Solutions Sample Final Exam 8AM (1).xlsx

Problem 1. (42 points) A dataset contains 93 observations (93 cars) of City Fuel Efficiency (y) vs Hi xbar = 29.183 r_xy 0.94045 SST 2897.172 SSE 334.7799 R^2 0.884446 SSR 2562.392 MSE 3.6789 alpha =.05 H0: Beta1 =0 HA: Beta1 neq 0 RR: |Z| > 1.96 since we have 91 df test stat: t = b1/sb1 Since |26.39148| > 1.96, at alpha =.05, we have evidence that Beta1 neq 0. .9867 +/- 1.645*(.037387) We are 90% confident Beta1 is in the above calculated interval. This is because if we w intervals would include Beta1. Beta1 is the slope of the true regression City Fuel Eff = we expect coty fuel eff to change by Beta1 units. xbar 29.183 29.183 +/- 1.645*(5.3486/sqrt(93)) s_x 5.348645 93 S 2 x = 28.608 S 2 y = 31.491 b 0 = -6.32 b 1 = .9867 A. Find r x,y , R 2 , s b1 , s e , 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 D. Construct a 90% CI for mu x , the true population mean of the x values (Highway M

ighway Fuel Efficiency (x). s_e 1.918046 sb1 0.037387 SS_xx 2631.936 tc 26.39148 were to repeat the process many times, approx 90% of the resulting Beta0 + Beta1*Hwy eff + epsilon. As Hwy eff increases by 1 unit 9 points) MPG). (9 points)

Problem 2. (20 points) Consider the following regression of Household rating (a rating that measures the popularity of tv sh Coefficients Term Coef SE Coef T-Value P-Value VIF Constant 4.096 0.397 10.32 0 1.453 0.539 2.7 0.008 1.37 0.759 0.561 1.35 0.18 1.37 Model Summary S R-sq 2.24578 6.84% 4.96% 1.13% Analysis of Variance Source DF Adj SS Adj MS F-Value P-Value Regression 2 36.679 18.34 3.64 0.03 Error 99 499.311 5.044 Total 101 535.99 alpha = .025 H0: Beta1 = Beta2 =0 HA: At least one such Beta neq 0 test stat: F = MSR/MSE and its p-value is .03. Since .03 is not less than .025, at alpha =.025, we do not have sufficient evidence that T 4.096 +/- 1.645*.397 We are 90% confident that Beta0 is the above interval. This is because if we were to repeat the pr would include Beta0. Beta0 is the true mean Household rating for Comedy shows. estimate for Drama 5.549 estimate for Reality 4.855 Estimate for difference in avg rating between Drama and Reality 0.694 Type_Dra ma Type_Reali ty/ Participatio n R- sq(adj) R- sq(pred) A. Is there evidence that Type is an important predictor Household Rating? Use alpha B. Construct a 90% CI for the average Household Rating for Comedy shows and inter C. Provide an estimate for the difference in average rating between Drama and Reality

hows by household) versus Show Type (Comedy, Drama, or Reality/Participation). Type is an important predictor of Household Rating. rocess many times, approx 90% of the resulting intervals a =.025. Explain your answer. (8 points) rpret the CI? (8 points) y shows. (4 points)

Problem 3. (24 points) Consider the following regression of Household rating (a rating that measures the popularity of tv shows Coefficients Term Coef SE Coef T-Value P-Value VIF Constant 4.008 0.409 9.8 0 1.229 0.441 2.79 0.006 1.38 1.283 0.464 2.76 0.007 1.41 1.893 0.461 4.11 0 1.31 -1.464 0.433 -3.38 0.001 1.31 Model Summary S R-sq R-sq(adj) 1.83362 39.15% 36.64% 32.68% Analysis of Variance Source DF Adj SS Adj MS F-Value P-Value Regression 4 209.840085 52.46002125 15.60209532 0 Error 97 326.149915 3.362370258 Total 101 535.99 alpha =.01 H0: Beta1=Beta2=Beta3=Beta4=0 HA: At least one such Beta neq 0 test stat: F = MSR/MSE p-value is 0. Since 0 < .01, at alpha = .01, we have evidence that at least one such Be for describing Household Rating. -1.464 +/- 1.96*.433. We are 95% confident that Beta4 is in the above calculated interval. This is because if Beta4 is the expected difference in Household rating for NBC network and ABC Networ The above calculated interval has both endpoints negative, thus, there is evidence tha This model is the complete one and Prob 2 model is the reduced one. Type_Dra ma Type_Reali ty/ Participatio n Network_C BS Network_N BC R- sq(pred) A. Is there evidence of model utility for describing/explaining Household Rating? Use alp B. Construct a 95% CI for the coefficient in front of NBC and interpret it in the context of C. Compare this regression model to the one from problem 2. Use alpha = .05. (7 points

Your preview ends here

Eager to read complete document? Join bartleby learn and gain access to the full version

Access to all documents
Unlimited textbook solutions
24/7 expert homework help