AP Statistics Linear Regression
Name_____________________ Hr____
1. The golf scores of 11 members of a women's golf team in two rounds of tournament play are
listed in the table below.
Round 1
89
90
87
95
86
81
105
83
88
91
79
Round 2
94
85
89
89
81
76
89
87
91
88
80
a) Plot the data with Round 1 as your independent (explanatory) variable. Do you think there
might be an influential observation? If so, list the point.
b) Find the regression equation first with the observation included, then without it. Is the point
influential?
Regression equation with point included:
Regression equation with point removed:
c) Make a residual plot. Is the data linearly related? Explain.
2. A study of nutrition in developing countries collected data from the Egyptian village of
Nahra. Listed below are the mean weights of 170 infants in Nahya who were weighed each
month during their first year of life.
Age (months)
1
2
3
4
5
6
7
8
9
10
11
12
Mean wt. (kg)
4.3
5.1
5.7
6.3
6.8
7.1
7.2
7.2
7.2
7.2
7.5
7.8
a) Plot the data. Find the regression equation and correlation coefficient (r).
b) Graph a residual plot. What does this plot tell you about the data?
3. Is the magnitude of an earthquake related to the depth below the surface of at which the quake
occurs?
Magnitude
Depth (km)
2.9
5.0
4.2
10.0
3.3
11.2
4.5
10.0
1.6
7.9
3.2
3.9
3.4
5.5
3.9
8.1
a) Sketch a scatterplot of the data. Find the correlation and the LSRL.
b) Does the data appear to have an influential point? Justify your answer.
c) Is the magnitude of an earthquake linearly related to the depth below the surface at which the
quake occurs? EXPLAIN.
4. A study compared the body weight (kg) of a child to his/her metabolic rate. Descriptive
statistics gives us the following results.
s x  6.568
x  22.5
y  5.888
s y  2.987
r  .984
a) Find the equation of the regression line.
b) Predict the metabolic rate of a child who weighs 17.5 kg.
5. Use the following data set to answer the questions.
x1
y1
1
2
3
1
4
6
7
5
x2
y2
2
1
1
3
a) Find the correlation and LSRL for each data set. What do you notice?
b) Add 5 to each number in x1 . What does this do to the correlation of the data?
c) Multiply each number in x1 by 5. What happens to the correlation?
6
4
5
7
6. After teaching AP Statistics for several years, Mrs. Sapp has found that the correlation, 𝑟,
between the students’ total number of points before the final exam and the number of points
scored on their final exam is 0.8. The pre-final-exam point totals for all students in this year’s
course have mean 280 and standard deviation 30. The points on the final exam have mean 75
and standard deviation 8. Mrs. Sapp’s dog ate Julie’s final exam, but Mrs. Sapp knows that her
total number of points before the exam was 300. She decides to predict Julie’s final exam score
from her pre-final-exam total. What score is Julie predicted to have?
7. The following are data gathered by anthropologists digging in Mayan ruins. X represents the
depth of the soil in centimeters and Y is the percent of the mineral montmorillonite in the soil.
Depth
a)
Make a scatterplot on your calculator and determine the
association (pos or neg) and describe it in a sentence.
40
50
60
70
80
90
100
b)
Find the equation of the least squares linear regression line.
c)
Describe the meaning of the slope of the line in a sentence.
d)
Find the correlation coefficient. What does it tell you about the data?
e)
What is 𝑟 2 and what does it tell you about the data?
f)
Make a residual plot on your calculator and interpret the plot.
%
montmorillonite
58
34
32
30
28
27
22
g)
Are there any outliers/influential points? If so, remove them and recalculate the
regression equation. What effect was there on the correlation and regression equation?
8. The following are data on various fast food hamburgers for various states.
X represents the grams of fat in the burger and Y is the number of calories.
a) Make a scatterplot on your calculator and determine the association
(pos or neg) and describe it in a sentence.
b) Find the equation of the least squares linear regression line.
Fat
19
31
34
35
39
39
43
Calories
410
580
590
570
640
680
660
c) Describe the meaning of the slope of the line in a sentence.
d) Find the correlation coefficient. What does it tell you about the data?
e) What is 𝑟 2 and what does it tell you about the data?
f) Make a residual plot on your calculator and interpret the plot.
g) Are there any outliers/influential points? If so, remove them and recalculate the
regression equation. What effect was there on the correlation and regression equation?
9. Which of the following is true of the least-squares regression line?
A)
The slope is the change in the response variable that would be predicted by a unit
change in the explanatory variable.
B)
It always passes through the point ( x , y ), where x and y are the means of the
explanatory and response variables, respectively.
C)
It will only pass through all the data points if r = ± 1.
D)
All of the above.
10. The following is a scatter plot of the calories and sodium
content of several brands of meat hot dogs. The least-squares
regression line has been drawn in on the plot.
Estimate the value of the residual for the point labeled 𝑥.
Are there any influential points? If so, what makes it
influential?