Applied Statistical Methods: Regression Analysis

STA 108 Spring 2024 Homework 06 Due 11:55 PM Friday, May 24 on Canvas No late homework is accepted. You are allowed to use a calculator and should round your final result to two decimal digits, if applicable. Show all the relevant work. If you use R, your solution should include the pdf/html-output of a R-Markdown file. 1. (8/50 pts) (Problem 4.1 of textbook) When joint confidence intervals for β0 and β1 are developed by the Bonferroni method with a family confidence coefficient of 90 percent, does this imply that 10 percent of the time the confidence interval for β0 will be incorrect? That 5 percent of the time the confidence interval for β0 will be incorrect and 5 percent of the time that for β1 will be incorrect? Discuss. 2. (15/50 pts) (Problem 4.5 of textbook) Refer to Plastic hardness Problem 1.22. (a) Obtain Bonferroni joint confidence intervals for β0 and β1 , using a 90 percent family confidence coefficient. Interpret your confidence intervals. (b) Are b0 and b1 positively or negatively correlated here? Is this reflected in your joint confidence intervals in part (a)? 3. (20/50 pts) Refer to the copier maintenance problem (HW5 Problem 1) (dataset: copier.txt) (a) Obtain Bonferroni joint confidence intervals for β0 and β1 , using a 95% family confidence. (b) A consultant has suggested that β0 should be 0 and β1 should be 14.0. Do your joint confidence intervals in part (a) support this view? (c) Estimate the expected number of minutes spent where there are 3,5, and 7 copiers to be serviced, respectively. Use interval estimates with a 90% family confidence coefficient based on the Working-Hotelling procedure. (d) Two service calls for preventive maintenance are scheduled in which the number of copiers to be serviced are 4 and 7, respectively. A family of prediction intervals for the time to be spent on these calls is desired with a 90% confidence coefficient. Which procedure, Sheffe or Bonferroni, will provide tighter prediction limits here? (Answer it without direct continuations at this question.) (e) Obtain the family of prediction intervals required in part (d), using the more efficient procedure. 4. (7/50 pts) Consider the simulatenous equations: 5y1 + 2y2 = 8 23y1 + 7y2 = 28 (a) Write these equations in matrix notation. (b) Using matrix methods, find the solutions for y1 and y2 . (Show all the work.) 1 Hint: The inverse of a 2 x 2 matrix a b c d is given by (when ad − cd ̸= 0) 1 d −b ad − cd −c a 2