AP Stats – Minitab
Name_________________________________
1. After analyzing the salaries and batting averages of many baseball players in both leagues, a sports commentator
concluded that higher-paid players will have higher batting averages. Let n = 10.
a. Determine the least-squares regression line.
b. What is the correlation coefficient?
c. What percent of the variation in batting average can be explained by the least squares line?
d. What is the estimated batting average for any player who is earning $875,000?
e. Determine an estimate of the slope using a 90% confidence level. Interpret it.
f. Use a 5% level of significance to test the sports commentator’s claim.
Predictor
Constant
Annual Salary (x)
S = 0.00845737
Coef
0.285630
0.00000004
R-Sq = 72.5%
SE Coef
0.004830
0.00000001
T
59.14
4.59
P
0.000
0.002
R-Sq(adj) = 69.1%
2. Galton believed that a very close relationship exists between the heights of fathers and the heights of their sons.
To test this claim, a scientist selected ten men at random and recorded their heights and the heights of their sons.
a. Determine the least-squares regression line.
b. What is the correlation coefficient?
c. What percent of the variation in son’s height can be explained by the father’s height?
d. What is the estimated height of a son whose father is 71 inches tall?
e. Determine an estimate of the slope using a 90% confidence level. Interpret it.
f. Use a 5% level of significance to test the sports commentator’s claim.
Predictor
Constant
Dad Ht (in inches)
S = 0.501934
Coef
12.023
0.84238
SE Coef
3.232
0.04658
R-Sq = 97.6%
T
3.72
18.08
P
0.006
0.000
R-Sq(adj) = 97.3%
3. City officials believe that the number of complaints to the city’s heat complaint control board (for lack of heat) is
negatively related to the outdoor temperature. Let n = 7.
a.
b.
c.
d.
e.
f.
Determine the least-squares regression line.
What is the correlation coefficient?
What is the coefficient of determination? Interpret it
What is the estimated number of complaints for 22˚F?
Determine an estimate of the slope using a 98% confidence level. Interpret it.
Use a 4% level of significance to test the sports commentator’s claim.
Predictor
Constant
Temp (in F)
S = 2.22807
Coef
125.536
-2.26429
SE Coef
1.518
0.08421
R-Sq = 99.3%
T
82.69
-26.89
P
0.000
0.000
R-Sq(adj) = 99.2%
4. Six students were asked to indicate how many hours they studied before taking their statistics examination. Their
responses were then matched with their grades on the exam which had a maximum score of 100.
 y  y
2
 y  y
 438.86
2
 45.11
a. What proportion of observed variation in scores can be attributed to the linear relationship between
number of study hours and test scores?
b. Calculate the typical deviation from the least squares line and the standard error of the slope.
5. There have been numerous studies on the effects of radiation. The following data on the
relationship between degree of exposure to alpha particles (x) and the percentage of
exposed cells without aberrations (y) appeared in a research journal as follows.
alpah part (x)
% cells w/out
aberrations (y)
0.106 0.193 0.511 0.527 1.08
98
95
87
85
75
1.62
1.73
2.36
2.72
3.12
3.88
4.18
72
64
55
44
41
37
40
a. What is the least squares line?
b. Construct a residual plot, and comment on any interesting features.
c. Look back at the scatter plot – does the correlation coefficient tell the whole
story?
d. What’s the typical deviation about the least squares line?
e. What percent of variation in percentage of cells without aberrations can be
explained by the least squares line?