
Linear Regression Worksheet 1
Does a person's muscle mass decrease with age? To
explore this relationship in women, a nutritionist
randomly selected four women from each 10year age group,
beginning with age 40 and ending with age 79.
Obsn mus_mass age
1 82 71
2 91 64
3 100 43
4 68 67
5 87 56
6 73 73
7 78 68
8 80 56
9 65 76
10 84 65
11 116 45
12 76 58
13 97 45
14 100 53
15 105 49
16 77 78

The least squares regression line is:
Yhat = 148.0  1.023 x. (Yhat stands for a Y with a
caret (^) over it; the predicted value).
 The first observation has age = 71.0 and muscle
mass = 82. Identify this value on the plot.
 Carefully plot the line. Use x = 40 and x = 80 to
do so.
 From your plot alone, predict the muscle mass of
a 60 year old.
 Use the equation to check your answer to part 3.
 Complete the table below. For each observation
the table lists the age and muscle mass. You
should fill in the predicted value and residual.
(Some have been filled in for you.)
 Sum the residuals. What do you get?
 Sort the residuals.
 Report an 80% prediction interval for the muscle
mass of a 60 year old. Plot the interval.
 Report an 80% prediction interval for the muscle
mass of a 43 year old. Plot the interval.
 Complete your plot by drawing 80% prediction
bands.
 What %age of the data fall within these
prediction bands? (Count an observation falling
right on a band as being 1/2in and 1/2 out.)
Age 
Muscle Mass 
Predicted Y 
Residual 
71 
82 
75.4 
6.6 
64 
91 
82.5 
8.5 
43 
100 
104.0 
4.0 
67 
68 
79.5 
11.5 
56 
87 
90.7 
3.7 
73 
73 
73.3 
0.3 
68 
78 


56 
80 


76 
65 


65 
84 


45 
116 


58 
76 


45 
97 
102.0 
5.0 
53 
100 
93.8 
6.2 
49 
105 
97.9 
7.1 
78 
77 
68.2 
8.8 
ANSWERS
 1. 86.6
 6. Sum = 0.
(It works out to 0.1 due to accumulated rounding
errors in the residuals.)
 8. (75.1, 95.4).
(The "official method"covered in Math
258yields (75.0, 98.2).)
 9. (92.5, 112.8)

