Use Minitab , R, or your preferred software for this question. An exercise physi
ID: 3311351 • 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 shown below
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)
gender <- c(rep("male",10),rep("female",9))
data.df <- data.frame(Weight,BodyFat,gender)
## fir the regression
fit <- lm(BodyFat~.,data=data.df)
summary(fit)
The results are
> summary(fit)
Call:
lm(formula = BodyFat ~ ., data = data.df)
Residuals:
Min 1Q Median 3Q Max
-6.8079 -0.7755 0.2275 1.1095 5.6523
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 18.76383 4.56183 4.113 0.000814 ***
Weight 0.15339 0.07049 2.176 0.044877 *
gendermale -4.64300 1.80445 -2.573 0.020427 *
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 3.03 on 16 degrees of freedom
Multiple R-squared: 0.3076, Adjusted R-squared: 0.2211
F-statistic: 3.554 on 2 and 16 DF, p-value: 0.05282
the intercept is 18.76
the standard error of beta 1 is
0.07049
Residual standard error: 3.03 on 16 degrees of freedom
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