3bXr6vr19ePGUQTBrMJ0uoCjR3usWNF3zpzQ7dsJz+80\nxxLEDnu89tprPj4++kvkcvnzzz/vrvIAADwIBI52AMMa4uNvfPjhxb17y1esMJiiQ3T7dsyn\nn8ZNndp5zRrJ1avuKqOLQeywTYcOHfLy8iZOnOjj4+Pv7z99+vS8vDy5XO7ucgEAPAAMizXN\nY4bFWkQQhPE8HJhWG3D0aEhWls8ffxi/pKlv36rZs+vGj6cEAheW1AobhsWy5OKOHZ4+LJYh\nkUhIkmxlpp7zTDAslmtgWCynOHxYLHQabXcoHq9u0qS6SZPEN2+GZGUF7d9P6J0VssuXZZcv\nx3z2WXVycnVqqsrbO5ZCf1IAAHANuKXSfim7dLn9yisX9+0rXbWqpWtX/VW8+vrwrVv7paT0\nWLEi8PBh4ynFvAzcYQEAAGeDFo72TieRVKekVKek+Pz+e0h2dsCxY5hG89c6kqQf0aKKiqpK\nTa2ZMUPr5+fWwjoXtHYAAIDzQOAAf2kcOLBx4EB+ba189275zp2CqipmlbC8PPrLLyO/+aYu\nMbEqPd3gibVeBmIHAAA4A9xSAY/QBAXd+/vfL+3efWPduob4eKT3XC5crQ7Oze31t7/1+tvf\ngvfuxT38gXCWwU0WAABwLGjhACZQBFE/dmz92LGisrKQ7Ozg3Fz9iTqkhYWdCgujv/iiJjm5\nKjVVFRXlxqI6FbR2AACAo0ALB7CkNSam7LnnLuzfX7JmTUuPHvqreA0NYd9/3y89/a+OpTqd\nuwrpbNDaAQAA9oMWDmAdKRDUJCXVJCVJi4vlOTlB+/b93/2Uhx1LNXJ59axZVenpmkefWOs1\noLUDuIVWq+Xx4EINvAG0cIA2aI6NLV216uKePeXPPGMwRQe/ujriP//pP2NG5zfekF2+7K4S\nOhu0dgDXuHv37tKlS7t06dKhQ4epU6cWFBS4u0QA2AtmGjXNi2cadRiS9D13Tp6TE3D0qPFE\nHcqOHatTU6uTk0mJxP4/5byZRu1hQ2sHzDTKKZydabS5uXn8+PG3bt1ilgiFwp07d8bHx5t7\nCcw0yikw06hJ0MIBbIXjDfHxN99//3JWVkVGhtbfX3+luLQ05tNP46ZN6/j+++KbN91VRqeC\n1g7gJJs2bdJPGwghlUr1xhtvuKs8ADgEBA5gL1VUVPmKFRdzc0veeKO5d2/9VURzszwnp8+C\nBT2eeSbgyBGv7FgKsQM43JUrV4wXXvbeO5WgnYC+SMAxSIGgZvr0munT/+pY+vPPuFL51zqK\n8j171vfsWU1QUM20aVXp6eqwMLcW1vFKSkqgPylwFImpG5Eymcz1JQHAgaCFAzjYXx1L9+69\n889/qqKj9Vfxa2vDt23rl5raZdUqn/Pn3VVCJ4GmDuAoM2bMYLkQAA9CrFmzxt1lsItGo9Ew\nz/5wHIFAUFNT4+k9+3Ac5/P5JEnqXH4vgxQKm/r1q5w9u7lfP6K5WXjnDvawezJGkuKSkuC8\nvMBDhxBCrR07UgKB5b1hGMbn851R0Q6nUCgUCkWAmbHBQqGQIAilUunpnbX5fD5FUZ7esw/H\ncbFYrNPp1Gq1u8vyiM6dOzc2Np47d45Z0qdPn40bNwqFQnMvEYvFSqZN0WMJBAIej9fa2urp\n114ej4dhmEdcsizAMIzuHt6mYQcm2+f+2qGnX/hglIoFzh2l0hb86uqQXbvkWVn8+nqDVaRE\nUjt5clV6eku3buZezs1RKlYZ32SBUSqcwtlRKrTTp08fOnSoqalpwIABaWlplmfjgFEqnAKj\nVEzvEAKHSRA4nAFTqwOPHAnJypJdumS8tnHAgKq0tPpx4yg+3/CFnhk4aPqxAwIHp3A8cLQJ\nBA5OgcBhEnQaBa5DCQS1U6bUTpkiuXYtJDv7kY6lCPn88YfPH39ogoKqZ86sTk1Vh4S4sagO\nBFOUAgAAgk6jwC1auncvXbXqwr59patWKbt21V/Fr62N2Ly5f3JyjxUr/PPzkYe3wDGgSykA\noJ2DFg7gNjqptDolpXrWLN/z50OysvyPH/+/iToePqKltUOHqrS02unTkVjs1sI6xtWrV3k8\nXmhoqLsLAgAArgaBA7gbhjUMHtwweDC/tjY4Ly8kM1NQWcmsFN2+HfPpp1Hr1zdMnnx3zhyD\nJ9Z6qFu3blEUBTdZAADtCtxSAVyhCQqqyMi4tHv39U8+aYiPRxjGrMLVav+9e3svWtQrI0Oe\nk4Nzow+sneAmCwCgXYFRKqbJZDK1Wq1Wqz36I4Fro1TaRFRWFrxnjzwnh2c0gkDn41OTlFQ5\nf74qIsItZbOZSCTi8XjNzc0G553HtXbAKBWugVEqnAKjVEzvEAKHSUzg0F/oceHDowMHDW9p\nCfrll5CsLMn160br8IbBg6tTUurHjaNwz2irMxc4aB4UOyBwcA0EDk6BwGES9OFoA/3PA48L\nHx6KlEiqU1JqUlMDS0p8fvwxKC8PZ1Lgw46lqsjI6pSU6uRkgyfWehwYQAsA8GLQwmGayRYO\nk7icPLyghYPGTPzFr6sLzs2VZ2cLKyoMtqEEgvpRo6pTUhri491SSDYst3Do43jsgBYOroEW\nDk6BFg6ToIXDXtDs4UqawMCKjIz7Cxf65+eHZGX5njnDTNSBqdWBhw8HHj7c3LNnVVpa3eTJ\npPkHTziWQqGoqKgQCATR0dECa8+FYQlaOwAAXgZaOExj38JhEkeSh/e1cBgsF965I9+9W757\nN88ogOtksrpJkyrnzVM68zOboqg9e/YUFBTQU5X7+PjMnj27d+/e5rZn38Khj4OxA1o4uAZa\nODgFWjhM7xACh0l2Bg59bgwfXh84aHhra9CBAyFZWZLiYuNXPhg6tCot7cGoUc7oWPrrr7/u\n3r1bf4lQKHzuuefkcrnJ7W0LHDROxQ4IHFwDgYNTIHCY3qGnBw61Wk0QhMN3i+M4RVGO/ecU\nG38cOhmGYRiGOfyNuAWO41YfeCYuLAzIzPTbuxc3+iDUhoQoZsyoW7BA49BZPlevXl1bW2uw\ncNKkSampqSa3p2vEnie3xcbG2vxaB8IwDCHkBccVQRAURXn6s/QQQgRB6JiJej0WjuP0CeLp\nh5b9ZzpHtPUEIUmSb/T0TYbHBw7ut3CY5Jpmj3bSwmGAp1DI9+6VZ2cL790zWEXx+XXjx1el\npTXFxTmkYC+99JLxqRgXF7do0SKT29vTwqHP7a0d0MLBNdDCwSnQwmESdBp1D+YDgyO9PbyJ\n1t+/YtGiisce8z91KiQz0+/0afQwE2AaTdAvvwT98ktL165V6em1U6aQEok9f8vPz6++vt5g\nYUBAgD37ZAO6lAIAPA6xZs0ad5fBLhqNRqPROHy3AoFAp9O5oIkyQI9CoXDsznEc5/P5JEl6\nelsrhmF8Pr9tFY1hrTExtVOm1E6dSgqF4tu39e+z8Ovq/AsKQnfsEFZUqMLDtYGBthUMx3GD\nO2VCoXD27NkSMzmGx+PhOO6oI1ahUCgUChfkG2N8Pp+iKE//GorjuFgs1ul0zmvLdBmxWKxU\nKt1dCnsJBAIej9fa2urpNyN4PB6GYc74bHIlDMPotsw2tZGbu/ohCBzmuCxw6HN48mjXgeMh\nna9vQ3x81dy5qqgoQU2NoLqaWYVrNNLi4pCdO33++IMUi1UxMaiNHUujo6M1Gs2dO3foWyR+\nfn4LFiyIiYkxt71jAwfNLbEDAgfXQODgFAgcpncIfThMcnYfDvbsuefSPvtwWCYtKgrJygo8\ncMD4CXBqubx61qzqWbM0ZsaYmNPY2Hjv3j2hUBgZGWmhwxRyXB8Oc1x2kwX6cHAN9OHgFOjD\nYXqHEDhM4k7gYNiQPCBwmEM0NQUePBi6fbvY6L9K4fiD4cMr581rGDJE/4m1DuHswEFzQeyA\nwME1EDg4BQKHSdBp1GPAlKYOpJPJqlNSqmfO9DtzRp6d7Z+fjzEdS0nSv6DAv6BA2alTVXp6\nbVKSTip1b2nbCrqUAgA4CFo4TONgC4dJlpMHtHCwxK+uDt6/P2THDkFVlcEqUiConzjx/mOP\ntXTrZv8fck0Lhz4nxQ5o4eAaaOHgFGjhML1DCBwmeUrg0GccPiBwtO2vaDQBv/4qz8nxPXsW\nGZ0XzbGx1SkptUlJ9jyixfWBg+bw2AGBg2sgcHAKBA7TO4TAYZInBg4GkzwgcNhGcuOGPCsr\n+OefcaO/qAkMrJk5syolRR0WZsOe3RU4aA6MHRA4uAYCB6dA4DC9QwgcJnl04GDw+fx79+5B\n4LAN0dwclJcXkp1tsmOpYtSoqvT0hvj4NnUsdW/goDkkdkDg4BoIHJwCgcMk6DTq5Xr27KlU\nKpubm6GfaVvppNKqOXOq5syRFheHbt8eeOAA9vAiiJFkwPHjAcePq6Kjq2fOrJ45U+vn597S\nsgddSgEAbgEtHKZ5TQuHn58fHTj0l3tc+HBLC4cBfnW1fNeukF27+HpTh9FIkah28uSqtLQW\na09W40ILhz6bYwe0cHANtHBwCrRwmN4hRy58NoPAYYG5wMHwlOTBhcDxF5L0P3Ei9KefLHUs\nnTqVFIlMvpprgYNmQ+yAwME1EDg4BQKH6R1y6sJnAwgcFlgNHAyOJw8OBY6HRGVlwXv2yHft\n4jU0GKzS+fjUJCVVzpuniow0fBUnAwetTbEDAgfXQODgFAgcpnfIwQtfm0DgsIB94NDHwfDB\nwcBBw1tagn/+WZ6VJblxw2gdrkhIqE5PVyQkMI9o4XLgoLGMHRA4uAYCB6dA4DAJOo0CQ8xH\nDgeTB9eQEklVampVaqq0uFiekxO0b9//PaKFJP1PnPA/cUItl9fMmlWZnq51x2Nd2wq6lAIA\nnARaOExrzy0cJrk3fHC2hcMAv64uePfukJwcwf37BqsogaBu4kTFggXqgQO53MKhz0LsgBYO\nroEWDk6BFg7TO/SIC58FEDgscGDgYLglebAJHBRFXbly5d69exKJpGfPnkFBQS4rngGMJP3y\n80OzsnzPnDHuWNraq9f91NTaxERzHUs5yDh5QODgGggcnAKBw/QOIXCYBIGDDZeFD6uBo7W1\ndePGjWVlZfSvPB4vJSVl2LBhrimeOcI7d+S7d8t37+YZna46qbQuMbFy7lxl585uKZsN9GMH\nBA6ugcDBKRA4TMIdUSrQTnV6yN0FQbt27WLSBkJIq9Xm5ORUVFS4sUgIIVV0dPmKFRf37i1d\nvdpgig6iuVmek9Nn/vweK1cGHD/OPKuWy0pKSqBbDwDAZtBpFDiAe/uZkiT5xx9/GCzUarUX\nLlwIDw93fXkMkCJRdXJydXKy9M8/w3Ny/A8cwJiOpRTl+9tvvr/9pg4NrU5NrU5O1rjvThBL\ndBX37t3b3QUBAHgYCBzAkfRbO1wWPjQajckGWK61Zzb36VM+eHDV6tWi3btD/vc/cWkps0pQ\nWRm5YUPEpk31o0dXp6Q0DBnSpke0uN7169cpioqKinJ3QQAAHgMCB3AWlzV7CIVCf39/hUJh\nsDw0NNSpf9c2pI9PdUpKVXKy3+nTIVlZ/idPoof3UzCNJvDw4cDDh5Vdu1alp9dMmUJKJO4t\nrWUwhhYAwB6xZs0ad5fBLhqNRqPROHy3AoFAp9PpdDqH79mVCIIQiURardYZ/yL2AvQYxwI2\nMAzj8/kW3oVMJrt8+bL+kpCQkPT0dIIgbPhzzsPj8XAc12g0CMNU0dF1kyfXJiWRAoG4rAzX\n64DJr6vzLygIzcwU1NSoIyK0/v5uLLNJ9D+WJEmEkEKhUCgUAZ4wy4gBHMfFYrFOp/P07uEI\nIbFYrFQq3V0KewkEAh6P19raSnpCryYLeDwehmHuvfDaD8Mwunt4m543LjH/NQkCh2kQOOxR\nX19/+fJltVrt5+eHPXprwLbkYTVwRERE+Pv737lzR6VS4Tjes2fPxx57TCaT2f4enOP/AsdD\nOh+fhvj4ynnzlN268RobhXfvMqtwjUZ65UpIZqZ/fj4lFCo7dWJmLHU7/cBB88TYAYGDayBw\ncIrDAwcMizUNhsXaRqvVvvHGG1u2bKE7VcTFxX355Zc9e/a08BI2N1zYT/zV2NgoFot5PI7e\nK7Q6tbmkuDgkKyvowAHcaMSpRi6vnjWratYsjVzu/JJaIRAIKIoydz31lJssMCyWa2BYLKfA\nPByGIHBY4PrA8d5773322Wf6Szp06HD06FEfHx82LzcXPjxlplGrWD5LhWhuDjxwIPSnn8S3\nbhmsonD8wfDhlfPmubdjqeXAweB48mAfOO7fv69SqWJiYjCuduaFwMEpEDhM4koLLfACarX6\nm2++MVh4+/btXbt2sdwDdyb2cC+dVFqdkvLn9u1F335bN2ECpdcTBSNJ/4KCHitW9J09O3zb\nNuNn1XKKF0zd8dtvv40cObJv376DBw/u27dvTk6Ou0sEgKfiaMsz8ERVVVUm7yLfvn27rbuC\nB8jRmuLimuLi+DU1wfv2hezYIaiqYlaJysqi1q+P+Pbb+okT7y9Y0NK9uxvLaZnnDmYpKytb\nsGBBw8NUV1lZuXTp0sDAwDFjxri3YAB4ImjhAA4TFBTE5/ONl4eFhdm8T6bNI/bRmTrbFU1w\ncEVGxqWcnJvvvNMYF6e/Clerg/bt671wYc+lSwN/+QXjcCc1T2zt2LBhQ4NRG9K6devcUhgA\nPB0EDuAwYrF47ty5BgsDAwNnzpzpkP238xsuFJ9fl5hY/O23lzMzKzIytI92i5FduNDl9df7\nT58etX698N49dxXSKs+KHTdv3mS5ELiYpw8hbJ8gcABHeueddxITE5lfw8PDN23aJHf0qIp2\nnjxaO3QoX7Hi0p49t196SfnoP4FfXx++bVvf1NRuL77od+oU4urYQk+JHYGBgcYLLfSJA85G\nUdT27dsTEhIiIyP79Omzdu1al/WIB/azcZSKTqfbv38/SZJjx4719fV1eLHYg1EqFrh+lArt\nzz///PPPP0NDQ+Pj46VSqf07xDDM39+/vr7ewjYe8QHGcpRKm0iLi0O3bw88cAAz6tivioqq\nnjWrOjnZ4VOHsRylwpK7sqPVUSrHjx9PT083WPjWW289/fTTzi9d27STUSqbN29+5ZVX9JdM\nmTJl27ZtXBs9BKNUTO+Q5YWvubn52Wef/fXXX69evYoQmjFjRm5uLkKoc+fOR48ejYmJYV8a\nx4LAYYG7AofDsQkcDC4nD2cEDhq/pkaekxOyaxe/utpgFSkU1iUmVqWnN1ucEKVNHBs4aK6P\nHWyGxX7++ecfffQRcymYO3ful19+iXNmBjZGewgcra2tsbGxxlezrKwsrnXjhcBhEtvT5s03\n39y0aVNcXBxC6NSpU7m5uUuWLNmzZ49CoXjnnXfYFwUAZ2ufN1w0wcH3nnzy4p49N95/v2Hw\nYP0pOnCVKnjv3l6LF/d6/PHgvDycqzGam/dZnn322RMnTnz66acffPDBoUOH1q9fz8G00U6U\nlJSY/O5k8FgDwFlsh8VmZ2dPnz79p59+Qgjl5uYKhcKPP/7Yz89v1qxZhw8fdmYJAbCRWx5d\n614UQdRPmFA/YYK4tFSelRW8bx/R1MSslV650unKlejPP69JTq5KTVVFRrqxqOZwcAxtx44d\nO3bs6O5SAGTuYQUcfIgBMIltVL9///7QoUPpnwsKCuLj4/38/BBCPXr0uMfhLvEA0Npbs4ey\nY8eyF1+8kJtbumpVS7du+qt4Dx6E/b//1y8trftzz/mfOMHNjqXcbO0A7hUdHd2vXz+DhWKx\neMKECW4pD2grtoEjMjLywoULCKHy8vITJ04wFXzlyhWHj0EAwHnaVfIgJZLqlJQrP/xQ9J//\n1E6eTAkEeutIvxMnuj33XL/U1PBt23g2PcXX2UoecndBAFd8/fXX+l0EBALBunXroqOj3Vgk\nwB7bWyrp6emffPLJs88+m5+fT1HUnDlzWlpaNm7cmJWVlZyc7NQiAuAMfRKpVAAAIABJREFU\n7eqGS1P//k39+9+prw/eu1eenS2sqGBWCe/di1q/PnLjxvrRo6tTUhri491YTnM4eJ8FuEWP\nHj1+++23H3/88dq1a2FhYbNmzer2aAMe4DK2o1QaGxsXLVq0Z88ehNDatWtXr1599erV2NjY\nTp06/fLLL26schilYkH7HKViD2cnD+eNUmEPI0m/goKQrCy/M2eM76e0xMZWpaXVTp5MikQW\nduKMUSosOTB2wNNiuQYe3sYpbn5abENDA4Zh9JM/Hzx4cO7cuWHDhjlkogWbQeCwwDsCR2Fh\n4Y4dO2prayMjIxcvXhweHu6CP+qk5MGFwMEQlpfLd+2S79ljfD9FJ5XWJSZWzp2r7NzZ5Gvd\nGDgY9icPCBxcA4GDU7jyeHqY+MsjeEHg2L59+wsvvMBUhFQqzczMHDJkiMsK4NjkwanAQcPU\n6oD8/NDt22UXLxqvberfv3LevPqxY/WfWIu4ETho9sQOCBxcA4GDU2DiL0MQOCzw9MBRUVEx\nbNgwg/qNiYk5c+YM8ejnnws4JHlwMHAwpMXF8pycoP378dZWg1Wa4OCapKSq2bPVoaH0Eu4E\nDpptsQMCB9dA4OAUmPgLtCP5+fnGZ2xZWVlRUZHrC9NJj+v/ugs0x8aWrlp1Yd++0lWrlI9O\nO8GvqQnftq1famqXVat8z5xB3EtLMJgFAO6Dib8Ad7UafdWmKZVKF5fEAJM5vO9DTieTVaek\nVM+c6XvunDwnJ+DYMezhYzkxjSbw8OHAw4dbO3SonzWrJjVVIxa7t7QGmOrw1lAIgEeDib8A\nd9EtagZEIlFPxz0TxE5e2+aB4w3x8Tfff//yzp0VixdrAwL0V4pu3w7/4oteSUkd1q0T37rl\nrjJaAA0eAHAQ2xYOg4m/Xn/9dXo5m4m/FArFli1bLly4oFare/To8be//Y2eJ1in023duvXk\nyZNarTY+Pv7JJ5/k8/kWloP2pl+/fgsXLvz+++/1F7755pscnMnYW9s8VOHh5c88c3fp0oBf\nf5Xn5PieOcOsIpqbQ7KyQrKymmNjq+bNq01MpHhsryeuAbN3AMApxJo1a9hsd+/evS1bttTV\n1X344Yf379//97//LZVK169fv379+kmTJhk/wVnfu+++W1lZuWLFiokTJ964cePHH38cP368\nWCz+7rvvTpw4sWzZsoSEhL1795aUlCQkJCCEzC03SaPROKPnmkAg0Ol0uoeNyR6KIAiRSKTV\narnTua+txo8f7+vre+/ePZVK1bNnz7fffnvBggVcexS1voCHFKbm7uTxeDiOe151EISyc+fa\npCTFmDEYSYpv38b0+vQJamoCjh2T795NNDWpOnTQuXWcvDHFQwGPttMghHAcF4vFOp3O07uH\nI4TEYrHbbzXaTyAQ8Hi81tZWkpMz7rPH4/EwDPO8M/1RGIZJJBKSJFUqFftXSSQSszt09sRf\ntbW1jz/++Lp162JjYxFCOp0uIyMjIyNj9OjRixcv/uc//zlixAiE0Pnz5999990tW7YIBAKT\ny+k7OMZglIoFnj5KheGyib+chGn24PIoFfaIxsbQn38OzswUlpYarKIIQjFmTFV6esOgQYiT\nuVC/wQNGqXANjFLhFIePUmHbBOrj47Nr1y79ib/CwsIOHTpkdeIvkiTnz5/fpUsX+letVqtW\nq0mSvH37dmtrK3OTvn///jqd7tatW2Kx2OTyAQMG0EuUSuWmTZuY/Q8aNIhZ5UB0PvX0Wzn0\nc7T5fL57J2dzCBzHPfdd9OnTh/7h1q1bCCGB/jNNPJFQWJ+RUbdokeT334P/9z/fI0eYBg9M\npws4ciTgyBFVTExdSkpdWprOzFcFd6H7nNHfkeimMh6P57mHFgPDMC94FzweDyEkFos9vYWD\nIAjvqBGEEEEQ7N+I5Ypr2z1XHx+f27dvnzlzRqvVdu/efdy4cfRHmgVyuXz+/Pn0zyqV6vPP\nP/fx8Rk5cuSff/6pf57zeDyZTFZXVyeRSEwuZ3bY2tq6detW5lehUDh8+PA2vQuWeBy7IW0z\nHo/nHe9FzLExETbo3bs3/YNbRvY6nDo+/l58fNX9+wE7dvhnZfFqaphVwrKy8C++CP3224YZ\nM+rnz2/t0cP+P6dSqe7evUuSZFRUlMjizOtWlT5sm+nZsydBEF5waCGvOEFoQqHQ3UVwDE//\nykqj7zyy3NhyP4Q2fA4dPHjwxRdfvHTpErOkd+/en3322aRJk6y+lqKoo0ePfv/996GhoZ99\n9pmPjw9FUcZ34nU6nbnlzM8ymezrr79mfg0ODm5Taw9LYrHYo7s+0OjoplKpzI0v9RQYhslk\nMi9o95ZIJHw+v6GhISIigl5y8+ZN9xbJNnw+n6Kov9q9/fwan3zyzt/+5n/0qDwzU/b778xm\nuFLpv2OH/44dzf37V8+ZUz9+PGVr687Zs2dzcnLoNmqRSJScnGz/Nw0Mw4qKirRarRunLnQU\nX1/fhoYGd5fCXmKxWCAQNDU1eXr/OYFAgOO4F1x4fX19tVptm27Km+v/gNgHjnPnzk2bNi0k\nJGTt2rV9+vTBcfzKlSsbNmyYNm3a6dOnBw4caOG1Dx48+PDDDysrKxcvXjx69Gg6TwQGBmo0\nGqVSSUcnnU7X1NQUHBwskUhMLmf2xufz4/UeaOmkPhxCodALAgeNJElPfyMYhnFqXkub0V03\ntFot0/DIfNR51vAWgiAoinrkUwHHayZMqJkwQXT7dvDevfKcHJ5eQJRevCi9eDHax6cmKaly\n/nzVw7zFUmlp6Q8//MD82traumPHDn9//x72NZwwDbTXrl2jf/DcIS3ecYLQbRtardbT+3DQ\nJ4in1wj9Ye3AN8I2cKxevToiIuL8+fNBQUH0kpkzZy5btmzQoEGrV6/et2+fuRdSFPXWW28F\nBgZ+9dVX+p1XY2JihELh5cuX6fRQWFiI43inTp2EQqHJ5ba/RQA8gdcMrG3t0KF8xYqKv/89\n8JdfQjIzJTduMKuIxsbQn34KzcxsGDy4OiWlftw4yto9Wdrx48eNFx47dszOwGEMRtIC4Dxs\nA8eFCxeeeOIJJm3QAgMDFy5cqN+F09ilS5du3rw5c+bM69evMwsjIyODg4MnTpy4ZcuWoKAg\nDMM2bdo0ZswYetyaueUAtAfekTx0Ekl1Skp1Sspfj2jJy8OZMV8k6XvmjO+ZM6qoqOpZs6qT\nk7X+/pb3ZnKAkvMGZUDsAMAZ2AYOC6P4LA/wKykpoSjqk08+0V/41FNPTZs2bcmSJZs3b373\n3XdJkhw6dOiSJUvoteaWA9CueEfyaI6NbV616u5TTwXn5oZkZwsqKphVwvLyqPXrI7/9tn7U\nqMp585r69ze3Ez8/vzt37hgsdPb3EJgoHQDHYjsPx5QpU65evXru3Dn9Ro76+vrBgwf36NHD\nwi0VZ4N5OCyAeTi4xtfXVyAQ1NXV2TbqjzvJw8anxZKk77lzodu3+584YfwEuObY2OqUlNqp\nU0mjESjXrl3buHGjwcLHH3+cGW9sGxzHJRKJVqtl07mP47ED5uHgFJiHw/QOWQaOs2fPjhgx\nIiQkZPny5fRJXlhYuGHDhvv37584cWLIkCHsS+NYEDgsgMDBNXYGDobbk4edj6cX3b4dkp0d\nnJdHGI080vr61iQnV6WkqKKj9ZcXFBTk5eXRpySfz588efK4ceNs++uMNgUOBjeTBwQOToHA\nYXqH7Gc8PHDgwPPPP3/lyhVmSa9evT755JMpU6awL4rDQeCwAAIH1zgqcDDclTzsDBw0XK0O\nPHQo9McfJVevGq3D/+pYOnYsRRD0subm5rKyMpIkY2Ji6OkH7WRb4KBxLXZA4OAUCBymd9im\nKZZJkiwtLb1x4wZFUV26dOncubPVib+cDQKHBRA4uMbhgYPh4uThkMDBkF2+HJKVFXj4MGZ0\nxqnCw6tTU6uTk7VO6LFhT+BgcCR5QODgFAgcpnfo0c90QBA4LILAwTXOCxwM1yQPxwYOGq++\nXr53rzw7W6jXsZRGCQR148dXzZ7d1LevA/+iQwIHze2xAwIHp0DgML1DC4Fj1KhRLP9Afn4+\n+9I4FgQOCyBwcI0LAgfDqcnDGYHjLyTpe+6cPCcn4OhRzOi/pOzYsTo1tXrmTNIR03g7MHAw\n3JU8PD1wqNXqjRs35ubm1tbWxsbGPvfcc4MGDXJ3oWwHgcP0DiFwmASBg1MgcNjDGcnDiYHj\nIWF5ecjOncF79vCMZuzW+fjUTJtWlZbW2qGDPX/CGYGD5vrY4emB4/HHH8/NzdVfkp2dPXr0\naHeVx04QOEzvEG6pmASBg1MgcDiEA5OHCwIHDVepAg8cCMnOlhYWGq7DsIYhQ6rS0hSjRzMd\nS9u2c6cFDobLkodHB45Dhw4xz/hkdOjQ4ezZs8aP1vIIEDhM8oaHiAIA2PDEmcRIobBmxoya\nGTOkhYUh2dmBBw7gKtVf6yiKnrFULZdXp6RUz5qlMX+lcxeYtJSNs2fPGi+8fft2VVVVaGio\n68sDnAQCBwDtjicmj+ZevUp69brzz38G790bsnOnUG/iUUF1deS330Zs3lw/dmxVWloj9+79\nw6SllvF4pj+JvOPx7oDh5kGtAAA36vSQuwvCltbX9/5jj13KzLz2xReK0aP1n/2GabWBhw7F\nLl/eZ+7ckMxMgpO3EUsecndBuMXkHG5xcXGBgYGuLwxwHmLNmjXuLoNdNBqNM24kCwQCnU73\nyNO3PRBBECKRSKvVesFTkkUikfNutLuMUCgkCEKpVHKt71TAQwqFgs32BEEghNzSEwUhhDBM\nFR1dl5hYO20aKRSKy8pwvWODr1D4nzwZkpkpqKxUh4drzX9oYRjG5/NJknT9IEyFQqFQKBz4\nOBixWKxUKh21NxeLiIhoaWnRv7Hi4+Pz/fffy+VyN5bKHjweD8MwL7jwSiQSkiRVzH1MFvQf\nC2+4Q65d+NoKOo1aAJ1Guca9nUbbxPK3cJd1GmUDU6sDjxwJycyUXb5svLZxwICq9PT6sWMp\no/Z5F3QaZcn+RiaP7jRKO3jwYF5eXl1dXffu3ZcsWRIWFubuEtkOOo2a3iEEDpMgcHAKBA43\nMpk8OBU4GOLSUnl2tnzvXtzomqAJDKyZPr0qLU0dHs4s5E7gYNicPLwgcCCY+ItjIHAYgsBh\nAQQOrvHEwMHQTx7cDBw0oqkpeN++kKwsUWmpwSqKIBSjRlWlpzcMGYIwjIOBg2ZD7IDAwSkQ\nOEyCUSoAAFboT0Hud3jUyWSVc+ZUzp7te/58SFaW//Hj2MPOWJhOF3DsWMCxY60dOlSlpdXN\nmIHM3292IxjVArwStHCYBi0cnNKuWjjUavWBAwdKS0ujoqImTZoklUpdWUKWJBLJtWvXuNnC\nYYBfWxuclxeSlSW4f99gFSkQNE6ZUr1wYX3Hju4oWhtYTR7QwsEp0MJheocQOEyCwMEp7Sdw\nXL9+fcGCBaUP7wWEh4dv3bp1wIABrisiO3TfdfpOBPfbPBBCmFYbcPx4SFaWz/nzxmub+vat\nmj27bvx4SiBwfdnYsxA7IHBwCgQO0zuEwGESBA5OaSeBgyTJ8ePHX7lyRX9hTExMQUGB2BHP\nKnMg/cDB8IjkIb51KyQ7O2jfPuOJOrQBAdXJydWpqSq9jqXcZJw8IHBwCgQOk2DiLwC44vLl\nywZpAyFUVlZ28uRJt5SnrTxiGjFl5863X3rpYl5e6apVyu7d9Vfx6uvDt27tl5LSY8WKwMOH\njZ9Vyx0wgRjwRNBpFACuMPcNtba21sUlsRP3u5fqJJLqlJTatLTgwkK///3P7/BhjOmPQpL0\nI1pUUVFVqak1M2Zo/fzcWlhLmH8yTMoJuA8CBwBc0bVr1zYt5ziPeGJLy+DBDXFxpffuBefm\nhmRnCyoqmFXC8vLoL7+M+uab+lGjqlNSGuLj3VhOq4qLi5ubmznevATaObilAgBXREdHL1iw\nwGDh5MmTOdhptE24f6tFExhYkZFxMSfn6vr1ipEjkd4j0TG1OvDw4R4rVvTKyJDn5ODcnj4c\nbrUALoNnqZgGz1LhlPbzLJUxY8Y0NTVdvnyZJEmCIObNm/fRRx9xrccoQojP51MU1daefW19\nYouzGT5LBcNUkZF1kyfXTZ6MCEJ8+zau121cUFPjX1AQsnMnv65OHRnJtfssAoFA/zRXPOTA\nx7W4gEAg4PF4ra2tnjgznj54lorpHcIoFZNglAqntJNRKgy1Wl1WVhYVFSUSiVxWtjYxOUql\nrdz+RdzyTKN4a2vQL7+EZGdLiosN12HYg/j4qvT0B6NG6T+x1o2kUqnl0/z/t3fnAU2cid/A\nn5lJAgQIZ/ACBKyKJ2hRq62CR72vAFrXtqK+1l7WXuu2Wtva0+1q3VqVbdWq1V9tVSzetor1\nvvAC64FW8UQk4T5DQpL3j1mzMQkxQJKZid/PX+SZMPPAEPLNc/K5hckIs1R4BdNizSFw2IDA\nwTc0TdfW1np4eAj9A5xDAocRV8nDzqXNvXNy5OnpQbt30xZP08rlhcOGKceP14SEOLOmj/bI\nwGHE5+SBwMErmBYLIEhXr15NTEwMDg5u2bJlp06dNmzYwHWNeITngzyqoqNvzp6dvW3b3Rkz\nzJboEKtULdau7apQRM2d65OVxVUNGwSDPIAraOGwDi0cvCL0Fo7S0tL+/fvfvXvXtHD16tUj\nR47kqkr1UavV9vTjOLaFw4zL3g4bs3mbXi87fVqenh6wf7/lQh3qiAhlYqJq9Gi9y7dosb+F\nwwyvch5aOHgFLRwAwrNmzRqztEEI+fzzzzmpjFV6vX7lypWxsbFhYWHt2rX7+OOPOQypvG7w\noOnynj2vz5//Z1ra/RdfNBs66nnzZviiRbEjR4YvXGi5Vy0/YWILuAwCB4DTXbt2zbIwNzeX\nPx/jvv3229mzZ+fl5RFCSkpKUlNTX3/9da4rRfgbOwipDQ2988Yb2Tt33vj446rOnU0PMZWV\nzTZu7PLcc+1fey3gjz8ogUx2Q/IAZ8PCXwBO5+/vb1kok8lEIl68ACsqKhYsWGBWuHPnzuPH\nj/fu3ZuTKpni8wJieomkcMSIwhEjpDk5IenpQb/99r+FOgwG2enTstOntUFBhSNGKMeN0zRr\nxmll7WX8PfM27YFAoYUDwOmSkpIsC8ePH+/6mlh17do1q8OVLDd24Rafu1qq2YGlO3bceest\ndViY6SFxURE7sLTNnDlW96rlLbR5gGMhcAA4Xbdu3b788kuJydbnzzzzzEcffcRhlUz5+PhY\nLff19XVxTezE29hR5+t7f+LEP9PSrn77bWl8vOkSHVRdXWBGRvSrr3Z+7rmQTZss96rlMyQP\ncAjMUrEOs1R4ReizVFi5ubknTpyoqKho3759fHw8ZbJ+NrcMBkNCQsKlS5dMC2Uy2YkTJ+Ry\nudVvceoslYZq9BthY2apNIRYpQrevTtk40aJUml2SC+VFg0ZokxOrm7b1iHXavQslcZxUuDD\nLBVewcJf5hA4bEDg4Bs7Vxp1vcuXLycnJysfvC96eXmlpqbamLXLq8DBakTscHbgYFFabcCh\nQ/L0dNmpU8Ti/21VdLRKoSgaMUJv0gDWCC4OHEaOTR4IHLyCwGEOgcMGBA6+4W3gIIRUVFRs\n2rTpr7/+atmypUKhCA0NtfFkHgYOI/uTh2sCh5HnzZshmzfLt2+nLf5laQMDC0eOVCUlmS0s\nZj+uAoeRQ5IHAgevIHCYQ+CwAYGDb/gcOBqEz4GDZU/scHHgYDHV1YG//95s0yYvy8nSNF0e\nF1fw3HNmO9bag/PAYdSU5IHAwSsODxy8mJUHAOBYvJ1Mq5NKVQqFSqHwzslp9ssvgXv2UMY3\nV71elpkpy8ysDQtTjRmjGjOGb3vS2oMns2q1Wu1PP/10/PhxiqL69OkzceJEnsxCf5yhhcM6\ntHDwClo4+MaeFo4zZ85s3bpVpVK1b98+JSWF233SrcYOTlo4zIhVqpAtW+RbtohVKrNDek/P\nosGDlcnJ1dHRjzwPf1o4LNmfPBzVwqHRaMaMGXP69GljSY8ePbZs2SJp2kAZ+6GFw/oJETis\nQuDgFQQOvnlk4Fi2bNm8efOMDwMDA3fs2NHWQTMymsI0efAhcLAovd7v6NFmGzbYGlg6bJi+\n/m1u+Bw4jB6ZPBwVOBYuXPjVV1+ZFc6ePfudd95pymnth8BhFdbhAAAHy8nJmT9/vmlJcXHx\njBkzuKqPKX6u4WGg6dK+fa8sXXphwwbl+PG6h1dG8c7JiZg/P2b06NAlSzzu3eOqkk3nsvU8\nMjIyLAv37t3r7OuCbQgcAOBgGRkZtbW1ZoVnz55VWixHwRU2dkRFRXFdEXM1ERG3/v73rB07\nbr7/fvUTT5geEpWWtli3rmtiYtu33/Y7epQIuZHM2cnD8s+vvkJwJQyiAQAHq6+HgvOeC0sd\nOnSora09f/481xV5iF4qVSUmqhITvXNy5OnpQbt20cY3S73e/+hR/6NHNXJ54dixBcnJdZwO\njmkiJ40wffLJJy9cuGBWGBcX58BLQCOghQMAHCw2NtayUC6Xt2rVyvWVsQdvd2mpio6+OXv2\n+a1b81591WzvN4lK1XLFiphRoyI/+cTb4s1VcNgGj6tXrzrkbO+9957ZIrnNmjX7xz/+4ZCT\nQ6MxpgO7hEir1Wq1WoefViKR6HQ6nUD2la4PwzCenp51dXXO+BW5EkVRnp6ePPx83FAeHh4M\nw9TU1Ah9sLZYLDYYDPWN7IuMjMzOzr5+/bpp4bffftuhQweX1M5eNE17eXnpdDrj8PCAgICA\ngIDS0lJuK2ZG7+VV0a1bwYQJlbGxovJyzzt3jIconU7611/yrVt9DxwwGAzqiAiDWMxhVZtI\nJBIVFxcrlcqSkpKmTGvy9vYeM2ZMaWlpeXm5n5/f8OHDv//+++bNmzuwqraJRCKKomz/462p\nqcnIyDh06FB5eXlYWBhN8+7zP0VR7PDwBvVGSaXSek8o9H98NTU1zngfkkqlTooyriQSiXx9\nfdVqdY1xy2xhoihKJpM1aKQ0P/n4+IjF4tLSUqG/7jw9PQ0Gg41/Q9XV1f/+979//fXXgoKC\njh07vvvuu0OGDHFlDe3BMIxMJtNoNFbnd+Tm5rq+SvbwuH1bnpYWvGMHU15udkgnkxWOGqVK\nSqoND+ekbk0kkUhEIpFarTadxsXDoTaPJJFI2I8W9T3h7NmzkydPvnv3LvuwS5cu69ev51sT\nIDs9UKvVVlZW2vktBoMhMDCw3hMK/R+fRqNxxiZYDMMYDAahz12kKEokEun1eqE31RBCRCKR\n0BcfJIQwDEPTtNCDLCGE/TT2mLxArly54rIq2Y/SaGQHDgStWyfNyrI8Wt2tW9ELL5QPHGhg\nGNfXrdFomqYoSq/X1/fG1L59exdXqXHYH6S+v6vKysrY2Njbt2+bFvbt23ffvn0uqV0D2G7L\ntKTX6z08POo7KvjAgXU4bMA6HHzz+KzDIQgMwwQEBNTW1lZUVDzyyXxbsdTovwNLd++mLW6H\nVi4vHDZMOX68JiSEk7o1lIeHh1gsrq6ufuQLhIcDbkzZXodj165dKSkpluXHjx9/4uGpSdzC\nOhwAABzg56hS8mBg6V8HDtx+553ah9vkxSpVi7VruyoUbWbPlmVmWi4pJlwuW9LDGQoLC62W\nqyxWm3UzmBYLAGAv/m7R4utbMGFCwfjxstOn5enpAQcOUA/a8ymtNnDfvsB9+9QREcrERNXo\n0fr6h/UJDk+2bmmQiIgIy0KapgX0IzQOWjgAABqMpw0eNF3es+f1+fPPb9t276WXzJbo8Lx5\nM3zRotjhwyPmz7eyV63ACajN4+mnn37qqafMCp9//nlXzqPhBKbFWodpsbyCabF809ChZPxk\nOS22ofgzjVYikZi+zHXe3hVPPlkwYUJN27aiigqPvDzjIVqr9c7JCdm82f/wYYOHR01kJOHN\nhEyRSMQwjFarbcoLpPQBDvcLtD0tlqbpgQMH3rx586+//iKEMAyTkpLy+eefi3k2pRnTYs1h\n0KgNGDTKNxg0yisNGjRqDw4/XtvevE165UrIr78G/fYbbTFRUxsUVDhihDI5WcODj9f2Dxpt\nKBc3R9m5eVtxcfG9e/ciIiJ8Ht49hyewW6w5BA4bEDj4BoGDVxweOFicxA57dotlqqoC9+xp\ntmGDl+USIzRd2qdPwYQJ5T16ECcsNGAn5wUOI9ckD+wWaxUGjQIAOBL7lsbDwQQ6b2+VQqEa\nO1aWmRmyebP/oUOU8X1dr/c/csT/yJGaiAhVcnLh8OE6Xn7mbjohDjJ1GwgcAACOx9v5LISi\nynv1Ku/VS1JQIE9Pl2/dKi4qMh70unkzfOHC0NTUoqFDlUlJ1W3bclhTp0LycD10qViHLhVe\nQZcK36BLpaGcHTvs6VKxitJqA/bvD9m82ffcOcujlTExyuTk4gEDXLNFiwu6VGxwYPJAl4pV\nfBmcDADAQ/n5+a+//nrnzp3btm37t7/97eLFi407D0+n0RJiEIuLBw/O+f77Cz//rExM1D08\nxcAnOzvqww9jRo4M/c9/JPfvc1VJ17hhguu6uCe0cFiHFg5eQQsH3zwmLRzl5eX9+/c33fNC\nKpVmZGS0bVpHgzPezxrdwmGGqaoK2rUrJC3Ny6KSBpou69tXmZxc1rOnkwaWctvCYVXjYiJa\nOKzCGA4AAOuWLVtmtsNWdXX1xx9/vH79+qaclr/DOwjReXsrx41TjhvnnZPT7JdfAvfsoR6s\ntkLp9f4HD/ofPFgbFqYaM0Y1enSdvz+3tXUBDPVwIHSpAABYl52dbVmYZW131sbhbT8LIaQq\nOjp33rzsrVvzpk/XyOWmhzzu3AldujRm1KjIzz/3zsnhqoYuhg6XpkMLBwCAdZ6enpaFXl5e\njr0Kb6fREkK0cvm9adPuTZ0qO3262S+/+B89atwBjq6tDd62LXjbtqroaJVCUTRsmN7ar8st\nodmjcdDCAQBg3dChQy0Lhw0b5oxr8bm1g92i5a9Fi/5MS8ufNKlAsb0bAAAgAElEQVROJjM9\n6J2TEzF//n+3aLl5k6MqcgNtHg2CQaPWYdAor2DQKN88JoNGDQbDtGnTtm3bZizp3Lnzzp07\nbewW4RCNeANz1KBRe9AaTWBGRrP166VXr1oco8vj4lQKRUlCgoFhGnpmHg4abSg2NWLQqPUT\nInBYhcDBKwgcfPOYBA7Wzp07Dxw4UFtb26NHjwkTJrhyhy37k4crA8f/LpqTI09PD9q1i7bY\n3EsjlxeOHVuQnFzXkB3U3CBwsMRiMUVRrVq14roiTYLAYQ6BwwYEDr5B4OAVVy781RS2Y0dx\ncfGJEyfKy8tlMlmvXr2CgoJcVjEWU1ERvHNns19+8bh3z+yQQSwu6ddPpVCU9+xpz6ncLHAY\n30H421lmEwKHOQQOGxA4+AaBg1eEEjhYVmNHTk7OmjVrjNugi0SiSZMmderUybVVI4QQSq/3\nO3IkZPNmv5MnicWfd3X79srk5KLBg/U2h9y6a+AwElbyQOAwh8BhAwIH3yBw8IqwAgfLNHZo\nNJovvviisrLS9Ane3t5z5syxOr/GNTzu3pVv2SLftk1UWmp2SOftXTx4cMH48TVt2lj/XncP\nHKb4Hz6wtDkAwOPLdDLLrVu3zNIGIaSqqorbSRO1oaF3Z8zI3r79xocfVnXsaHqIqaqSp6d3\nnjix/YwZAQcOUAJPFU30GM5wwTocAAACw2aOS5cuWT1q7GHhkN7Do3DUqMJRo7wvXQpJSwvc\ns4c2ftw3GGSZmbLMTE2zZqrERNWYMdrAQE4ryzHTzMH/Zo+mQAsHAIAgde/e/dixY4cPHzYr\nDwsL46Q+VlV17Hjjo4+yfvvt5uzZNRERpockBQWt/vOfmFGj2syeLcvMJALv33cI9272YObN\nm8d1HZpEq9U6I85LJBKdTqfT6Rx+ZldiGMbT07Ouro4Pn3iagqIoT09PoY8YIIR4eHgwDFNT\nUyP0sVNisdhgMNQ92GVDoGia9vLy0ul0Ah2t5evrW1dXd/z48du3b9++fbt169aEkAEDBnTt\n2pXrqpkzSCTVHTook5KqOndmKis97941xgtKr/e6cSN4167AAwcomtZGRWkowQ8uZBiGoqim\nvIOUPhDQkHnFjkVRFDtaq9Zi2rMNNlapQeCwDoGDVxA4+AaBgyf69OnTvHnzO3fuVFdXi8X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GjQpdulRy/z5XlWwELPxlHRb+4hUs/MU3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\nQmCC", + "text/plain": [ + "plot without title" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "ggplotRegression(fit)" + ] + }, { "cell_type": "markdown", "metadata": { @@ -393,7 +467,7 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 33, "metadata": {}, "outputs": [], "source": [ @@ -409,7 +483,7 @@ }, { "cell_type": "code", - "execution_count": 40, + "execution_count": 34, "metadata": { "solution2": "hidden" }, @@ -484,6 +558,31 @@ "anova(fit)" ] }, + { + "cell_type": "code", + "execution_count": 35, + "metadata": {}, + "outputs": [ + { + "data": {}, + "metadata": {}, + "output_type": "display_data" + }, + { + "data": { + "image/png": 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kPgAAAAAMEhcAAAAIDgEDgAAABAcAgcAAAAIDgEDgAAABAcAgcAAAAIDoEDAAAA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\nASznWhsY1T0PAAAAAElFTkSuQmCC", + "text/plain": [ + "plot without title" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "ggplotRegression(fit)" + ] + }, { "cell_type": "markdown", "metadata": { @@ -515,7 +614,7 @@ }, { "cell_type": "code", - "execution_count": 41, + "execution_count": 36, "metadata": {}, "outputs": [ { @@ -593,6 +692,31 @@ "anova(fit)" ] }, + { + "cell_type": "code", + "execution_count": 37, + "metadata": {}, + "outputs": [ + { + "data": {}, + "metadata": {}, + "output_type": "display_data" + }, + { + "data": { + "image/png": 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AR6/fvf/9aawuH06dPbtm1zVn0AAICxIHAwkcNih95JWtlsaPcy1dmzZ3ULz5w5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OQtMVvXpV9OolUSqDtmwJTk8XGU3Kc795\nM3zRopDvvy8ZMqRw/PjaJ57gsKbNgS4VAAAQJBfrZCGEqIOC8l96KXv79uvz55ss0cFUVwdl\nZHSZOLHTpEmBu3YZ9qoVEAQOAABwlPz8/JkzZ/bp0yc+Pn7u3LmOWE3H9WKHXiIpGTToytKl\nF9euVcrlOg8P46OeubmR8+bFjB4dunSp5P59rirZBFj4yzIs/MUrWPiLb7DwF9/wc+GvgoKC\nhIQE44o98cQTmZmZnp6eFp9vvPBX067Ik04W44W/mo+pqvLfu7fFhg0eeXkmh/Q0Xd63b2FK\nSkXPnuTB5q62wMJfAADgOj799FOTGHTt2rUlS5Y47oou1tTB0np5KeXyCz//fHXJkrL4eOO9\n3yidzvfIkQ4zZnRJSQnetInh92dLDBoFAACHyMrKsrHQjlxtPKkBRZX37l3eu7dYqQzcvTt4\n40aJQmE46HHjRpsFC8IWLy4dPPj+88/XtGvHYU0bghYOAABwCJHIwmdai4V253oDOww0QUEF\nkyadz8i4/tlnVbGxxodotTpg167Ozz8fPX26/549/9urlh/QwgEAAA4xcODAPLNhBwMHDnRa\nBVy2tYMQvVhcMnRoydCh7jdvBm/eHLR9O200nNE7O9s7O1vj7180apQiKUn98MJiXEELBwAA\nOMTs2bOjoqKMS5566qlp06Y5uRou3NpBCFFFRNx+993snTtv/f3vtRERxofEJSWt1q7tJpc/\nMWuW7ORJ871qnQwtHAAA4BAymWz//v3Lly/PysqSSCT9+/d/8cUXndOlYs6FWzsIIVpPT8WE\nCYrx42VnzgRv3ux74IBhBzhKp/M7eNDv4EFVeLgiMbF49Oj6h3esdRpMi7UM02J5BdNi+QbT\nYvmGn9NiG6v502Jt5OjYYd9psU2pQHFx4M6dwenp5gt16CWS0n79mHff1fTsaf0kmBYLAADQ\nLK7dyUII0QQEFEyadP7XX6/Pn1/55JPGhyi12n/fPtlzz1G1tU6uFbpUAADgceTanSyEEL1I\nVDJoUMmgQe63bwdu2xaUkSF60JhX99xz+ocXMHUCtHAAAMDjy+VbOwghqvDwuzNm5GzffnP2\nbHaJjtpJk5xfDbRwAADA487lWzsIITqpVCmXK+Vy6dWrLTp2dH4F0MIBAABAyOPR2kEIqWnf\nnpPrInAAAAD8z2MSO5wPgQMAAMAUMofdIXAAAABYgKYO+0LgAAAAaBBih70gcAAAADyCIGJH\naWmpQqHg7ULGmBYLAABgE97Onr158+bGjRsLCwsJIVKpdNSoUb179+a6UqYQOAAAABqBb7Gj\ntLR05cqVtQ+WKq+pqdm4caOnp2eXLl24rZgJdKkAAAA0Gn86WY4cOVJrtjHKnj17OKmMFQgc\nAAAATcSH2FFUVGRjIbcQOAAAAJqF29jh5eVlYyG3EDgAAADsgKvY0bNnT/NCHg4aReAAAACw\nG+dnjoiICLlcLhaLDSVxcXEDBgxwcjUeCbNUAAAA7OmJJ56gafrixYtOu+IzzzzTpUuXa9eu\nqdXqNm3ahISEOO3StkPgAAAAsD8nz5719fWNi4tzzrWaBl0qAAAgGGfPnp0yZcozzzyTnJy8\nYcMGvV7PdY0egQ/TWHgCLRwAACAMe/funThxIvv1lStXDh48mJOT8+WXX3JbK1vwba0wTqCF\nAwAABECr1b799tsmhStWrMjJyeGkPk3wmLd2IHAAAIAA5OXlsXuFmDh+/LjzK9Mcj23sQOAA\nAAABoCjKYjlNC/KN7DGMHYK8TwAA8LiJiooKDQ01L3/mmWecXxl7eaxiBwIHAAAIAE3T3377\nrUQiMS58++23O3XqxFWV7OUxyRyYpQIAAMLQr1+//fv3p6WlXb16tWXLlhMmTBg2bBjXlbKP\nx2Eai+ADB0VRxuu52gtN0yKRiP8zvK0TiUSEEJqmHfErcjIH3WgnYzuhXeBPi6ZpF7gjbN+/\nC/wgLBf4Kdg7IhKJGhquQQjp3LnzsmXLnFippmAYpmn/eNu3b08IuX79ugMq9RBb6sbeBTu+\nQAQfOGiadnNzs/tpGYYhgh2LZMDWn2EYR/yKnIyiKBf4Kdi/Kzc3N6EHDjYzWXlXEAS2/niB\n8Af7AhGLxeyHJeFiGKY5d4TtJLp69apdK/UQ2+vWqDdZnU5n5aiwbyohRKvV1tTU2P20Xl5e\narVarVbb/czOJBaLJRKJRqOprq7mui7NwkbsqqoqrivSXDKZTCKRVFdXW39Z8p9UKtXpdCqV\niuuKNAsbNerr613gT0sikbjAT+Hl5cUwTG1tbX19Pdd1aRZ3d3eapq2/N1VVVe3bt6+goCAq\nKmrgwIHmGat169bEYZ0stvy1UBTl7u6u1Wob9acllUobOiT4wAEAACAsp06dmjp16v3799mH\n0dHR69evDwsLM3+mK43tEHaXAQAAgLBUVVW99NJLhrRBCMnNzX355ZetfItrzJ5F4AAAAHCe\nAwcO5OfnmxSeOnXqkYM2hB47EDgAAACcp6SkxGJ5cXGxLd8u3MyBwAEAAOA8UVFR5oU0Tbdt\n29bGMwi0qQOBAwAAwHn69u3br18/k8LJkycHBwc36jyCix0IHAAAAM5D0/Ty5cvHjh3LrgQj\nFotffvnlTz75pGlnE1DswLRYAAAApwoMDFy5cmVVVVV+fn5ERETzF20TxOxZBA4AAAAOeHl5\ndejQwY4n5HnsQJcKAACA6+BtJwsCBwAAgKvhYeZA4AAAAHBBfGvqQOAAAABwWfyJHQgcAAAg\nGDt37hw6dGhUVFSfPn2++eYboe/p7TR8iB2YpQIAAMLwyy+/vPHGG+zXlZWVX3zxxaVLl5Yv\nX85trQSE22ksaOEAAAABUKvVc+fONSnMyMg4duwYJ/URLq6aOhA4AABAAPLy8srLy83Lz507\n5/zKQBMgcAAAgAB4eHhYLHd3d3dyTaBpEDgAAEAAwsPDo6OjTQrd3NwGDhzISX2gsRA4AABA\nACiKSktLk8lkxoWffPIJ55MvwEaYpQIAAMLQtWvXEydOrFmz5urVqy1btkxOTo6JieG6UmAr\nBA4AABCMoKCgWbNmcV0LaAp0qQAAAIDDIXAAAACAwyFwAAAAgMMhcAAAAIDDIXAAAACAwyFw\nAAAAgMMhcAAAAIDDIXAAAACAwyFwAAAAgMMhcAAAAIDDIXAAAACAwyFwAAAAgMMx8+bN47oO\nzaLRaDQajSPOrNVq9Xq9I87sNEqlcsuWLWq1OigoiOu6NBdFUfX19VzXorkOHTp06NChyMhI\nhmG4rktz6XQ6nU7HdS2apaqqKj09vby8vFWrVlzXxQ5c4AVy6tSpP/74o2XLlm5ublzXpblc\n4AVSX1//yy+/FBQUhIWF2f5dUqm0oUOC3y1WKpVa+fEec7du3fruu+8mT57cr18/rutiB56e\nnlxXobn27dt36NChpKQkPz8/rusCpKam5rvvvhs5cuSzzz7LdV3swAVeICdPnvz111/79+8f\nGBjIdV3gvy+Q3r17jxkzxi4nRJcKAAAAOBwCBwAAADgcAgcAAAA4HCX0cZFghVarra6udnNz\nc4ERWK6hpqamvr7e29uboiiu6wJEp9NVVVWJxWIPDw+u6wKEEKJSqdRqtZeXF03jwzD39Hp9\nZWWlSCSy10BJBA4AAABwOKRIAAAAcDgEDgAAAHA4BA4AAABwOMEv/AXG0tPT165da3jIMExG\nRgYhRKvV/vjjj8eOHauvr+/Vq9dLL70kFou5q+ZjZN++fTt37szPz2/fvv0rr7wSEhJCcDs4\ncuzYsX/+858mhYMGDXrzzTdxRzhRVla2evXqc+fOabXamJiYqVOnsut94XZwRalUrl69+vz5\n8xKJJDY2dtq0aexwUXvdEQwadSmLFy8uLy8fNWoU+5CiqO7duxNCVqxYcezYsVdffVUkEv3n\nP//p1KnT22+/zWlNHwv79u37/vvvp0+fHhwcvGnTJqVSmZaWRtM0bgcnysrK8vLyDA/VavXi\nxYtnzpzZp08f3BFOzJ49W6vVJiYmMgyzZcuWqqqqxYsXE/y/4ohKpZo5c2ZYWNiECRPUavW6\ndevc3Nw+++wzYsc7ogcXMmvWrG3btpkU1tTUjB8//siRI+zD06dPy+XysrIyp9fu8aLT6V55\n5ZUdO3awD5VK5T//+c/CwkLcDp5IS0tbvny5Hi8QjtTV1Y0ZM+bcuXPsw8uXL48ePbq0tBS3\ngyvHjh1LSkpSqVTsQ6VSOXr06Js3b9rxjmAMh0vJz8/Pzs6eMmXKxIkTP/300/z8fELIrVu3\nVCpVbGws+5yYmBitVmv8UQ8c4e7du/n5+X369NHr9eXl5YGBge+9915wcDBuBx9kZ2efO3du\n8uTJBC8Qjkgkkk6dOu3Zsyc/P//+/fu7d++OiIjw9fXF7eBKdXW1SCSSSCTsQy8vL4qibt26\nZcc7gjEcrqOioqKyspKiqL///e9arXbDhg1z585dtmxZaWmpSCQybOwkEom8vLxKSkq4ra3L\nKy4uZhjmwIEDGzZsqK2t9ff3nz59et++fXE7OKfT6X744YfU1FS2Hxp3hCvvv//+a6+9duTI\nEUKIVCpdunQpwe3gTrdu3bRa7bp165KTk1Uq1Zo1a/R6fVlZmVgsttcdQeBwHZ6enqtXr/b3\n92dXsWzbtm1qauqpU6fEYrH5upZarZaLOj5GKioqtFptbm7ukiVLvLy8du3atXDhwsWLF+v1\netwObu3fv5+m6aeffpp9iDvCCZVKNXfu3CeffDIpKYmm6W3btn344YcLFizA7eBKcHDwe++9\nl5aWlp6eLhaLExMTvby8ZDKZHe8IAofrYBgmICDA8NDT07NFixZFRUWdO3fWaDS1tbXs+s1a\nrbaqqgq7Pzuaj48PIeTVV19ld6JPTk7+7bffzp071759e4TzIxAAAAfzSURBVNwObm3fvn3Y\nsGGGh/7+/rgjznfmzBmFQvHNN98wDEMIee2116ZMmZKVldW6dWvcDq7ExcWtWrWqtLTU29tb\nq9Vu3LgxICBALBbb645gDIfrOHXq1BtvvFFZWck+VKlUSqUyNDQ0PDzczc3tzz//ZMsvXbpE\n03RkZCR3NX0shISEUBRVVVXFPtRqtXV1dZ6enrgd3MrNzb1z5058fLyhBHeEE/X19exAQvah\nXq/X6XQajQa3gyvl5eULFiy4e/eun5+fSCQ6ceKETCbr2LGjHe8IWjhcR+fOnSsrK7/++utx\n48ZJJJKNGze2aNEiLi6OYZjBgwevXr06ICCAoqiVK1fGx8ezH7vBcQIDA59++ulFixZNnjzZ\n09Nz69atDMP06tVLKpXidnDo2LFj7du3N96MCneEEz169JBKpQsWLEhKSiKE7NixQ6fT4QXC\nIR8fn/z8/CVLlrzwwguVlZUrVqxITEwUiUQikchedwTrcLiUW7du/fDDD1evXnVzc4uNjZ0y\nZYqvry8hRKvVrlq16vjx4zqdrnfv3tOmTcNCOk6gVqtXrlx5+vTpurq6jh07Tp06tXXr1gS3\ng1Ovv/563759n3/+eeNC3BFO5Ofnr1279tKlSzqdrkOHDqmpqW3atCG4HdxRKBRpaWmXL18O\nDg5+9tlnx4wZw5bb644gcAAAAIDDYQwHAAAAOBwCBwAAADgcAgcAAAA4HAIHAAAAOBwCBwAA\nADgcAgcAAAA4HAIHAAAAOBwCBwAAADgcAgcANGj48OE9e/Z03Pm//vpriqLKy8sddwkA4AkE\nDgAAAHA4BA4AAABwOAQOAHCs2tra06dPc10LAOAYAgcAPMKNGzdGjx4dFBTUqlWradOmGQ+5\nWL9+fe/evf38/GQyWY8ePVauXGk4NHz48PHjx+/cubNFixbjx49nC3/++eenn37ax8cnLi4u\nLS3N+CrDhw+Xy+V3794dOnSol5dXq1atpk+fXlFRYVyN5557LiIiwsfHJz4+fteuXYZDlZWV\nc+bMadeunVQqbdu27axZs6qrqx95CACcSg8A0IBhw4a1bt06NDR0xowZK1asSExMJIRMmzaN\nPbp582ZCSO/evb/88stZs2Z17dqVELJp0ybD9/bo0cPPz2/ChAnLli3T6/ULFy4khHTs2HHO\nnDmvvPKKVCqNjIwkhJSVlbHP79u3b//+/dPT02/cuJGWlkZR1NSpU9mzZWdny2Sy1q1bv/fe\ne/PmzevSpQtFUStXrmSPjhs3TiQSJSUlffrppyNHjjSupJVDAOBMCBwA0KBhw4YRQpYvX84+\n1Ol0MTExUVFR7EO5XB4aGlpXV8c+VKlUMpls+vTpxt+7atUq9qFSqfT29o6Li6uurmZLjh07\nRlGUceAghOzdu9f46uHh4ezX8fHx4eHhxcXF7EO1Wp2QkODt7V1ZWVleXk5R1Jtvvmn4xgkT\nJrRv316v11s5BABOhi4VALDGy8tr6tSp7NcURcXExNTU1LAPV6xYcf78eYlEwj6srKzUarWG\no4QQX1/f1NRU9uuDBw9WVlZ+8MEHUqmULenTp8/w4cONr+Xv7z948GDDw5CQEPZspaWlBw8e\nnD59ur+/P3tILBbPmDGjsrLy5MmTbGo5fPhwfn4+e3TDhg1XrlxhK9zQIQBwMgQOALAmIiKC\nYRjDQ5r+3z+NgICA4uLidevWvfvuuwkJCaGhoSbDI0JCQgzP/+uvvwghsbGxxk+IiYkxfhge\nHm78kI0LhBA2IsydO5cykpycTAhhG04++eST7OzsNm3aJCQkfPDBBydOnGC/0cohAHAyBA4A\nsMbd3b2hQ0uWLOnUqdNbb72lUCj+9re/HT9+PCwszPgJHh4ehq9FIpH5GYyjTEPPIYSwjSjv\nv//+ATMJCQmEkA8//PD8+fNz587VarVff/11nz59xowZo9VqrR8CAGey/PIGALCuurp61qxZ\nEydO/OGHHwy5oa6urqHnR0VFEUJycnIiIiIMhRcuXLDlWk888QQhhKbp+Ph4Q2FBQcHVq1d9\nfX3Ly8vv378fGRk5b968efPmlZWVzZo1a+XKlbt37+7Xr19Dh0aNGtWknxsAmggtHADQFDdu\n3Kirq4uLizOkjd9//12hUOh0OovPT0hIkMlkX375ZW1tLVuSnZ29fft2W64lk8kGDRq0fPly\npVLJluh0utTU1JSUFLFYfPr06ejo6O+//5495OvrO2bMGPY5Vg418ccGgKZCCwcANEX79u1D\nQ0O//PJLpVIZFRWVlZW1efPm0NDQzMzMNWvWTJ482eT5/v7+H3/88bvvvtuzZ8/k5OTy8vJV\nq1b16dPnyJEjtlxuwYIF/fv3j4mJmTJlCsMwO3fuPHv27Lp16xiGeeqppyIjI+fOnZuTk9O5\nc+crV65s2bIlMjIyISGBYZiGDtn9FwIA1qGFAwCaQiKR7Nq1q3Pnzt98881HH31UWlp68uTJ\nTZs2RUdHHz161OK3vPPOO+vXr5fJZIsWLTp48ODnn3++cOHCwYMHNzR0g2EYPz8/9uvu3buf\nOXPmqaeeWrt27bfffuvh4bFjx44XXniBEOLp6fnbb7+NGjVq7969H3744b59++Ry+YEDB2Qy\nmZVDDvq1AEBDKL1ez3UdAAAAwMWhhQMAAAAcDoEDAAAAHA6BAwAAABwOgQMAAAAcDoEDAAAA\nHA6BAwAAABwOgQMAAAAcDoEDAAAAHO7/A8m/N/abbIELAAAAAElFTkSuQmCC", + "text/plain": [ + "plot without title" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "ggplotRegression(fit)" + ] + }, { "cell_type": "markdown", "metadata": {}, @@ -655,7 +779,7 @@ }, { "cell_type": "code", - "execution_count": 42, + "execution_count": 38, "metadata": {}, "outputs": [ { @@ -722,7 +846,7 @@ }, { "cell_type": "code", - "execution_count": 43, + "execution_count": 39, "metadata": {}, "outputs": [], "source": [ @@ -739,7 +863,7 @@ }, { "cell_type": "code", - "execution_count": 44, + "execution_count": 40, "metadata": {}, "outputs": [ { @@ -780,7 +904,7 @@ }, { "cell_type": "code", - "execution_count": 45, + "execution_count": 41, "metadata": {}, "outputs": [], "source": [ diff --git a/section5.1solutions.ipynb b/section5.1solutions.ipynb index cb823b8..4c7507a 100644 --- a/section5.1solutions.ipynb +++ b/section5.1solutions.ipynb @@ -18,9 +18,10 @@ }, { "cell_type": "code", - "execution_count": 14, + "execution_count": 4, "metadata": { - "hidden": true + "hidden": true, + "init_cell": true }, "outputs": [], "source": [ @@ -35,9 +36,10 @@ }, { "cell_type": "code", - "execution_count": 15, + "execution_count": 5, "metadata": { - "hidden": true + "hidden": true, + "init_cell": true }, "outputs": [], "source": [ @@ -88,6 +90,31 @@ "}" ] }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": { + "hidden": true, + "init_cell": true + }, + "outputs": [], + "source": [ + "# From https://sejohnston.com/2012/08/09/a-quick-and-easy-function-to-plot-lm-results-in-r/\n", + "ggplotRegression <- function (fit) {\n", + "\n", + "require(ggplot2)\n", + "\n", + "ggplot(fit$model, aes_string(x = names(fit$model)[2], y = names(fit$model)[1])) + \n", + " geom_point() +\n", + " stat_smooth(method = \"lm\", col = \"red\") +\n", + " labs(title = paste(\"Adj R2 = \",signif(summary(fit)$adj.r.squared, 5),\n", + " \"Intercept =\",signif(fit$coef[[1]],5 ),\n", + " \" Slope =\",signif(fit$coef[[2]], 5),\n", + " \" P =\",signif(summary(fit)$coef[2,4], 5))) + \n", + " theme(plot.title = element_text(size=12))\n", + "}" + ] + }, { "cell_type": "markdown", "metadata": {}, @@ -104,7 +131,7 @@ }, { "cell_type": "code", - "execution_count": 16, + "execution_count": 7, "metadata": {}, "outputs": [ { @@ -175,7 +202,7 @@ }, { "cell_type": "code", - "execution_count": 17, + "execution_count": 8, "metadata": {}, "outputs": [ { @@ -205,7 +232,7 @@ }, { "cell_type": "code", - "execution_count": 18, + "execution_count": 9, "metadata": {}, "outputs": [ { @@ -280,7 +307,32 @@ }, { "cell_type": "code", - "execution_count": 19, + "execution_count": 10, + "metadata": {}, + "outputs": [ + { + "data": {}, + "metadata": {}, + "output_type": "display_data" + }, + { + "data": { + "image/png": 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EDSSMaowUPgAAAASALJGzV4CBwAAAAJLdmjBg+BAwAAIEHV19e3tbXFu4roQOAA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+ "text/plain": [ + "plot without title" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "ggplotRegression(fit)" + ] + }, + { + "cell_type": "code", + "execution_count": 11, "metadata": {}, "outputs": [ { @@ -355,7 +407,32 @@ }, { "cell_type": "code", - "execution_count": 20, + "execution_count": 12, + "metadata": {}, + "outputs": [ + { + "data": {}, + "metadata": {}, + "output_type": "display_data" + }, + { + "data": { + "image/png": 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QSbIBAIkqDBSCgUxrqEjkro33OsJDgceDxeEmxF1H5BVFZWEkIi8W3yfD4/4FZE\naE85nU4/c2P8q5dhmN27d3/00Uddu3b929/+JpfLGYbhRjPPbZDJZOvXr3f/2KNHD6/WEP/E\nYrHdbvf/osQ5qVTK4/HatdVxSCaTtbS0xLqK0PF4PKlUarPZrFZrrGsJnVAoZBjGbrfHupDQ\nicVigUDQ0tKS0Fc4UlJSmpubY11F6CiKSklJcTqdZrM51rWEjv093draGuknOnfuXITWzG5C\nML/jIvQbhGGY1NTUtubGMnA0NDS89NJLN2/eXLZs2ZQpU9icoVQq7Xa7xWJh/2RxOp3Nzc1q\ntdr9KKFQmJ+f7/7RbDa36y0uFArtdntCn2HZVyahf89RFCWVShN6E/h8vlQqdTqdCb0VNE0z\nDJPQm8BenrHZbAn9V4RMJkvovcAGDpfLldBbwf65G9FNiHSvBkVRfD7f6XQ6HA7/S8ZkT8Us\ncDAM8/zzzyuVyldffVUqlbqn9+zZUyQSnTx5csyYMYSQ77//nqbpPn36xKpOAACADuokbaH+\nxSxwnDhx4vz58/Pnz6+qqnJP7N69u1qtzs/Pf++991QqFUVRb7/99tSpU9PT02NVJwAAQMgQ\nNdxiFjiqq6sZhvnrX//qOXHVqlXz5s1bvnz5u+++++KLL7pcrrFjxy5fvjxWRQIAAIQGUcML\n5f9DLPGvvT0ccrm8tbU1oXs4FAoFn883mUyxLiR0FEUpFAp2nLcExefzFQqFxWJJ6NZXiUTC\nMEwUuuQiRy6Xi0Siurq6hO7hUCqVnp/FSzgURalUKrvdntBjJgmFQqFQGJbu3VhFDYFAIBKJ\nWltbA/ZwRK5RwbPn0ksyfEAUAAAgHuCqhh8IHAAAAB2FqBFQNIY2BwAASGJIG8HAFQ4AAIAQ\nIWoED4EDAACg3RA12guBAwAAoB0QNUKDwAEAABAURI2OQOAAAAAIAFGj4xA4AAAA2oSoES4I\nHAAAAD4gaoQXAgcAAMBPIGpEAgIHAADAbYgakYPAAQAAQM6fP8/j8WJdRTJD4AAAgE6NvarB\n5+MXYmThu1QAAKDzwj2UqEGgA4AwaGlpOX36tNVqHTp0aHp6eqzLAQgMUSPKEDgAoKM2bdr0\n5JNP1tTUEEIkEsm6devWrl0b66IA2oSoERMIHADQISdOnHjooYesViv7o8Vi+d3vfpeVlbVg\nwYLYFgbAhagRQ+jhAIAOefvtt91pw+0f//hHTIoBaEt1dTXSRmzhCgcAdMi1a2VdK+0AACAA\nSURBVNe4E69evRr9SgB8Qs6IEwgcANAhmZmZ3Indu3ePfiUAXhA14gpuqQBAh9x///0ikchr\n4ooVK2JSDAALN1DiEAIHAHRIXl7eyy+/rFAo2B+FQuGTTz551113xbYq6LQQNeIWbqkAQEfd\nddddc+fO/e677+x2+/Dhw7t06RLriqAzQs6IcwgcABAGqampU6dOjXUV0EkhaiQEBA4AAEhU\niBoJBIEDAAASD6JGwkHgAACARIKokaAQOAAAIDEgaiQ0BA4AAIh3iBpJAIEDAADiF6JG0kDg\nAACAeISokWQQOAAAIL7EZ9RgGObIkSOVlZUWi6VHjx7Tpk1LSUmJdVGJBIEDAADiRXxGDdaH\nH3544sQJ9v9VVVWHDx9+5JFH0tPTY1tVe/Hr69N37yb/9V+EjvZ3myBwAABA7MVz1CCEnDhx\nwp02WC0tLZ9//nnCfE+hy5V69Ki6tDR9507aam0YPdo+eXKUS0DgAACAWIrzqME6e/Ysd+K5\nc+cYhqEoKvr1BE9486Zq61bNF1+Irl93TxT/v/+HwAEAAJ1IQqQNQojL5fI5MW4DB93amr5r\nl8ZgkB87RhjGa65gzx5isxGhMJolIXAAAEAMJErUYPXp0+ebb77xmti7d2866p0QAUlPnVJ+\n9ZVy2zZec7P3PIpqys016XSpv/xllNMGQeAAAIAoS6yowRo1atTRo0fPnTvnniIQCBYtWhTD\nkrzwm5pUu3drPv9cfOYMd65drTYVFprmz2/NyiKEyKXSqBeIwAEAANGSiFGDRVHUihUrvv76\n69OnT7e2tmZlZc2aNUutVse6LkK5XKkHD2oMBkV5OWW3e81lBIL6yZNNWm3D+PFMrC/GIHAA\nAEDEJW7UcOPz+TNnzpw5c2asC7nNZzeoW2vv3qaiIpNWa4+bD+4icAAAQAQlQdSIK7TNpigv\n12zcmHrkCLcb1JWSUj91qrGgoHHMmJiU5wcCBwAARASiRnjJzpxRbd6sKivjNzZy57ZkZ9cu\nXmxesMBM0w6HI/rlBYTAAQAAYYaoEUaCujpVWZlar5dcuMCda9NoaoqKjEVF1qwsgUAgEolI\na2v0iwwGAgcAAIQNoka4UC5X2sGDar1esW9fW92gRq22MQ66QYOEwAEAAGHwww8/WCyWWFeR\nDMRXrqgNBvXmzQKjkTvX0revUautKShwxE03aJAQOAAAIHTV1dUURd26dSvWhSQ82mJR7tql\n1uvlx49zu0GdKSm1s2cbtdqWIUNiUl7HIXAAAEAocPckXFJOnVLr9crt23ktLd7zKKoxL8+k\n1dbNnOkSiWJRXdggcAAAQPsgaoSFoK5OVVqq1uslvl5PW5cu7EAa1u7do19bJCBwAABAsBA1\nOo5yOv+vG5Tz+VVGKKybPNmk0zWOHZso3aBBQuAAAIDAEDU6Tnz5stpgUJeW+u4G7dfPqNPV\nzJ3rUCiiX1sUIHAAAIA/iBodRFssyp071Xq9vKLCRzeoXF4ze7ZJq20ZPDgm5UUNAgcAAPiG\nqNFBKSdOqPV65Y4dPLPZex5FNY4cadJq62bMSPRu0CAhcAAAgDdEjY4Q1NSoSkvVBoPk4kXu\nXFvXrqaiIlNRUdJ0gwYJgQMAAP4PokbIKJdLfvSoZuPG9K+/9tENKhA0jB1bM29e3bRpDI8X\nkwpjC4EDAAAIQdToAPGlS2q9Xl1WJjCZuHPN/fub2G7QtLTo1xY/Ej5w0DQtFouDX57H4wmF\nQl4ip0uapgkh7drqeENRFEVRCb0J7FuIz+cn9FYIBAKG08KWWNgdIRKJXC5XrGsJXcwPh3Pn\nzhFCBAJBR1ZCUVQH1xBbNE3TNN2uTaDNZsX27aqvvpIdP86d60xNrSsoqJ0/3zxoECGEIiTS\nrw57OPB4PIqi/C8Zofeb//NJwgcOQkjAV5a7fHsfEocSehPY4hN6E9wSfSuS5nBI9K2IVf1V\nVVUxed5EJ62sVH3xRfqWLTR3bFCabhk+vLaoqK6w0CWRtLUGm822bdu2Y8eONTU1ZWZmzpkz\nZ0iYxiwP5r0Uk/dbwgcOl8vVrq8L4vP5VqvVzvnmvQQiEolomk7oL0miKEokEiX0JvD5fIlE\n4nA4EnorCCEMw7TG65dZB4PP5/P5/NbWVqfTGetaQnHx4sX333//6tWrXbp0Wbp06eAofjAy\njDdQ2COaYZiEPrXy+XxCiP9NENTUKLdvV+v10nPnuHNtGk1NQYFxwQJrjx63J7WxNoZh3nnn\nncrKSvbHixcvvvnmm8uWLRs+fHhHNoEQwufzHQ6Hg9NB4iVyJ66UlJS2ZiV84AAASFC7d+++\n9957rVYr++MHH3zwyiuv3HnnnZF+XvRqtBfldKbt36/R69P276c40ZYRCuumTjXpdA2jR5Pg\nxgatrKx0pw23L7/8cujQoXRyjS7qCYEDACAGbDbbQw895E4b7JR169ZNnz5drVZH6EkRNdpL\nfPGixmBQlZYKamq4c80DBtzuBk1Nbddqr1y5wp3Y1NTU0NCQnmhfOh88BA4AgBioqKgwcsa3\nbmlpOXDggE6nC/vTIWq0C221Kvbt02zcmHrkiO9vip81y1RQ0JybG9r622pNTeiu24AQOAAA\nYsDz2kYw00OGqNEuKcePawwG5c6dNHdsUJpuHDXKqNXWT5/uEgo78iyDBg3avHmz18RevXr5\naYBIAggcAAAxMGTIEKFQaLPZvKbn5eWF6ykQNYInMJm6bNmi0utFPscGzcy8PTZoZmZYni4z\nM7OoqKikpMQ9RSaT/exnPwvLyuMWAgcAQAykp6c/++yzv/nNbzwnPvTQQ3379u3gmpEzgkc5\nHIr9+9V6fdqBA9xuUJdQWDdtmkmrbQy6GzR406dPv+OOO44fP97c3JyRkTF+/HipVBrep4g3\nCBwAALGxevXqjIyMN99889KlS926dVu2bNnSpUs7skJEjeBJLl5U6/Wq0lJBbS13rjk721hU\nVFtQ4JDLI1dDr169evXqFbn1xxsEDgCA2KAoqri4uLi4WKlU1vr6tRc8RI0g8cxmdiCNlJMn\nuXOdaWmmOXNMOp15wIDo15b0EDgAABIYokZQGEZeUaHW65U7d9LcMa9oumH06Lri4qaZM1sT\nfLD/eIbAAQCQkBA1giEwGtWlpWqDQXz5Mneule0G1WptGRl8Pp/H45Fwf0oI3BA4AAASDKJG\nQJTDodi373Y3KOeL/VxCYd306SadrnHkyLB3g0JbEDgAABIGokZAkgsX1Hq9qqxMUFfHnWvO\nzjZqtbVz50a0GxR8QuAAAEgAiBr+8VpalNu2qQ2GlFOnuHMdqak1BQUmnc7cv3/0awMWAgcA\nQPxCzgiAYeTHj6s3bVLu2kVzv/eYphvGjDHpdHVTpjAdGxsUOg6BAwAgHiFq+Cc0GlWbN6sN\nBrGvL0Kzdu/Ojg1q69o1+rWBTwgcAADxBVHDD8rlkh89qtm4MX3PHt/fFD95srG4uHH0aEJR\nMakQ2oLAAQAQLxA1/BBfvKguKVEbDD67QS19+tTMm2ecP9+Rlhb92iAYCBwAALGHqNEWthtU\nYzDIfHaDpqXd7gbt1y/6tUG7IHAAAMRSdXX1rVu3Yl1F/GEY+XffafT69La6QceONel0dZMn\noxs0USBwAADEAC5ptEVgNKrLyjSbNol8dYPaunSpmTvXuHChtVu36NcGHYHAAQAQVYgaPlF2\nu2LvXo3BkHrokI+xQUWiuhkzTDpdY14eukETFAIHAECUIGr4JDl3TmMwqMrK+PX13Lktgweb\ndLqa2bOdKSnRrw3CCIEDACDiEDW4bo8NWlqaUlHBneuQy+vy828tXGgeODD6tUEkIHAAAEQQ\nooY3hkk9dkzNdoNyvpqVoenG8eONWm395MmMQBCTAiFCEDgAAMIPOYMrQDdo1641c+YYFy2y\nZmZGvzaIAgQOAIBwQtTwQtls6eXlar0+9ZtvfHSDisW1M2aYdLqmESPQDZrcEDgAAMIDUcOL\n5OJFVdtjg7ZkZ9cUFtYUFjpSU6NfG0QfAgcAQEchanjiNTWptm1T6/WyykruXEd6ek1BgVGn\ns9xxR/RrgxhC4AAACBFyxk+4XKlHj6r1+vTdu312gzaMH29CN2gnhsABANBuiBqehDdvqrds\nSdu4Ufjjj9y51qwsY1FRTVGRTaOJfm0QPxA4AADaISZRw263Hz9+3Gg0pqWlDRs2LDU+mh4o\nmy197161Xp92+DBpqxt0/vym3Fx0gwJB4AAACFKsrmoYjcY333yz7j99l5s3b166dOngwYNj\nUgxLUl2t2rxZYzDw0Q0KQUPgAADwJ+Z3Tz7++OM6j9/rVqv1X//611NPPSWTyaJcCa+pSbV1\nq1qvl505w53rUCpNBQUmnc7Sp0+UC4OEgMABAOBbzKMGIcRkMl3hDJNlNpsrKytHjRoVpSJc\nrpQTJ9RlZaotW2iLxXsuTTeOGtW0ZEn91KlmhyNKJUECQuAAAPAWD1GDZeH+gvc7PbyEN26o\nS0rUJSWia9e4c1uzskw6namw0NGli0wmY5xOgsABbUPgAAC4LX5yhptarebxeE6n02t6RkZG\n5J6UHRtUtXlz2sGDFOepXUJh/eTJxuLixtGj2W5QdIRCMBA4AADiMWqwJBLJzJkzt23b5jkx\nOzu7X79+kXg66Q8/qA0G1ZYt/MZG7tzmYcNMOl3trFlOqTQSzw7JDYEDADq1uI0abrNmzRII\nBHv27GlpaREIBKNHjy4sLKTC+kFTflOTsqxMYzBIf/iBO9euVNagGxQ6DIEDADqj+M8ZbjRN\nz5gxY8aMGS0tLVKpNJxRw+VKPXJEYzAo9uyhbTavmQyP1zBhgkmnq584keHjlwV0FN5DANC5\nJFDU8BLGz8EKjUZVWZlm40aRr7FBW3v2rJ0zx6jV2iLZKQKdDQIHAHQWiRs1woW22RS7d2sM\nhtSjR32MDSqV1s6cadRqm3NzY1IeRIHL5bp06dK3337bq1evkSNH0jQdtadG4ACAJIecQQiR\nXLigKi3V6PX8+nru3JbsbGNxce2cOegGTWJ9+vS5cOHC8uXLT506xU4ZMWLEO++8k5WVFZ0C\nEDgAIGkhavCampQ7dmg2bvQ5NqhdparNzzfNn2+OzGdeIOb6ePT5OhyOFStWuNMGIeS7775b\ntWpVSUlJdK5zIHAAQLJBzvi/sUHLyujWVq+ZDE03jRplLC6umzoV3aBJZtCgQY2NjTZOCzAh\n5OjRoydOnPCaeOTIkYqKihEjRkShNrzVACB5IGqIrl9XGwzqkhLhjRvcua29e5u0WlNhoV2l\nin5tECHuyxgSicTPYjd8vSX8TA87BA4ASHgXLlxwcVogOxXaZkvfvVut16d++63vbtD8fKNW\n25yTE5PyIOz6tH9MlLZ6NXr16tXhcoKCwAEACezs2bP8zn1TQHbmjFqvV23dymtq4s5tzskx\narW1+fkudIMmvhBChqcRI0ZMmjRp3759nhNnzpw5ePDgjtUVrE59oAJAgnLfOhGLxbGtJFb4\nDQ2qLVvUer20qoo7165Ws98U3xqtP14hQjoYMjzRNL1hw4Zf//rXO3fuZKcUFBT87W9/C9f6\nA0LgAIBE0tm7NFyutMOH1Xp9+t69FHdsUD6/YeJEo07XMGECw+PFpEDooDAmDK6uXbv++9//\nvnLlypUrV3r27NmjR4/IPRcXAgcAJIDOnjMIEV27drsb9OZN7lxL794mna6msNCuVEa/Nuig\niIYMrqysrKiNveEJgQMA4lonjxq01fp/3aAM4zXXKZXWzppl0mqbhw+PSXkQsiiHjHiAwAEA\n8aiT5wxCiKyyUq3Xq7Zt89ENSlHNOTlGna525kyX309CQlzphCHDEwIHAMSXTh41+PX1t7tB\nz53jzrWr1abCQpNO19qzZ/RrgxB08pDhCYEDAOJCJ88ZlMuVeuiQxmBQ7N1L2e1ecxk+v37i\nRBO6QRMEQoZPCBwAEGOdPGqIrl7tsnVr6saNwlu3uHMtffqYdLqaggJ0g8YzJIxgIHAAQGx0\n8pxB22yK8nLNxo2pR4746AaVyeqnTjUVFjaOHk0oKiYVgn8IGe2FwAEA0dbJo4bs9GmNwaDc\nto3X3Ow9j6KacnNNOl3tjBnoBo1DCBkdEb3A4XA4li1btmHDBrlczk5xOp0ffPDBgQMHHA7H\nmDFjVqxYIRAI/EwHgITWyXMGv75eVVam0esl589z59o0mpp580xabWssBkgAPxAywiUagcNm\ns505c2bLli1NP/1w17vvvnvgwIE1a9bw+fw33njjtddee+SRR/xMB4BE1MlzBnG5Uo8eVZeW\npu/cSVutXjPZb4pv/NnPbowfj27Q+IGQEQnRCBwlJSUlJSX2n/ZdWyyW7du3//rXvx4zZgwh\nZPXq1S+++OIvf/lLoVDoc3paWloUSgWAMOrkUUN486Zq61bNF1+Irl/nzm3t3dtUVGTSau3p\n6TKZjGlpiX6F4Klv375CobCZe58LwiQagWPhwoULFy48d+7co48+6p546dKl1tbW3Nxc9sec\nnByn03nhwgWJROJz+ogRI9gpdrv9u+++c69HrVarVKrgi6FpOtG/W5KiKEJIQt9moiiKoqiE\n3gQej8f+m+hbwTBM2Dfh/H9uGfCi9Sc7TdNU3HRW0q2tip07VZs2yY8d89kNWjdnTs38+S1D\nh7JT2Ncoaq9VJLAvPkVRCbcVffv2df+fz+fTNJ3oRzQhhM/nM5w3XjyI2a/euro6Pp8vk8lu\n18Hnp6Sk1NbWSqVSn9PdD2xubn7wwQfdP65cuXLlypXteuqEfj+5JcElnyTYBKFQKBQKY11F\nR0nC1JxYWVkZ3hUGL06+M1Zy4oTiyy9Ty8poX2ODmkeNql+4sGnOHJdYTAjxeo2i/6KFHU3T\nCbEVgwYN8jM3CY5oqVQaq6d2Op1+5sYscDAMw/2LxOl0tjXd/X+xWLxs2TL3j0OHDrVYLME/\nr1AodDgcLper/SXHC5FIRNN0u7Y6DonF4tbW1lhXETqapkUikcPhsHPGaEog7F9C/s8RAVX5\n+nr0qOHxeDRNx3Yv8Bob07ZtU336qeSHH7hz7Wp1vU5XU1xsc48NyqmWz+c7HI5I1xlRAoGA\nYZi43Yr+/fu7/9/WyZOmaR6Pl+hHtEAgsNlsHTyoQ+ZyudzXC7hiFjiUSqXdbrdYLGwidjqd\nzc3NarVaKpX6nO5+oEQiWbt2rftHs9nc0p57nzRNt7a2JvRbSiAQ0DTdrq2ONxRFCYXChN4E\nPp8vEonsdntCb4VEImEYJuTkFw8tGmKxmA0c0f8rgnK50g4eVOv1in37fIwNKhDUT55s1Gob\nx49naJoQQjgdo258Pt/a9tz4x94hdblccbUVno2fwRyn7AXLRD+iBQJBa2urzWaLVQ3xGDh6\n9uwpEolOnjzJNod+//33NE336dNHJBL5nB6rOgHASzzkjNgSX7miNhjUmzcLjEbuXEvfvkat\ntqagwJGeHv3aOjn8sohnMQscUqk0Pz//vffeU6lUFEW9/fbbU6dOTU9PJ4S0NR0AYgg5g7ZY\nlLt2qfV6+fHjPrpBU1JqZ882arUtQ4bEpLzODDkjIcTy8xrLly9/9913X3zxRZfLNXbs2OXL\nl/ufDgDRh5xBCEk5dUqt1yu3b+dxr7dTVFNenlGrrZs50yUSxaK6TgohI+FQ8fnhmeCZzWaz\n2Rz88nK5PNF7OBQKBZ/PN5lMsS4kdBRFKRSKurq6WBcSOj6fr1AoLBZLot/x9dPDkRBRQywW\n8/l8s9kciR4OQV2dqrRUrddLfL0Uti5dTEVFpqIia48eHXwimUyW0G8kiqJkMpnT6Yx0M3tE\nQwbbw5HQ43BIJBKZTNbY2BjDHg7PnksviT0iBQCEXULkjIiiXK60Awdud4NyPnbBCAR1U6aY\ntNrGceNud4NCJOFKRtJA4AAAQpAzCCGEiC9fVhsM6tJS392g/foZdbqauXMdCkX0a+tUEDKS\nEgIHQKd27ty5hL7DGBa0xaLcuVOt18srKnx0g8rlNbNnm7TalsGDY1JeJ4GQkfSCDRz33nvv\nM888k52d7TW9vLz8k08+ee2118JdGABEEHs9IzlG3e2IlBMn1Hq9cscOHrcVjKIa8/JMOl3d\njBnoBo0QhIxOJUDgqKmpYf/z0Ucf3XnnnRqNxnOuy+UqKyt77733EDgAEgLum7AEtbW3u0Ev\nXuTOtXXtersbtHv3qJfWKSBndE4BAodnu+n8+fN9LjNjxoxwVgQA4YacwaKczrQDBzR6fdr+\n/T66QYXCuilTTDpdw5gxBN2g4YaQAQECx1/+8hf2P48//viaNWs8v1iPJRAIFixYEJHSAKBj\nkDPcxJcu3e4G9fV5cnP//ia2GzTxv1AwriBkgKcAgeOxxx5j/1NSUrJq1aqcnJzIlwQAHYKc\n4UbbbIrycs3GjalHjvgeG3TWLFNBQXNubkzKS1bIGeBTsE2ju3fv9jn9/fff379//1tvvRW+\nkgAgFMgZnmRnzmg2blRu3eqjG5Smm4cNMxUW1syd60qEr1NPCIMGDbLb7Q0NDbEuBOJXOz4W\n+9lnn+3YscNzWE+Xy7Vjx45BgwZFoDAACApyhidBTY2qtFRjMIh9doNmZNzuBu3WLeqlJSH3\nlQyKomJbCSSEYAPHW2+9tXLlytTUVIfDYTabs7KyrFbrrVu3evTosX79+oiWCABcyBmeKJcr\n9fBhzcaN6V9/7bMbtGHMmJp58+qmTWN4vJhUmExwxwRCE2zgeP3114cPH3748OHGxsasrCy9\nXp+bm7t169Zly5ZlZmZGtEQAcEPO8CK6eFG5dWvqF18Ib9zgzrX06VMzb55Rq8U3xXcQQgZ0\nXLCB4/z58w8++KBIJNJoNGPHjj18+HBubu6cOXMWLlz49NNPf/zxxxGtEqCTQ87wwjOblTt2\nqPX6lBMnuHMdcnnt3LlGrdbMGasQgoeQAeEVbOCgaTr9P38ijBw5ct++fStXriSEjBkz5rnn\nnotQcQCdHHIGV8rx4xqDQblzJ+2rG7Rx1CijVls/fbpLKIxFdckAOQMiJNjA0b9//6+++urR\nRx8VCoW5ubmPPvqo0+nk8XgXLlyor6+PaIkAnQ1yBpegpka5fbtGr5ecO8eda+/SxTR3rrG4\nGGODhgYhA6Ig2MDxyCOPLF26tF+/fhUVFRMmTGhoaHjggQdGjRr11ltvjRkzJqIlAnQSyBlc\nlMOh2L9frdenHThAOZ1ec11CYePMmY2LFxuHDXOF4+kcDkdzc3NaWlon+dgFcgZEU7CB4+c/\n/7lYLP74449dLle/fv1efvnldevWffDBB1lZWX/9618jWiJAckPO8On22KAlJYLaWu7c292g\nOh0/I4PP5xOzmbg6FDmam5s3bdp0/Phxl8slEommTZuWn59PJ+MA5wgZECsUwxl9L0gtLS3V\n1dUDBgwQxvReqdlsNnNv5bZNLpe3trYm9PdxKxQKPp9v8jVCc6KgKEqhUNTV1cW6kNDx+XyF\nQmGxWFpaWkJ4eJyEDPbbYuPqcOCZzcrt29UGg+9u0NTUmrlzTTqdecAAdopYLObz+Waz2dWB\nwOFyuTZs2HD+/HnPifn5+QUFBSGvs11kMllob6TgRTRnUBSlUqkSfeAvoVAoFAqbm5tjXUjo\nJBKJTCZrbGy02WyxqsHzK9i8tGPgL0JIc3PzN998YzQap02bplAoBg0axMOH2gGCFic5Iz6x\nY4Oqtm712Q16e2zQggKXWBz2pz579qxX2iCE7N69e/r06eIIPF3U4GIGxJV2BI633nrrscce\na2pqIoTs2bOHELJkyZI///nPP//5zyNUHEByQM7wQ2A0qktL1QaD+PJl7lxrZqapqMik1doy\nMiJXw61bt7gTnU6nyWTq0aNH5J43QpAzID4FGzg2b968atWqqVOnrl27dtGiRYSQAQMGDBky\nZOnSpenp6YWFhZEsEiAhIWf4QTkcin37bneDcu6GuITCumnTTDpd46hRUfimeEkb36gik8ki\n/dRhhJwBcS7YwLF+/fqhQ4du376dz7/9kMzMzK1bt44ePXr9+vUIHAAshIyAJNXVar1eVVoq\n8NXEY87ONmq1tXPnOuTyqJU0ePBgbhfFHXfckR7345MiZEACCTZwVFRUPP744+60waJpet68\nea+++moECgNIJMgZAfFaWpTbt6v1+pRTp7hzHampNQUFJp3O3L9/9GuTyWT33HPPxx9/7O5A\n79Klyz333BP9SoKEnAGJKNjAkZ6e3trayp3ucDjkUfxDBCCuVFVVWa3WWFcR7/x3gzaOGlVT\nWFg7Y0YkukGDl52d/dRTT50+fbqhoaFr165DhgyJt454hAxIdMEGjrFjx3744Yfr1q3zvMZ4\n69at999/f9y4cZGpDSAesRczaJqWSqWxriWuCYxG9ebNaoNBfOUKd661WzeTVmsqKrJ17Rr9\n2nySyWRxOIwhcgYkjWADx0svvZSTk5Obm7tq1SpCyJYtW7Zu3frWW2+1tra+9NJLkawQIC7g\npkmQKJdLfvSon2+Kr5s8uaawsGHiRCYZh9UKF+QMSD7BBo4+ffqUl5c//PDDzzzzDCFk/fr1\nhJCZM2f++c9/7h+Le64A0YGcETzJhQtqvV5VVuazG7Rl0CCTVlszZ44TN2HbhpwBSawd43Dk\n5OR8/fXXtbW1Z8+eFQqF/fr1S01NjVxlALGCkNEuvJaW9K+/VpWWph4+zJ3rlMtr8/NvFRfj\nm+Lb0qdPH6VSWetrBHeAZNK+kUYJIUqlEk0bkJSQM9qHYeTHjmkMhvRdu2huRzlNN4wda9Jq\n66ZMYfBN8b7gYgZ0NsEGjoaGhscff3zXrl0+v7jk+vXrYa0KIEoQMkIgvHWL7QYVXb3KnWvt\n3t1UVBRX3aBxBTkDOq1gA8ejjz767rvv5ubmTpo0KSm/QRE6FeSMEFB2e9qhQ6rS0vQ9e7jf\nFM92gxqLixtHjyad47vd2wU5AyDYwFFSUrJo0aLPPvuMwqkEEhNCRsgkAw7bVgAAIABJREFU\nFy+qSkrUBoPvbtDs7JrCwpqCAkdaWvRri3PIGQBuwQYOl8tVUFCAtAEJBzkjZLzmZtW2bWq9\nXvb999y5DoWipqDAqNNZ+vaNfm1xDjkDgKsdA3+dOHEioqUAhAtCRgfdHht0yxbaYvGe5x4b\ndOZMl0gUi+rilFfIYBjm9OnTV65c6dmz5+DBg/HXGkCwgePvf//7tGnThg4d+stf/jLeRvwF\nIAgZ4SAwGtVlZZpNm0S+xga1de1aM2eOcdEia2Zm9GuLWz4vZly9enXVqlWH//M54fHjx2/Y\nsKFbt27RLQ0gvvgLHKNHj/b80el0rly58tFHH+3du7f4p996cOTIkYhUBxAIckbHUXZ7+t69\naoMh9dAhH98ULxbXzZhh1Gqb8vLQDerm56aJy+VauXKl51nx4MGDq1at2rRpEzruoTPzFzjU\narXXj8OHD49wPQCBIWSEi6SqSvnVV+mlpfz6eu7cliFDjFpt7ezZzpSU6NcWn4Jpzjh27Bj3\nb7BDhw6dOHEiNzc3MnUBJAB/gaOsrCxqdQD4h5ARRrymptvdoJWV3LmO9PSaggKjVotuULd2\nNYG2NS7Rjz/+iMABnVm7RxoFiCbkjHBimNRvv1Xr9em7d9NWq/dMmm4cP96o1dZPnswIBDEp\nMN6E9mGT7t27+5yelZXVsXIAEhsCB8QdhIywE968qS4pURsMomvXuHOtWVnGoqKaoiKbRhP9\n2uJQBz/UmpubO27cuEOHDnlOnDRp0rBhwzpWF0BiQ+CAuICQEQmUzZa+d69ar087fJj46gat\nz8+vLS6uGzoU3aAkfINn0DT95ptvPvjgg/v372enTJky5fXXX8cnY6GTQ+CAWELOiBBpVZVa\nr1dt2cJvaODObR461KTT1c6aRSsUhBBit0e7vngSiUG6unXr9tVXX505c+by5cu9evUaOHBg\n2J8CIOEgcEC0VVdXUxQlkUh8fhEgdASvqUm1datar5edOcOda09PrykoMM2fb/nPr9hO/hnN\nSI8Hmp2dnZ2dHdGnAEggCBwQDbiSEVku1/91g9psXjMZmm6YMMGk09VPmsTwcchj3HGA2MDZ\nByIFISMKhDdu3O4G9fVRzNasLJNWa5o3z45uUOQMgFhD4IBwQsiIDtpmU+zZozYY0o4c8dEN\nKpHUzphhmj+/KScH3aDIGQBxAoEDOgohI5qkP/ygNhhUW7bwGxu5c5uHDTPpdLX5+U6ZLPq1\nxRXkDIB4g8ABIULOiCZec7Ny+3Z1aWlKRQV3rkMur8vPv7V4sbl//+jXFleQMwDiFgIHtANC\nRrS5XKlHjqgNhvQ9e3x0g/J4t7tBJ05ENyiiBkCc6+wnKQgIISMmhNevq0tKNCUlQp/doL16\nmbRaU2Gh/affsNgJDRgwQCQS1dXVOZ3OWNcCAP4gcIAPCBmxQtls6eXlqs2b0w4c8PFN8UJh\n/eTJxuLixtGjO3k3KK5nACQcBA64DSEjtiQXLqhKSzV6ve9vis/ONhYX186Z45RKo19b/EDO\nAEhcCBydGkJGzLHdoJqNG32ODepITa2bOfPWnXea+/WLfm1xBVEDINEhcHQ6CBlxweVKOXFC\nXVamKiujW1u9ZjI03TRqlLG4uG7q1E7eDYqcAZA0OvW5rPNAyIgfQqNRVVam2bhR9OOP3Lmt\nPXvWzplj1GptGRnRry1+IGcAJB8EjqSFkBFXaJtNsXu3xmBIPXrUx9igUmltfr5Rq23OyYlJ\nefEDUQMgWSV84KAoSiAQBL88TdP8BL9GTVEUIcTnVp8/f979fx6PF72a2omiKIqi4rnCgGia\nJoQEsxXSykqVXq/csoXnc2zQnJya+fPrZs1ySaWEkCi/IuxWxMOO6Nu3b2gPZA8HPp/Pbkvi\natd5LN6we6G9Z+N4w76LEnoT2GOZz+czDBPrWnxI7F+9hBCapsVicbuWFwqFCZ052BOre6vP\nnj3rnpVYh0piVeuTn9MTr75esXmz8quvxD/8wJ3rUKvriorqioutffoQQnhRjxosd2yKxZMT\nQsiAAQM6uAb2DCsSieLzDBskiqLadR6LT+09G8cbmqYTfRPYw0EgEMTqrwj/h2EC/95lOZ1O\ns9kc/PJyuby1tdVut0eupEhTKBRVVVXNzc2xLiR0FEVJJJJWTrNkAmEvlTmdTqvV+pMZLlfa\n4cNqvT59717K59igEycadbqGiRMZ9owQ0xeBTUsxORzYWydNTU0dXI9cLufxeC0tLQk98JdS\nqez4SxFDFEWJRCKn05nQWyEUCoVCYUKfWiUSCZ/Pt1gsNs7JJ2r8JLaEDxydh7snQyqVJvrV\n46QkunZNbTCoS0qEN29y57b27m3UamsKC+0qVfRrix9o0QDotBA44he6PhNCgLFBRaL6SZMw\nNihB1ADo9BA44gtCRgIRnzrV5fPPFWVlPO5lZIpqzskx6nS1M2e6JJJYVBcvkDMAgIXAEXsI\nGYmF19Sk3LGjy8aNUl9jg9pVqtr8fOP8+RaMDYqoAQAeEDhiAyEj8bhcad98o9br08vLfXSD\n8vn1EyeadLqGCROYOPiUaQwhZwCATwgc0YOQkaCEt26ptmzRfPml6No17tzb3xRfVGRXKqNf\nW/xAzgAA/xA4IgshI3HRVmv6rl1qvT712DHC+XC5UyptKiw06XR12dkxKS9+IGoAQDAQOMIM\nCSMJyL7/Xq3Xq7Zt43E/kU9RTTk5Jp2uftYssUplt9uJ1zgcnQZyBgC0CwJHGCBkJIfb3aBf\nfin1NTaoXa2unTnT3Q3amYdCQdQAgBAgcIQozkOGxWK5fPmy1Wrt0aOHsnP3FgREuVyphw5p\nDAbF3r0UZ8xNhs+vnzTpdjdoJw4ZLEQNAAgZAkc7xHnIcKuoqPj888/dI75PmjRpwYIFMfy+\njLglunpVbTCoN28W3rrFnWu54w6TTldTUGBPT49+bXEFOQMAOg6BI4BECRlu169f/9e//uX5\n7Rj79u1TKpVTp06NYVVxhbbZFOXlmo0bU48c8dENKpPVT51qKizE2KAEUQMAwgeBo00JFzVY\n33zzDfe7uPbt24fAQQiRnTmj2rxZtWULv6GBO7clO9tYXFwzZw77TfGdGXIGAIQdAkeyaWxs\nDHJi58Gvq1OVlWkMBsn589y5No2mpqjIWFRkzcqKfm3xBlEDACIEgSPZpPtqOPA5MelRLlfa\nwYNqg0FRXu6jG1QguN0NOn48ukGRMwAg0hA4ks2ECRMOHjxo/engENOnT49VPTEhvHlTtXVr\nly++EF6/zp3b2ru3qajIpNWiG5QQ0q9fv9bW1lhXAQDJD4Ej2ahUqmXLln322Wd1dXWEEIFA\nMHPmzLFjx8a6rmigW1uVO3eq9Xr58eM+ukFTUmpnzzYWFbUMHRqT8uJNnz59JBIJw3mhAAAi\nAYEjCQ0cOPCpp566ceOGzWbLzMyUdIKvR085dUqt1yu3b+e1tHjPo6imvDyjVls3Y4ZLLI5F\ndfEFd08AICYQOJITn8/v0aNHrKuIOH5TU/qOHV0+/1xaVcWda9doTAUFxvnz0Q3KQtQAgBhC\n4IDEQ7lcaQcOqPV6xb59lMPhNZcRCOqnTDFqtY3jxqEblIWoAQAxh8ABiUR85YpqyxZ1SYnP\nblBL79416Ab1gJwBAPEDgQMSAG2xKHftUm/aJK+o8NkNWjN7tkmnaxk8OCblxSFEDQCINwgc\nENdujw1aVsb3NXbZ7bFB5851dYLG2CAhagBAfELggHgkqK1VlZaqDQaJrwHmbV26sANpWLt3\nj35t8Qk5AwDiHAIHxBHK6bzdDbp/v49uUKGwbvJkk07XOHYsukHdEDUAICEgcEBcEF+6pDYY\n1KWlApOJO9fcr59Jp6uZO9ehUES/triFqAEACQSBA2KJNpuVO3dqDIaU48e5c51y+e1u0EGD\nol9bPEPUAICEg8ABsSE9frzLp58qd+zgmc3e82i6MS/PpNPVTZ/uEoliUV2cQs4AgMSFwAFR\nxW9sTN+5s+vnn0t8jQ1q02hqCgqMCxZYO8Ewqe2CqAEAiQ6BA6KBcjrT9u/XGAxpbXWDTpli\n0ukaxowh6Ab9KUQNAEgOCBwQWeJLl9R6vbq0VFBTw51r7t/fpNPVFBQ4UlOjX1ucQ9QAgGSC\nwAERQVutin37NBs3ph454nNs0MaCghuzZjXn5sakvHiGnAEASQmBA8JMduaMZuNG5datPrtB\nm4cNMxUW1hYUiJRKM3eBzg1RAwCSGAIHhIfAZFKXlqoNBvGlS9y5towMk1ZrKiqyZmYSQiiK\ninqBYWa3269evSqVSoVCYcfXhqgBAEkPgQM6hHI40vbv1+j1aQcOUE6n11yXUFg/bZpJq20Y\nPTppukFdLldZWdnevXsdDgchpH///nfeeadKpQptbYgaANBJIHBAiG6PDVpSIqit5c619OlT\nM2+eUadLvrFBt23btmvXLvePVVVV77333q9//WuBQNCu9SBqAECngsAB7cMzm5U7dqj1+pQT\nJ7hzHXJ5bUGBUas1DxwY/dqiwG6379mzx2vi9evXT548mZeXF8wakDMAoHNC4IBgsd2gqq1b\n6ba7QWsKClxicSyqi5KGhga73c6dbjQaAz4WUQMAOjMEDgjgdjeoXi++fJk715qZaSoqMhUV\n2TIzo19b9EmlUoqiGM4HfeVyuZ9HIWoAACBwgG+UyyU/elSzcWP611+39U3xNYWFDRMndqpv\nipdKpcOHD6+oqPCcKJPJhg0b5nN5RA0AABYCB3iTVFer9XpVWZnPblBzdrZRq62dO9fh92/6\nJLZ48eKGhoaLFy+yP8pksp///OfcKxyIGgAAnhA44DZeS4ty+3a1wZBy8iR3riM1tWbuXJNO\nZx4wIPq1xRWpVPqrX/2qurq6pqZGJpP16dNHIpF4LoCoAQDAhcDR6TGM/PhxtV6v3LWLtli8\n59J0w+jRJp2ubupUJhwjXCUHiqL69es3fPhwu91utVrd0xE1AADagsDReQmMRvXmzWqDQXzl\nCneutVu3292gGRnRry2xIGcAAASEwNHpUHa7Yt8+tV6fdvAg5XJ5zXUJhXXTp5t0usaRI5Nm\nbNDI6d+/f0tLS6yrAABIAAgcnYjkwoXb3aB1ddy5LdnZJp2uZs4cZ2ftBm2Xvn37KhQKC/cm\nFAAA+ILAkfx4LS3Kbds0BoPs1CnuXEdaWs3cuab58839+kW/tkSEGygAACFA4EhebDfopk3K\nXbvo1lbvuTTdMHasSautmzIF3aBBQtQAAAgZAkcSuj026KZNPrtBbV261Myda1y40NqtW/Rr\nS1CIGgAAHYTAkTwou11RXq4xGFJ9doOKRHUzZpi02saRI8n/b+/+g6Oo7z+O795t7pK7XH5c\nfljlZwig/KiAlQhYhCEokpJgoMwwdVoIIhBoRRywrdARpczgYFUqVX5JKtWOvwqSBEihIqUQ\ni/yIlAEDUihTQgwJ+XW53OXu9vb7x9l8I/lhftze3l2ej7/Yzy577+Vzy71u93OfFUVNKgxF\nRA0A8AsCRziI+ve/k/LzE4qKpDZHgw4bVpWVdeuRRxgN2iVEDQDwIwJHCNPb7fF//3vC/v0x\nn3/eeq1ssVRPnXpz1qxwfVK8eogaAOB3BI6QFHn+fOKf/5xQVNTm3KD1999/KyOjOj3dazRq\nUV2oImcAgHoIHKHEcPNm4r59SYWFhjbnBu3btyozs+pHP3IlJwe+tpBG1AAAtRE4QoDodsf+\n858J+/fHHzkiyvJta70GQ+3EiZXZ2fVjxzIatKuIGgAQGASOoBb1n/8kFBYmFhS0NzforYyM\nW9One2JjA19bqCNqAEAgETiCkb6hIeHgwcT8fPOFC63XeuLj6zMzb0yf7khNDXxtYYCoAQCB\np2XgqK2tzcvLKykpkWV51KhRCxYsSExMFARBluW33367uLjY4/GkpaU9+eSTERERGtYZOIoS\nc+ZMYn5+/OHDuhYPPf9mpU5XP358ZWama9o00Wh0NDRoUmNII2oAgFa0DBwvvfSSLMtLly7V\n6/Uff/zxunXrNm3aJAjCzp07i4uLc3NzJUl68803N2/evGLFCg3rDABDRUViYWFiYaGxrKz1\n2qZ+/b55UnxSkiAIpogIRmp0FVEDALSlWeBwuVwXLlx44YUXRo8eLQiCxWJ59tlna2trjUbj\noUOHli9fnpaWJgjCkiVL1q9fv2DBgthwHKYgulzxR48m5ufHfv650Hpu0MjImilTKrOybGPG\nMBq024gaABAMNAscBoNh+PDhBw8eTEpK0uv1Bw4cGDhwYFxcXGlpqdPp9KUQQRBGjRoly/KV\nK1fGjBnja/F6veXl5S33I0ldOApRFHU6nV6v/84tdTpdVw6oa6IuXUrMz7ceOCDV1bVeax85\nsiorq2baNNlsFgShzTpULS8w1D6EQYMGqbdz31uok++loCWKoiiKoX4Iwv+6I6SF9CH4eiHU\n30s6nS4MDkHQ9P8lRVE6WKvlLZVf/epXS5cuPXbsmCAIJpNp8+bNgiDU1NRIkmQ2m7+pT5Ki\no6Orq6ub/1ZdXd3MmTObFxctWrRo0aIuva6hcw9HNZlMXdptZ+hstpgDB+Ly86POnGm9Vo6J\nsT36aM3cuc577hEEoeNJu9QoL8DUO4Rhw4aptOfbGI1GY+jPrhYG76WYmBitS+ip+Ph4rUvo\nKUmSwuAowuCMjo6O1uql5VYTN7SkWeBwOp1r1qz5wQ9+MHv2bJ1Ol5+f/5vf/Gbjxo2Kooit\nbh+0PAaDwTB16tTmxQEDBjS1Gl/ZgYiICFmWva3uX7Tm8Xg6v9vv4PVGnzwZ//HHsX/7m9jW\naNCGiROrH3vMNmmS4rta0+FL6/V6URT9WZ4W9Hp9x2/N7hk6dKggCF16S3SPKIoGg0GW5ZDu\nCN/XIDU6ImAkSdLr9S6Xq+OvVkHOYDC4XC6tq+gRo9Ho9XrdbrfWhXSfTqfT6XShfkZLkuR2\nuzvzGacGRVE6uLiiWeA4ffr0zZs3X3vtNV9xS5cuzcnJ+fzzz++66y632+1wOKKiogRBkGW5\noaHB9+sVH7PZvGHDhubFxsZGm83W+de1WCxOp7MzZ4XT6ezC8bTDUFmZcOBA0scfG69fb+Ml\n+vWrfvTRyhkzXHfeKQiC4PF0HDV8TCaTKIp+KU8roihGRUX59xB8YzW69GboCUmSfB8Sdrs9\nMK+ohqioKEVRQvq9ZLFY9Hq93W4P6dhktVoD9tZVgyiKRqNRluWQPgqDwWAwGBpC+QeAUVFR\nkiQ5HA4N82tkZGR7qzQLHB6PR1GU5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+ "text/plain": [ + "plot without title" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "ggplotRegression(fit)" + ] + }, + { + "cell_type": "code", + "execution_count": 13, "metadata": {}, "outputs": [ { @@ -442,7 +519,7 @@ }, { "cell_type": "code", - "execution_count": 21, + "execution_count": 14, "metadata": {}, "outputs": [ { @@ -478,7 +555,7 @@ }, { "cell_type": "code", - "execution_count": 22, + "execution_count": 15, "metadata": {}, "outputs": [ { @@ -510,7 +587,7 @@ }, { "cell_type": "code", - "execution_count": 23, + "execution_count": 16, "metadata": {}, "outputs": [ { @@ -543,7 +620,7 @@ }, { "cell_type": "code", - "execution_count": 24, + "execution_count": 17, "metadata": {}, "outputs": [ { @@ -608,29 +685,42 @@ }, "metadata": {}, "output_type": "display_data" - }, - { - "name": "stdout", - "output_type": "stream", - "text": [ - " Df Sum Sq Mean Sq F value Pr(>F) PctExp\n", - "oxygen 1 75555.216 75555.2158 528.403 1.419964e-28 91.197836\n", - "Residuals 51 7292.381 142.9879 NA NA 8.802164\n" - ] } ], "source": [ "fit <- lm(ventil ~ oxygen, data = anaerobic)\n", "summary(fit)\n", - "anova(fit)\n", - "af <- anova(fit)\n", - "afss <- af$\"Sum Sq\"\n", - "print(cbind(af,PctExp=afss/sum(afss)*100))" + "anova(fit)" + ] + }, + { + "cell_type": "code", + "execution_count": 18, + "metadata": {}, + "outputs": [ + { + "data": {}, + "metadata": {}, + "output_type": "display_data" + }, + { + "data": { + "image/png": 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HhTb5C5yPLxxx+Txm4UeuKJJ+y/afTF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\nSujC+vp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+ "text/plain": [ + "plot without title" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "ggplotRegression(fit)" ] }, { "cell_type": "code", - "execution_count": 25, + "execution_count": 19, "metadata": {}, "outputs": [ { @@ -663,7 +753,7 @@ }, { "cell_type": "code", - "execution_count": 26, + "execution_count": 20, "metadata": {}, "outputs": [ { @@ -727,7 +817,7 @@ }, { "cell_type": "code", - "execution_count": 27, + "execution_count": 21, "metadata": {}, "outputs": [ { @@ -797,25 +887,12 @@ }, "metadata": {}, "output_type": "display_data" - }, - { - "name": "stdout", - "output_type": "stream", - "text": [ - " Df Sum Sq Mean Sq F value Pr(>F) PctExp\n", - "oxygen 1 75555.2158 75555.21580 7441.5695 4.587875e-56 91.1978362\n", - "oxy2 1 6784.7247 6784.72473 668.2398 1.357823e-30 8.1894044\n", - "Residuals 50 507.6565 10.15313 NA NA 0.6127594\n" - ] } ], "source": [ "fit <- lm(ventil ~ oxygen + oxy2, data = anaerobic)\n", "summary(fit)\n", - "anova(fit)\n", - "af <- anova(fit)\n", - "afss <- af$\"Sum Sq\"\n", - "print(cbind(af,PctExp=afss/sum(afss)*100))" + "anova(fit)" ] }, { @@ -827,7 +904,32 @@ }, { "cell_type": "code", - "execution_count": 28, + "execution_count": 22, + "metadata": {}, + "outputs": [ + { + "data": {}, + "metadata": {}, + "output_type": "display_data" + }, + { + "data": { + "image/png": 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JdUAAAAPMaWLVuMaYNx586dt99+203NaQCBAwAAwEOYpQ3GsWPHWrwhjUDgAAAA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\nKgCgtxk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+ "text/plain": [ + "plot without title" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "ggplotRegression(fit)" + ] + }, + { + "cell_type": "code", + "execution_count": 23, "metadata": {}, "outputs": [ { @@ -847,7 +949,6 @@ } ], "source": [ - "layout(matrix(1:4,2,2)) \n", "autoplot(fit)" ] }, -- 2.34.1