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40T5 #31 The Cincinnati Zoo and Botanical Gardens had a record attendance of 1.3? million visitors in 2017 (Cincinnati Business Courier Website). Nonprot organizations such as zoos and museums are becoming more sophisticated in their use of data to improve the customer experience. Being able to better estimate expected revenue is one use of analytics that allows nonprots to better manage their operations. You have been tasked with estimating the following equation: 3(3) = n + 31F + 132D +3351 + .5452 +3553 Where revenue (R), measured in dollars, is a function of the number of family members {F}, the distance the family lives from the zoo [D]. measured in kilometers, and the time of year. Time of year is measured using three dumm'gir variables to capture the four seasons: \"Enter {51}, Summer [32] and Spring ($31, leaving Fall as the reference case. The results of the estimated regression and its standardized residuals can be found on page 6 of this exam. aj Write the estimated regression equation. b} Interpret the estimated coefcients on the number of family membersfFL and Summer {32] cl Interpret the interval estimates of the coefficients on Distance ID}, and on Winter {31 I. d} Interpret the adjusted R-square. e) State the null and alternative for the Ftest and interpret the results. Page 4 f') Interpret the results of the t-tests [interpret them in relevant groups. rather than individually}. g) Do you have any reason to believe there may be a problem with multicollinearity'? Briefly explain. [1) Evaluate the standardized residual plot. in What would it mean to commit a Type I error for the t-test on the number of family.r members [F]. h) Evaluate the standardized residual plot. 6 of 6 i)) What would it mean to commit a Type I error for the t-test on the number of family members (F), i) According to our in-class discussion, what did I say are the two primary uses for regression analysis? 1) 2) j) Use the estimated regression equation in part a) to predict revenue from a family of three who live 43Km from the zoo and who visit in the Fall. k) Based on these estimate regression results, suggest a way to potentially improve the current model. Page 5 SUMMARY OUTPUT Regression Statistics Multiple R 0.85 R Square 0.71 Adj. R Square 0.70 Std. Error 46.52 Observations 89 ANOVA Significance of SS MS F Regression 5 450395.01 90079.00 41.63 0.00 Residual 83 179583.31 2163.65 Total 88 629978.33 Standard Coefficients Error t Stat P-value Lower 95% Upper 95% Intercept 100.57 17.63 5.71 0.00 65.51 135.63 Winter -27.12 13.13 -2.07 0.04 -53.24 -1.01 Spring 61.06 12.47 4.90 0.00 36.26 85.86 Summer 44.08 19.02 2.32 0.02 6.25 81.92 Size 41.28 3.50 11.78 0.00 34.31 48.25 Distance 0.17 0.35 -0.50 0.62 0.51 0.86 Standard Residuals N 1 0 50 100 150 350 400 -1 .. -2