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.
|
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
|
33
|
23
|
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=β0+β1X1+β2X2+e.
1. What is the estimated value of the regression coefficient for variable Weight?
2. What is the estimated value of the intercept?
3. What is your computed value of SSE?
4. What is your computed value of MSE?
5. What is the standard error of the estimate of β1?