Use Minitab , R, or your preferred software for this question. An exercise physi
ID: 3310393 • Letter: U
Question
Use Minitab, R, or your preferred software for this question.
An exercise physiologist used skinfold measurements to estimate the total body fat, Y, expressed as a percentage of body weight, X1, for 19 participants in a physical fitness program. Body fat percentage and body weight are shown in the table below.
Note that participants 1-10 are male and 11-19 are female. Define a variable X2 which is 1 for males and 0 for females, and fit the model Y=0+1X1+2X2+e.
What is the estimated value of the regression coefficient for variable Weight? [2 pt(s)]
What is the estimated value of the intercept? [2 pt(s)]
What is your computed value of SSE? [2 pt(s)]
What is your computed value of MSE? [1 pt(s)]
What is the standard error of the estimate of 1? [2 pt(s)]
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 Weight (kg) 89 88 66 59 93 73 82 77 100 67 57 68 69 59 62 59 56 66 72 Body Fat (%) 28 27 24 23 29 25 29 25 30 23 29 32 35 31 29 26 28 23 23Explanation / Answer
The complete R snippet is as follows
Weight <- c(89, 88 ,66, 59, 93 ,73, 82, 77, 100, 67, 57, 68, 69, 59, 62, 59, 56, 66, 72)
BodyFat <- c( 28, 27, 24, 23 ,29, 25, 29, 25, 30 ,23 ,29, 32, 35, 31, 29, 26, 28 ,23, 23)
WeightSquare <- Weight^2
## fit the regression
fit <- lm (BodyFat ~ Weight +WeightSquare)
summary(fit)
summary(fit)
Call:
lm(formula = BodyFat ~ Weight + WeightSquare)
Residuals:
Min 1Q Median 3Q Max
-4.3992 -2.1591 -0.2588 1.6352 8.4361
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 52.457055 29.864627 1.756 0.0981 .
Weight -0.716439 0.801491 -0.894 0.3846
WeightSquare 0.004945 0.005237 0.944 0.3591
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 3.506 on 16 degrees of freedom
Multiple R-squared: 0.07277, Adjusted R-squared: -0.04313
F-statistic: 0.6279 on 2 and 16 DF, p-value: 0.5464
Regression coefficient of weight is -0.716
(Intercept) 52.457055
standard error is 0.801491
Residual standard error: 3.506
> fit <- aov(lm (BodyFat ~ Weight +WeightSquare))
> summary(fit)
Df Sum Sq Mean Sq F value Pr(>F)
Weight 1 4.48 4.478 0.364 0.555
WeightSquare 1 10.96 10.958 0.891 0.359
Residuals 16 196.67 12.292
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