Applied Statistical Methods: Regression Analysis
STA 108 Spring 2024 Homework 05 Due 11:55 PM Friday, May 17 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. Instruction: Use R to fit a linear model lm() and use estimates from the lm() result and to find percentiles/quantiles. Otherwise, solve them manually. 1. (11/25 points) Refer to the copier maintenance problem. copier.txt has the following columns: Column 1: Y The total number of minutes spent by the service person. Column 2: X The number of copiers serviced. (a) Test for lack of fit of a linear regression at α = 0.05. State the alternative, decision rule and conclusion. (b) Does the test in part (a) detect other departures from regression model, such as lack of constant variance or lack of normality in the error terms? Could the results of the test of lack of fit be affected by such departures? 2. (14/25) A chemist studied the concentration of a solution (Y ) over time (X). Fifteen identical solutions were prepared. The 15 solutions were randomly divided into five sets of three, and the five sets were measured, respectively, after 1,3,5,7, and 9 hours. solution-concentration.txt has the following columns: Column 1: Y Solution Column 2: X Time (a) Fit a linear regression function. (b) Perform the F test to determine whether or not there is lack of fit of a linear regression function at α = 0.025. State the alternatives, decision rule, and conclusion. (c) Does the test in part (b) indicate what regression function is appropriate when it leads to the conclusion that lack of fit of a linear regression function exists? 1
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