Stat 351 Homework #2 Due date: Tuesday, June 23, 2020 at 11.59 p.m. CDT. Submit your homework via one of the following methods. 1. Type your answers in a word document and submit as a word document...

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Stat 351 Homework #2 Due date: Tuesday, June 23, 2020 at 11.59 p.m. CDT. Submit your homework via one of the following methods. 1. Type your answers in a word document and submit as a word document file or pdf file. 2. Write down your answers in separate sheets of paper and submit the scan copy of the answer. 3. Write down your answers in separate sheets of paper and submit snapshot of the answer. Make sure to show your work for full credit. Questions 1 and 2 are based on Sections 14.4 -14.5 Model assumption and testing. 1. A Regression analysis was applied between sales data (y in $1000s) and advertising expenditure (x in $100s) and the estimated regression equation is obtained as ŷ = 12 + 1.8x. Suppose SST = 300, SSE = 75, sb1 = 0.2683 and ? = 17 a) Carry out a t-test to see whether the advertising expenditure is significant. Use α = 0.05 and critical value approach to draw your conclusion. Make sure to show all your steps. b) Carry out an F-test to see whether the advertising expenditure is significant. Use α = 0.05 and critical value approach to draw your conclusion. Make sure to show all your steps. 2. A sales manager collected data on annual sales for new customer accounts and the number of years of experience for a sample of 15 salespersons. The following is the Regression Analysis run by Minitab for developing an estimated regression equation to predict annual sales using the independent variable years of experience (x). Note that ? = ????? ?? ??????????, ? = ?????? ?????. Regression Analysis: Annual Sales versus Years of Experience Regression Equation Annual Sales = 53.86 + 8.361 Years of Experience Coefficients Term Coef SE Coef T-Value P-Value VIF Constant 53.86 4.79 11.25 0.000 Years of Experience 8.361 0.462 18.11 0.000 1.00 Model Summary S R-sq R-sq(adj) R-sq(pred) 8.98845 96.19% 95.89% 95.17% Analysis of Variance Source DF Adj SS Adj MS F-Value P-Value Regression 1 26491.0 26491.0 327.89 0.000 Years of Experience 1 26491.0 26491.0 327.89 0.000 Error 13 1050.3 80.8 Lack-of-Fit 11 690.3 62.8 0.35 0.901 Pure Error 2 360.0 180.0 Total 14 27541.3 Settings Variable Setting Years of Experience 9 Prediction Fit SE Fit 95% CI 95% PI 129.109 2.32101 (124.095, 134.123) (109.054, 149.165) a) Carry out a t-test to see whether the years of experience and the annual sales are related. Use α = 0.05. Please use the P-value approach to answer this question. b) Carry out an F-test to see whether years of experience and the annual sales are related. Use α = 0.05. Please use the P-value approach to answer this question. c) Find a 95% confidence interval for the mean annual sales for all salespersons with nine years of experience. d) The company is considering hiring Tom Smart, a salesperson with nine years of experience. Find a 95% prediction interval of annual sales for Tom Smart. e) Discuss the differences in your answers to part c) and d). That is, which interval estimation is wider? And why? Questions 3 is based on Sections 14.8 -14.9 Residual analysis. 3. The following data were used to develop a regression analysis. x 2 3 4 5 7 7 7 8 9 y 4 5 4 6 4 6 9 5 11 a) The graph shown below is the residual against the fitted value (�̂�) to check the constant variance assumption. Does the above plot support the assumptions about the error ?? Explain. b) The graph shown below is the normal probability to check the normality assumptions about the error ?. Does the above plot support the assumptions about the error ?? Explain. c. The following results are part of the Regression Analysis for the above data from Minitab. Below is a table with statistics necessary for analyzing the residuals. SRES stands for standardized residual and HI for leverage values. Table 1: Residual Analysis Observation SRES HI 1 0.259783 0.42439 2 0.440919 0.280488 3 -0.46692 0.180488 4 0.257577 0.12439 5 -1.4616 0.143902 6 -0.40935 0.143902 7 1.169025 0.143902 8 -1.33051 0.219512 9 1.765634 0.339024 I. Can any of the observations be classified as an outlier? II. Can any of the observations be classified as an influential observation? Questions 4 is based on Sections from chapter 15. 4. This question is from the textbook: Problem 25 on Page 705. The Minitab output for this question is given below. Regression Analysis: Overall versus Itineraries/Schedule, Shore Excursions, Food/Dining Coefficients Term Coef SE Coef T-Value P-Value VIF Constant 35.6 13.2 2.69 0.016 Itineraries/Schedule 0.110 0.130 0.85 0.407 1.05 Shore Excursions 0.2445 0.0434 5.64 0.000 1.07 Food/Dining 0.2474 0.0621 3.98 0.001 1.01 Model Summary S R-sq R-sq(adj) R-sq(pred) 1.38775 74.98% 70.29% 58.09% Analysis of Variance Source DF Adj SS Adj MS F-Value P-Value Regression 3 92.352 30.784 15.98 0.000 Itineraries/Schedule 1 1.398 1.398 0.73 0.407 Shore Excursions 1 61.261 61.261 31.81 0.000 Food/Dining 1 30.539 30.539 15.86 0.001 Error 16 30.813 1.926 Total 19 123.166 Prediction for Overall Settings Variable Setting Itineraries/Schedule 90 Shore Excursions 80 Food/Dining 88 Prediction Fit SE Fit 95% CI 95% PI 86.8896 0.595008 (85.6283, 88.1510) (83.6887, 90.0905) Please answer ONLY for parts of a, b, c (Do not answer for part d) and the following part e and f. e. Provide a 95% confidence interval for the mean value for all ships that got Itineraries/Schedule score 90, Shore Excursions score 80 and Rood/Dining score 88. f. Provide a 95% prediction interval for the mean value for one specific ship that got Itineraries/Schedule score 90, Shore Excursions score 80 and Rood/Dining score 88.