WORK ON THE 4 QUESTIONS – BE VERY DESCRIPTIVE
Sample Final Exam Statistics for Business You must show your work. Problem 1. (42 points) A dataset contains 93 observations (93 cars) of City Fuel Efficiency (y) vs Highway Fuel Efficiency (x). S2x = 28.608 S2y = 31.491 b0 = -6.32 b1 = .9867 xbar = 29.183 A. Find rx,y, R2, sb1, se, SSR, SSE, SST, MSE. (16 points) B. Is there evidence that Beta1 is not equal to 0? Use alpha =.05. (8 points) C. Construct a 90% CI for Beta1 and interpret it within the context of this problem. (9 points) D. Construct a 90% CI for mux, the true population mean of the x values (Highway MPG). (9 points) Problem 2. (20 points) Consider the following regression of Household rating (a rating that measures the popularity of tv shows by household) versus Show Type (Comedy, Drama, or Reality/Participation). Coefficients Term Coef SE Coef T-Value P-Value VIF Constant 4.096 Type_Drama 1.453 Type_Reality/Participation 0.759 0.397 0.539 0.561 10.32 2.70 1.35 0.000 0.008 1.37 0.180 1.37 Model Summary S R-sq R-sq(adj) R-sq(pred) 2.24578 6.84% 4.96% 1.13% Analysis of Variance Source DF Adj SS Adj MS F-Value P-Value Regression Error Total 2 36.679 99 499.311 101 535.990 18.340 5.044 3.64 0.030 A. Is there evidence that Type is an important predictor Household Rating? Use alpha =.025. Explain your answer. (8 points) B. Construct a 90% CI for the average Household Rating for Comedy shows and interpret the CI? (8 points) C. Provide an estimate for the difference in average rating between Drama and Reality shows. (4 points) Problem 3. (24 points) Consider the following regression of Household rating (a rating that measures the popularity of tv shows by household) versus Show Type (Comedy, Drama, or Reality/Participation) and Network (ABC, CBS, and NBC). Coefficients Term Coef SE Coef T-Value P-Value VIF Constant 4.008 Type_Drama 1.229 Type_Reality/Participation 1.283 Network_CBS 1.893 Network_NBC -1.464 0.409 0.441 0.464 0.461 0.433 9.80 2.79 2.76 4.11 -3.38 0.000 0.006 1.38 0.007 1.41 0.000 1.31 0.001 1.31 Model Summary S R-sq R-sq(adj) R-sq(pred) 1.83362 39.15% 36.64% 32.68% Analysis of Variance Source DF Adj SS Adj MS F-Value P-Value Regression Error Total ___ _______ 97 _______ 101 535.990 A. ______ ______ ________ 0.000 Is there evidence of model utility for describing/explaining Household Rating? Use alpha =.01. (7 points) B. Construct a 95% CI for the coefficient in front of NBC and interpret it in the context of this model. (10 points) C. Compare this regression model to the one from problem 2. Use alpha = .05. (7 points) Problem 4. (14 points) Consider the following regression of Household rating (a rating that measures the popularity of tv shows by household) versus Show Type (Comedy, Drama, or Reality/Participation), Network (ABC, CBS, and NBC) and their interactions. Coefficients Term Coef SE Coef T-Value P-Value VIF Constant 4.440 Type_Drama 0.541 Type_Reality/Participation 0.745 Network_CBS 1.249 Network_NBC -2.135 DramaCBS 1.49 DramaNBC 0.46 RealityCBS -0.47 RealityNBC 1.23 0.545 0.729 0.771 0.790 0.771 1.04 1.07 1.26 1.05 8.14 0.74 0.97 1.58 -2.77 1.42 0.43 -0.38 1.18 0.000 0.460 3.87 0.337 3.99 0.117 3.96 0.007 4.29 0.158 4.03 0.668 3.19 0.708 2.29 0.242 4.52 Model Summary S R-sq R-sq(adj) R-sq(pred) 1.80848 43.25% 38.37% 32.41% Analysis of Variance Source DF Adj SS Adj MS F-Value P-Value Regression Error Total 8 ________ ________ ___ ________ ________ 101 535.990 A. B. ______ 0.000 Fill in the blanks (6 points) Compare this regression model to the regression model from problem 3 using a Nested F-test (alpha =.05). Which model would you prefer to use – the regression model from Problem 3 or from Problem 4. (8 points)
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