120 110 100 90 80 70 0.0 0.5 1.0 Sample -1.0 -2.0 O O 60 -1.5 O O Scatterplot for average O 80 -1.0 O 100 -0.5 Body Weight (kg) O Q-Q Plot O 120 0.0 0.5 Theoretical Quantiles O 1.0 T 140 1.5 O stdres 0.0 0.5 1.0 -1.0 -2.0 stdres 1.0 0.5 -0.5 0.0 -1.0 -2.0 -1.5 Std residuals versus explanatory variable O 60 O 80 O 80 O O 90 Body Weight (kg) Std residuals versus fits O 100 O T 100 fits O 120 110 120 140 O T 130

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter5: Inverse, Exponential, And Logarithmic Functions
Section5.6: Exponential And Logarithmic Equations
Problem 6E
Question
Could you please explain what the standard residuals in the given data imply, in context to the topic (strengths dependency on body weight). Also what the Shapiro test implies in context.
100 110 120
Bench press standards per class of body weight (kg) - Average
Sample Quantiles
06
80
70
0.0 0.5 1.0
-1.0
-2.0
O
O
60
Scatterplot for average
O
80
-1.5 -1.0
0
100
-0.5
Body Weight (kg)
O
Q-Q Plot
O
120
0.0 0.5
Theoretical Quantiles
O
O
1.0
140
O
1.5
O
stdres
0.0 0.5 1.0
stdres
-1.0
-2.0
1.0
0.5
0.0
-0.5
-1.5 -1.0
-2.0
Std residuals versus explanatory variable
O
T
09
o
80
O
O
80
90
O
O
Body Weight (kg)
O
Std residuals versus fits
O
100
100
O
fits
O
120
110
O
120
140
130
O
Transcribed Image Text:100 110 120 Bench press standards per class of body weight (kg) - Average Sample Quantiles 06 80 70 0.0 0.5 1.0 -1.0 -2.0 O O 60 Scatterplot for average O 80 -1.5 -1.0 0 100 -0.5 Body Weight (kg) O Q-Q Plot O 120 0.0 0.5 Theoretical Quantiles O O 1.0 140 O 1.5 O stdres 0.0 0.5 1.0 stdres -1.0 -2.0 1.0 0.5 0.0 -0.5 -1.5 -1.0 -2.0 Std residuals versus explanatory variable O T 09 o 80 O O 80 90 O O Body Weight (kg) O Std residuals versus fits O 100 100 O fits O 120 110 O 120 140 130 O
Residuals:
Min
-10.531 -4.989
Coefficients:
10 Median
3Q
1.869 5.267
(Intercept)
`Body Weight (kg) `
Signif. codes: 0 *** 0.001
`Body Weight (kg) `
Residuals
Estimate Std. Error t value Pr (>|t|)
42.62755
6.209 0.000157
0.62692
8.402 1.49e-05 ***
7
Residual standard error: 7.077 on 9 degrees of freedom
Multiple R-squared: 0.8869, Adjusted R-squared:
F-statistic: 70.6 on 1 and 9 DF, p-value: 1.492e-05
8
> abline (Regression.model, col=4, lwd=3)
> anova (Regression.model)
Analysis of Variance Table
6.86517
0.07461
1**/
Response: Bench press standards per class of body weight (kg) - Average
Sum Sq Mean Sq F value
Pr (>F)
2
Max
7.950
Signif. codes:
1**/
0 *** 0.001
> stdres<- rstandard (Regression.model)
> print (stdres)
1
9
Df
1 3536.0 3536.0 70.601 1.492e-05 ***
9 450.8
50.1
0.01 * 0.05 ¹.0.1 1
3
data: stdres
W = 0.91857, p-value = 0.3069
10
Shapiro-Wilk normality test
-1.4864868 -1.0645996 -0.5043759 0.2843252 0.6513863 1.1083291
1.1786018
0.8744
0.01 1*1 0.05. 0.1 1
4
0.9248828 0.5985440 -0.3245869 -2.0230776
11
5
> plot (Body Weight (kg)`, stdres, main="Std residuals versus
explanatory variable")
> fits<- fitted (Regression.model)
> plot (fits, stdres, main="Std residuals versus fits")
> qqnorm (stdres, main="Q-Q Plot")
>qqline (stdres)
> shapiro.test (stdres)
6
Transcribed Image Text:Residuals: Min -10.531 -4.989 Coefficients: 10 Median 3Q 1.869 5.267 (Intercept) `Body Weight (kg) ` Signif. codes: 0 *** 0.001 `Body Weight (kg) ` Residuals Estimate Std. Error t value Pr (>|t|) 42.62755 6.209 0.000157 0.62692 8.402 1.49e-05 *** 7 Residual standard error: 7.077 on 9 degrees of freedom Multiple R-squared: 0.8869, Adjusted R-squared: F-statistic: 70.6 on 1 and 9 DF, p-value: 1.492e-05 8 > abline (Regression.model, col=4, lwd=3) > anova (Regression.model) Analysis of Variance Table 6.86517 0.07461 1**/ Response: Bench press standards per class of body weight (kg) - Average Sum Sq Mean Sq F value Pr (>F) 2 Max 7.950 Signif. codes: 1**/ 0 *** 0.001 > stdres<- rstandard (Regression.model) > print (stdres) 1 9 Df 1 3536.0 3536.0 70.601 1.492e-05 *** 9 450.8 50.1 0.01 * 0.05 ¹.0.1 1 3 data: stdres W = 0.91857, p-value = 0.3069 10 Shapiro-Wilk normality test -1.4864868 -1.0645996 -0.5043759 0.2843252 0.6513863 1.1083291 1.1786018 0.8744 0.01 1*1 0.05. 0.1 1 4 0.9248828 0.5985440 -0.3245869 -2.0230776 11 5 > plot (Body Weight (kg)`, stdres, main="Std residuals versus explanatory variable") > fits<- fitted (Regression.model) > plot (fits, stdres, main="Std residuals versus fits") > qqnorm (stdres, main="Q-Q Plot") >qqline (stdres) > shapiro.test (stdres) 6
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