MTH4230_exam_1_review(2).pdf

# H the following shows cis for the intercept and slope

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(h) The following shows CIs for the intercept and slope of the model. Interpret them. What seems wrong with your interpretation of the intercept CI? What R function and confidence level did I use to get this output? 2.5 % 97.5 % (Intercept) -302.47351 -246.98253 Chest 12.12824 13.63211 (i) In part (e) the residual standard error is missing. Use the following ANOVA table to calculate it: Analysis of Variance Table Response: Weight Df Sum Sq Mean Sq F value Pr(>F) Chest 1 1107073 1107073 ***** < 2.2e-16 *** Residuals 81 77198 ***** (j) Now use the above ANOVA table to test whether there is a linear relationship between weight and chest girth. State the null and alternative hypotheses, the p -value, your decision to reject the null or not, and your conclusion (in context). Then calculate the F value two ways: using the ANOVA table and using the t -statistic from part (e). 4

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(k) We found another bear whose chest girth is 35 inches. We wish to use the SLR model to predict weight based on this chest girth. Someone calculated both a prediction interval and a confidence interval for the bear. Which of the following is the CI and which is the PI and why? Which one should you use and how should you interpret it? > predict(lm_chest,newdata=data.frame(Chest=35),interval="*****") fit lwr upr 1 176.0781 114.2812 237.8751 > predict(lm_chest,newdata=data.frame(Chest=35),interval="*****") fit lwr upr 1 176.0781 169.3095 182.8467 3 Application (take-home exam) For the take-home exam, you will be required to analyze real data by applying linear regression. Assumptions should be checked and discussed, appropriate tests should be carried out, and all interpretations should be reported in the context of the problem. For this portion of the exam the only resources allowed are your brain, your four labs, and your cheat sheet for the in-class exam. This means no notes, internet, books, people, etc. For practice, use R to do the following in ALRM (4 th ed.): “Projects” 1.43, 1.44, 2.62, 2.63, 3.24, 3.25, and 3.26 (these are given after the “Problems” at the end of each chapter; data are in CD-ROM and on book website).
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