Name: ______Period: ______

CH. 8 & 9 Regression WorksheetAP Statistics

1. The Career Planning Office wants to use the least-squares technique to find the equation that related the number of math courses taken and starting salary. They use this data:

#of math courses / 1 / 1 / 2 / 3 / 4 / 6
Starting salary / $26,284 / $25,470 / $26,777 / $27,269 / $28,553 / $30,054

A. Find the least-squares regression line for the data. Show all work and use the formulas.

B. Explain what the LSRL tells the Career Planning Office about math courses and starting salary.

C. Is the LSRL a good predictor of starting salary? Explain.

2. The weights of autos (in thousands of pounds) and their miles per gallon (mpg) ratings are determined for a wide variety of cars and truck in Europe. The data are as follows:

Predictor Coef SE Coef T P

Constant 49.442 2.343 21.10 0.000

Weight -3.5645 0.4199 -8.49 0.000

S = 2.582 R-Sq = 90.0% R-Sq(adj) = 88.8%

A. Find the LSRL for the data. Interpret the slope and coefficient of determination.

B. Predict the mpg of a car that weighs (show work):

1. 5000 pounds

2. 7500 pounds

3. 8200 pounds

3. In an emergency, the typical driver requires about 0.75 seconds to get his or her foot onto the brake. The distance that the car travels during the reaction time is called the reaction distance. The table shows reaction distances for cars traveling at various speeds.

Speed(mph) / 20 / 30 / 40 / 50 / 60 / 70
Reaction Distance(ft) / 22 / 33 / 44 / 55 / 66 / 77
Predicted

A. Plot reaction distance versus speed. Describe form, direction, and strength.

B. What should the y-intercept be?

C. Find the slope of the LSRL (show work). What does the slope represent in this situation?

D. Find the equation of the line that fits these data (use calculator).

E. Find the predicted reaction distance for each speed. Enter the information in the table above.

F. Comment on the validity of the LSRL.

4. In looking at the effects of shopping center expansion, the Commerce Department decided to examine the relationship between the number of shopping centers and the retail sales for different states in the same region. The department collected these data for the North Central sales:

State / Number of Shopping Centers / Retail Sales(billions) / Residuals
Illinois / 2096 / $41.8
Indiana / 905 / 21.4
Iowa / 308 / 7.5
Kansas / 481 / 11.6
Michigan / 1018 / 25.3
Minnesota / 471 / 13.9
Missouri / 887 / 22.7
Nebraska / 264 / 5.7
North Dakota / 87 / 2.1
Ohio / 1704 / 41.6
South Dakota / 58 / 1.3
Wisconsin / 625 / 14.6

A. Find each of the following:

= ______=______

=______=______

r =______LSRL______-

B. Fill in the table above by finding the residuals.

C. Find the coefficient of determination (show work).

D. Graph the residual plot on your calculator. Draw the graph below (number of shopping centers is on the horizontal axis and the residuals are on the vertical axis). Is the LSRL a good predictor of retail sales?