Unit 6: Multiple Regression Introduction The Staffing Problem (II) Introducing Multiple Regression Summary Adapting Basic Concepts Interpreting the Multiple Regression Equation Summary Performing in Excel Residual Analysis Summary Quantifying the Predictive Power of Multiple Regression Summary Solving the Staffing Problem (II) Exercise 1: Empire Learning Exercise 2: The Empire Strikes Back Challenge: Children of the Empire New Concepts in Multiple Regression The Staffing Problem (III) Multicollinearity Diagnosing and Treating Multicollinearity Summary Lagged Variables Summary Dummy Variables Summary Solving the Staffing Problem (III) Exercise 1: The Kiwana Quandary Exercise 2: The Return of the Empire At left you will see an outline of the topics covered in Unit 6: Multiple Regression. There are two homework problems associated with this unit. There is one tab for each problem in this workbook. Once you have completed the unit online, you should attempt these problems and submit them to your coach for assessment and feedback. 1 MPG 43.1 19.9 19.2 17.7 18.1 20.3 21.5 16.9 15.5 18.5 27.2 41.5 46.6 23.7 27.2 39.1 28.0 24.0 20.2 20.5 28.0 34.7 36.1 35.7 20.2 23.9 29.9 30.4 36.0 22.6 36.4 27.5 33.7 44.6 32.9 38.0 24.2 38.1 39.4 25.4 31.3 34.1 34.0 31.0 27.4 22.3 28.0 17.6 34.4 20.6 Horsepower Weight 48 1985 110 3365 105 3535 165 3445 139 3205 103 2830 115 3245 155 4360 142 4054 150 3940 71 3190 76 2144 65 2110 100 2420 84 2490 58 1755 88 2605 92 2865 139 3570 95 3155 90 2678 63 2215 66 1800 80 1915 85 2965 90 3420 65 2380 67 3250 74 1980 110 2800 67 2950 95 2560 75 2210 67 1850 100 2615 67 1965 120 2930 60 1968 70 2070 116 2900 75 2542 68 1985 88 2395 82 2720 80 2670 88 2890 79 2625 85 3465 65 3465 105 3380 A consumer organization wants to develop a regression model to predict gasoline mileage (MPG) based on the horsepower of the car's engine and the weight of the car (in pounds). A sample of 50 recent car models was selected, with the results shown at left. Q-12a: Write the multiple regression equation. (Use four decimals of precision.) Q-12b: Interpret the meaning of the slope for horsepower in this model. Q-12c: Interpret the meaning of the slope for weight in this model. Q-12d: Predict the miles per gallon for a car that has 60 horsepower and weighs 2000 pounds. (Use one decimal of precision.) Page 2 2 Sales Radio Newspaper 973 0 40 1119 0 40 875 25 25 625 25 25 910 30 30 971 30 30 931 35 35 1177 35 35 882 40 25 982 40 25 1628 1577 1044 914 1329 1330 1405 1436 1521 1741 1866 1717 45 45 50 50 55 55 60 60 65 65 70 70 A bicycle company wants to measure the effectiveness of different types of advertising media in the promotion of its new bicycle. Specifically, the company is interested in the effectiveness of radio advertising and newspaper advertising. A sample of 22 cities with approximately equal populations is selected for study during a test period of one month. Each city is allocated a specific expenditure level both for radio advertising and for newspaper advertising. The sales of the bicycle (in thousands of dollars) and also the levels of media expenditure (in thousands of dollars) during the test month are recorded. Q-2a: State the multiple regression equation. 45 45 0 0 25 25 30 30 35 35 40 40 Q-2b: Interpret the meaning of the coefficients in the regression equation. Q-2c: Interpret the meaning of the regression coefficient, b0. Q-2d: Which type of advertising is more effective? Explain. As bicycle sales increases more by unit increase in newspaper expenditure as compared to unit increase in radio expenditure, so newspapr advertising is more effective. Q-2a: State the multiple regression equation. Sales = 156.4304 + 13.0806 ( radio expenditure) + 16.7953 (newspaper expenditure) Answer: Q-2b: Interpret the meaning of the coefficients in the regression equation. Answer(radio): Answer(Newspaper): Q-2d: Which type of advertising is more effective? Explain. Newspaper advertising tends to increase the sale of bicycles more so than radio advertising. Regression Statistics Multiple R 0.899273 R Square 0.808692 Adjusted R Square 0.788555 Standard Error 158.9041 Observations 22 ANOVA df Intercept X Variable 1 X Variable 2 SS MS F Significance F 2 2028033 1014016 40.15823 1.50E-007 19 479759.9 25250.52 21 2507793 Coefficients Standard Error t Stat 156.4304 126.7579 1.234089 13.08068 1.759374 7.434851 16.79528 2.963378 5.667613 $13,080.68 $16,795.28 Q-2c: Interpret the meaning of the regression coefficient, b 0. b0 = number of bicycle sales without the use of radio or newspaper advertising. SUMMARY OUTPUT Regression Residual Total Increased by 1 Increased by 1 P-value Lower 95%Upper 95% Lower 95.0%pper 95.0% U 0.232217 -108.8768 421.7377 -108.8768 421.7377 4.89E-007 9.39827 16.76309 9.39827 16.76309 1.83E-005 10.59286 22.9977 10.59286 22.9977 Page 3