METH 201, Exercise Set 8, Due 10 December 2015 1. A sales manager collected the following data on Years of Experience and Annual Sales (in $000s) for 10 salespersons: Salesperson Years of Experience Annual Sales ($000s) 1 1 80 2 3 97 3 4 92 4 4 102 5 6 103 6 8 111 7 10 119 8 10 123 9 11 117 10 13 136 a. Construct a scatterplot for the data above with Years of Experience as the explanatory, or X, variable. b. Estimate the straight-line simple regression (or ) equation that can be used to predict Annual Sales Y given Years of Experience. c. Interpret the value of the estimated slope coefficient for Years of Experience. d. Predict Annual Sales, in dollars, for a salesperson with 9 Years of Experience. 2. Using data from the 2007 Major League Baseball season (World Series champions: Boston Red Sox), Sammy Stat estimated the following simple regression (or Y) equation: Expected Team Wins (in number of games) = Wins = 70.097 + 0.132Team Salary (in $millions) a. Interpret the value of the estimated slope coefficient for Team Salary. b. Is the baseline value (or intercept) meaningful? Explain briefly. c. If team A spent $10,000,000 more on salaries than team B, how many more games would you expect team A to have won than team B? d. If a team spent $110,000,000 on salaries and won half (or 81) of its 162 games, did the team \"get its money's worth?\" Explain briefly. 3. This question is based on data for a random sample of 638 air routes in the United States collected by a former colleague of Erich S-E at the University of Maryland, College Park. Use the MS Excel output below, based on a simple regression analysis with FARE (average fare for an air route, in $) as the response variable and DISTANCE (length of an air route, in miles) as the explanatory variable, to answer/complete Parts a through f: SUMMARY OUTPUT Regression Statistics Multiple R 0.6700 R Square 0.4489 Adjusted R Square 0.4481 Standard Error 56.4794 Observations 638 ANOVA df Regression Residual Total Intercept DISTANCE 1 636 637 SS MS F Significance F 1652697.4 1652697.4 518.1004 2.39E-84 2028787.3 3189.9 3681484.7 Coefficients Standard Error 83.9765 4.0514 0.0788 0.0035 t Stat P-value 20.7277 2.60E-73 22.7618 2.39E-84 Lower 95% Upper 95% 76.0208 91.9323 0.0720 0.0856 a. What percent of the total variation in FARE does the regression equation, or DISTANCE, explain or determine? b. What is the value of the bivariate correlation coefficient between FARE and DISTANCE in the sample? c. State the null and alternative hypotheses to test whether the slope coefficient for DISTANCE is significantly greater than zero. d. If = 0.01, determine the critical value for the test statistic associated with the hypotheses in Part c. e. Given the MS Excel output and Part d, state your decision regarding the null hypothesis in Part c. f. You are an airline industry executive. Can you conclude longer air routes have higher fares than shorter air routes, on average? 4. [Background] Senior executives for a chain of pharmacies are considering opening a pharmacy in Kansas City, Missouri. The executives have asked you to analyze data on annual profit, in $, [PROFIT] for one of the company's pharmacies in each of 110 U.S. cities (therefore, the sample contains data for 110 pharmacies). The executives want a model that: a) predicts pharmacy profits by city, b) provides information to help select communities for expansion, and c) helps identify underperforming sites. For each city, you have data on the following additional variables: i. DISP_INC = median annual individual income in $, after taxes ii. BIRTH_RT = number of births per 1,000 persons in the local population iii. %65+ = percent of persons in the local population age 65 or older Use the MS Excel output below, based on a multiple regression analysis with PROFIT as the response variable and DISP_INC, BIRTH_RT, and %65+ as explanatory variables, to answer/complete Parts a through e: SUMMARY OUTPUT - PROFIT = f(DISP_INC, BIRTH_RT, %65+) Regression Statistics Multiple R 0.8672 R Square 0.7521 Adjusted R Square 0.7450 Standard Error 13455.4575 Observations 110 ANOVA df Regression Residual Total Intercept DISP_INC BIRTH_RT %65+ 3 106 109 SS MS 58210320762 19403440254 19191229770 181049337.4 77401550532 Coefficients Standard Error 10044.6085 15344.7924 3.2386 0.4137 1874.0454 526.5008 6619.2075 465.5340 t Stat 0.6546 7.8277 3.5594 14.2185 F Significance F 107.1721141 5.72543E-32 P-value 0.51415 3.9755E-12 0.00056 2.5900E-26 Lower 95% Upper 95% -20377.9349 40467.1520 2.4183 4.0589 830.2063 2917.8846 5696.2411 7542.1739 a. Provide a specific interpretation (meaning, include variable names and the value) for R Square. b. Provide a specific interpretation (meaning, include variable names and the value) for the estimated coefficient for %65+. c. Which explanatory variable has the most [statistically] significant relationship with PROFIT (controlling for effects of other explanatory variables)? d. Which explanatory variable has the least [statistically] significant relationship with PROFIT (controlling for effects of other explanatory variables)? e. Predict, or estimate, PROFIT for a new pharmacy in Kansas City, Missouri, given the following values for explanatory variables in Kansas City: DISP_INC = $22,642, BIRTH_RT = 14.4 (per 1000), and %65+ = 11.4