CHAPTER 13 Simple Linear Regression

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522 CHAPTER THIRTEEN Simple Linear Regression PROBLEMS FOR SECTION 13.2 Learning the Basics PH Grade ASSIST 13.1 Fitting a straight line to a set of data yields the following prediction line: a. Interpret the meaning of the Y intercept, b 0 . b. Interpret the meaning of the slope, b 1 . c. Predict the mean value of Y for X = 3. 13.2 If the values of X in Problem 13.1 range from 2 to 25, should you use this model to predict the mean value of Y when X equals a. 3? b. −3? c. 0? d. 24? PH Grade ASSIST 13.3 Fitting a straight line to a set of data yields the following prediction line: Yˆ = 16 − 0. 5X a. Interpret the meaning of the Y intercept, b 0 . b. Interpret the meaning of the slope, b 1 . c. Predict the mean value of Y for X = 6. Applying the Concepts PH Grade ASSIST SELF Test Yˆ 13.4 The marketing manager of a large supermarket chain would like to use shelf space to predict the sales of pet food. A random sample of 12 equal-sized stores is selected, with the following results (stored in the file petfood.xls): i i = 2 + 5X Shelf Space (X ) Weekly Sales (Y ) Store (Feet) ($) 1 5 160 2 5 220 3 5 140 4 10 190 5 10 240 6 10 260 7 15 230 8 15 270 9 15 280 10 20 260 11 20 290 12 20 310 i i a. Construct a scatter plot. For these data, b 0 = 145 and b 1 = 7.4. b. Interpret the meaning of the slope, b 1 , in this problem. c. Predict the mean weekly sales (in hundreds of dollars) of pet food for stores with 8 feet of shelf space for pet food. 13.5 Circulation is the lifeblood of the publishing business. The larger the sales of a magazine, the more it can charge advertisers. Recently, a circulation gap has appeared between the publishers’ reports of magazines’ newsstand sales and subsequent audits by the Audit Bureau of Circulations. The data in the file circulation.xls represent the reported and audited newsstand sales (in thousands) in 2001 for the following 10 magazines: Magazine Reported (X ) Audited (Y ) YM 621.0 299.6 CosmoGirl 359.7 207.7 Rosie 530.0 325.0 Playboy 492.1 336.3 Esquire 70.5 48.6 TeenPeople 567.0 400.3 More 125.5 91.2 Spin 50.6 39.1 Vogue 353.3 268.6 Elle 263.6 214.3 Source: Extracted from M. Rose, “In Fight for Ads, Publishers Often Overstate Their Sales,” The Wall Street Journal, August 6, 2003, pp. A1, A10. a. Construct a scatter plot. For these data b 0 = 26.724 and b 1 = 0.5719. b. Interpret the meaning of the slope, b 1 , in this problem. c. Predict the mean audited newsstand sales for a magazine that reports newsstand sales of 400,000. 13.6 The owner of a moving company typically has his most experienced manager predict the total number of labor hours that will be required to complete an upcoming move. This approach has proved useful in the past, but he would like to be able to develop a more accurate method of predicting labor hours by using the number of cubic feet moved. In a preliminary effort to provide a more accurate method, he has collected data for 36 moves in which the origin and destination were within the borough of Manhattan in New York City and in which the travel time was an insignificant portion of the hours worked. The data are stored in the file moving.xls.
13.2: Determining the Simple Linear Regression Equation 523 a. Construct a scatter plot. b. Assuming a linear relationship, use the least-squares method to find the regression coefficients b 0 and b 1 . c. Interpret the meaning of the slope, b 1 , in this problem. d. Predict the mean labor hours for moving 500 cubic feet. PH Grade ASSIST 13.7 A large mail-order house believes that there is a linear relationship between the weight of the mail it receives and the number of orders to be filled. It would like to investigate the relationship in order to predict the number of orders, based on the weight of the mail. From an operational perspective, knowledge of the number of orders will help in the planning of the orderfulfillment process. A sample of 25 mail shipments is selected that range from 200 to 700 pounds. The results (stored in the file mail.xls) are as follows: Weight Weight of Mail Orders of Mail Orders (Pounds) (Thousands) (Pounds) (Thousands) 216 6.1 432 13.6 283 9.1 409 12.8 237 7.2 553 16.5 203 7.5 572 17.1 259 6.9 506 15.0 374 11.5 528 16.2 342 10.3 501 15.8 301 9.5 628 19.0 365 9.2 677 19.4 384 10.6 602 19.1 404 12.5 630 18.0 426 12.9 652 20.2 482 14.5 a. Construct a scatter plot. b. Assuming a linear relationship, use the least-squares method to find the regression coefficients b 0 and b 1 . c. Interpret the meaning of the slope, b 1 , in this problem. d. Predict the mean number of orders when the weight of the mail is 500 pounds. 13.8 The value of a sports franchise is directly related to the amount of revenue that a franchise can generate. The data in the file bbrevenue.xls represent the value in 2005 (in millions of dollars) and the annual revenue (in millions of dollars) for 30 baseball franchises. Suppose you want to develop a simple linear regression model to predict franchise value based on annual revenue generated. a. Construct a scatter plot. b. Use the least-squares method to find the regression coefficients b 0 and b 1 . c. Interpret the meaning of b 0 and b 1 in this problem. d. Predict the mean value of a baseball franchise that generates $150 million of annual revenue. 13.9 An agent for a residential real estate company in a large city would like to be able to predict the monthly rental cost for apartments, based on the size of the apartment, as defined by square footage. A sample of 25 apartments (stored in the file rent.xls) in a particular residential neighborhood was selected, and the information gathered revealed the following: Monthly Size Monthly Size Rent (Square Rent (Square Apartment ($) Feet) Apartment ($) Feet) 1 950 850 14 1,800 1,369 2 1,600 1,450 15 1,400 1,175 3 1,200 1,085 16 1,450 1,225 4 1,500 1,232 17 1,100 1,245 5 950 718 18 1,700 1,259 6 1,700 1,485 19 1,200 1,150 7 1,650 1,136 20 1,150 896 8 935 726 21 1,600 1,361 9 875 700 22 1,650 1,040 10 1,150 956 23 1,200 755 11 1,400 1,100 24 800 1,000 12 1,650 1,285 25 1,750 1,200 13 2,300 1,985 a. Construct a scatter plot. b. Use the least-squares method to find the regression coefficients b 0 and b 1 . c. Interpret the meaning of b 0 and b 1 in this problem. d. Predict the mean monthly rent for an apartment that has 1,000 square feet. e. Why would it not be appropriate to use the model to predict the monthly rent for apartments that have 500 square feet? f. Your friends Jim and Jennifer are considering signing a lease for an apartment in this residential neighborhood. They are trying to decide between two apartments, one with 1,000 square feet for a monthly rent of $1,275 and the other with 1,200 square feet for a monthly rent of $1,425. What would you recommend to them based on (a) through (d)? 13.10 The data in the file hardness.xls provide measurements on the hardness and tensile strength for 35 specimens of die-cast aluminum. It is believed that hardness (measured in Rockwell E units) can be used to predict tensile strength (measured in thousands of pounds per square inch). a. Construct a scatter plot. b. Assuming a linear relationship, use the least-squares method to find the regression coefficients b 0 and b 1 . c. Interpret the meaning of the slope, b 1 , in this problem. d. Predict the mean tensile strength for die-cast aluminum that has a hardness of 30 Rockwell E units.
Page 1 and 2: CHAPTER 13 Simple Linear Regression
Page 3 and 4: 13.1: Types of Regression Models 51
Page 5 and 6: 13.2: Determining the Simple Linear
Page 11: 13.2: Determining the Simple Linear
Page 15 and 16: 13.3: Measures of Variation 525 REG
Page 17 and 18: 13.3: Measures of Variation 527 COM
Page 19 and 20: 13.4: Assumptions 529 13.15 If SSR
Page 21 and 22: 13.5: Residual Analysis 531 FIGURE
Page 23 and 24: 13.5: Residual Analysis 533 Equal V
Page 25 and 26: 13.6: Measuring Autocorrelation: Th
Page 27 and 28: 13.6: Measuring Autocorrelation: Th
Page 29 and 30: 13.7: Inferences About the Slope an
Page 37 and 38: 13.8: Estimation of Mean Values and
Page 39 and 40: 13.8: Estimation of Mean Values and
Page 41 and 42: 13.9: Pitfalls in Regression and Et
Page 43 and 44: 13.9: Pitfalls in Regression and Et
Page 45 and 46: Key Equations 555 You have learned
Page 47 and 48: Chapter Review Problems 557 (GPA),
Page 49 and 50: Chapter Review Problems 559 f. At t
Page 51 and 52: Chapter Review Problems 561 sured f
Page 53 and 54: References 563 in other months. In
Page 55 and 56: E13.2: Creating Scatter Plots and A
Page 57 and 58: E13.6: Example: Sunflowers Apparel
Page 59: E13.6: Example: Sunflowers Apparel

CHAPTER 13 Simple Linear Regression

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