A.P. Stats
Linear Regression
Name______________________________________
Find each of the following for problems 1 – 4.
A. Describe the scatter plot.
B. Compute Person's sample correlation coefficient.
C. Find and interpret the slope
D. Find and interpret the y-intercept
E. Compute the least squares regression line
F. Make the given prediction
1.
The following data for road resurfacing projects in the past year are shown in the table below. Find the
approximate cost to resurface a 6 mile stretch of road. Find the residual for a mileage of 4.
Mileage (x)
1
3
4
5
7
Cost (y) in thousands of
dollars
6
14
10
14
26
2. In a study conducted to examine the quality of fish after 7 days in ice storage, ten raw fish of the same
kind and approximately the same size were caught and prepared for ice storage. Let y denote a
measurement of fish quality (on a 10-pt scale) after 7 days of storage, and let x denote the time after
being caught that the fish were place in ice packing. Predict the quality of a fish that is packed in ice 5
days after being caught. Find the residual for x = 7.
x
0
0
3
4
6
7
9
9
12
12
y
8.5
8.4
7.9
8.1
7.8
7.4
7.3
7
6.8
6.7
3. A store manager wishes to find out whether there is a relationship between the age of his employees and
the number of sick days they take each year. How many sick days will an employee who is 50 years old have
taken.
Age
Days
18
16
26
12
39
9
48
5
53
6
58
2
4. The Indianapolis 500 auto race is held each year on Memorial Day. The table below gives the average
speed, in miles per hour, of the winner for selected years from 1911 to 1996. Let x be the number of years
since 1900.
5.
Year
Average
Speed
1911
74.602
1915
89.01
1925
101.127
1940
114.277
1955
128.209
1960
138.767
1970
155.749
1990
185.984
1996
147.956
An educator wants to see how strong the relationship is between a student’s IG and his or her grade
point average. What is the grade point average for a student with an IQ score of 105? Find the
residual for an IQ score of 105.
IQ, x
GPA, y
105
2.4
100
3.2
100
2.7
106
2.2
95
2.3
116
3.8
112
3.4