AP Stats
Review: Linear Regression Models
S xx   x 
2
 x
Name________________________
2
se 
n
SSresid
n2
sb 
se
S xx
r2  1
SS resid
SS total
1. Do heavier people burn more energy? Metabolic rate, the rate at which the body consumes energy,
is important in studies of weight gain, dieting, and exercise. Lean body mass is an important
influence on metabolic rate. Below are the data on mass (in kg) and metabolic rate (in calories).
Mass (x)
Rate (y)
62
1792
62.9
1666
36.1
995
54.6
1425
48.5
1396
42
1418
47.4
1362
50.6
1502
43.1
1256
48.7
1614
a. Estimate the equation of the population regression line.
b. Determine the residual for a person whose body mass is 42.
c. Estimate the mean change in rate for a one unit increase in body mass.
d. What proportion of the observed variation in metabolic rate can be attributed to the simple
linear regression model?
e. Determine and interpret the point estimate of  .
f. What is the probability that a 42 kg person has a metabolic rate of at least 1500 calories?
f. Estimate  with a 99% confidence interval.
g. Does the data suggest that there is a positive linear relationship between lean body mass and
metabolic rate?
2. The mean length of a part for a dam is suppose to be 1.75 meters. We sampled 50. We know that
  0.3 and we are using a significance level of 0.05. Find the power of the test if the mean
 H o :   1.75
 H A :   1.75
length is really 1.6 meters. Use 
3. For each of the following, determine the residuals and plot the residual plot. Does the residual
plot suggest that the simple linear regression is appropriate?
a.
x
y
b.
10
8.04
x
y
10
9.14
8
6.95
8
8.14
13
7.58
13
8.74
9
8.81
11
8.33
9
8.77
14
9.96
11
9.26
14
8.1
6
7.24
4
4.26
12
10.84
7
4.82
5
5.68
4
3.1
12
9.13
7
7.26
5
4.74
6
6.13
4. Thirty students were measured to determine the relationship between their heights and weights.
Using the data shown below, find the coefficient of determination, the typical deviation from the
least squares line, and the standard error of the slope.
 x  1090
x
2
 y  y
 74,546
2
 12,989.75
  y  y   4,365.865
5. An Archaeopteryx is an extinct beast having feathers like a bird but teeth and a long bony tail like
a reptile. Here are the lengths in centimeters of the femur (a leg bone) and the humerus (bone in
upper arm) for the five fossil specimens that preserve both bone. The MINITAB print out is
shown below
Predictor
Constant
Femur
Coef
-3.660
1.19690
S = 1.98203
SE Coef
4.459
0.07509
R-Sq = 98.8%
T
-0.82
15.94
P
0.472
0.001
R-Sq(adj) = 98.4%
a. What is the equation of the least squares line?
b. What is an estimate of the standard error of the estimate ( se )?
c. What is an estimate of the standard error of the slope ( sb )?
d. Determine the estimate of the amount of change of the humerus for every additional cm increase in
the femur length using a 90% confidence interval.
e.
Is there a relationship between the length of the humerus and the length of the femur?