Stat 139 Final Exam - Fall 2016_v2.pdf - Stat 139 Final Exam Fall 2016 Name Harvard ID This exam is open-notes and open-book(feel free to use the

# Stat 139 Final Exam - Fall 2016_v2.pdf - Stat 139 Final...

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Stat 139 Final Exam Fall 2016 Name Harvard ID This exam is open-notes and open-book (feel free to use the internet as well). You cannot discuss the contents of the exam with anyone except the teaching staff. There are 2 questions. Your answers can be hand-written and scanned or typed (or a combination of the two). Please include all pages in one document. The online version of PDFMerge! may be helpful to merge all pdf files together: . Due at 9am on Tues, Dec 13 . Problem 1 [25 points total] The following is the R-output for a regression to predict the number of bowls of noodle soup sold at a hip new pho restaurant in town based on the high temperature outside the restaurant that day, along with the relevant scatterplot: > mean(temp) [1] 58.10 > sd(temp) [1] 19.10 > mean(soup) [1] 163.69 > sd(soup) [1] 49.11 > summary(lm(soup~temp)) Coefficients: Estimate Std.Err t value Pr(>|t|) (Intercept) --- --- --- <2e-16 temp --- --- --- <2e-16 --- Residual standard error: ---- on 98 DF Multiple R-sq: 0.8254, Adj R-sq: 0.8236 F-stat: 463.3 on 1 and 98 DF, p-val: < 0.0001 a) [3 points] What is the estimated correlation between temp and soup ? b) [6 points] Calculate the estimated simple regression line for these data. Also estimate the standard deviation of the residuals around this line. c) [6 points] Calculate a 95% confidence interval for estimating the mean number of bowls of soup sold when the high temperature outside is 58.1 degrees. d) [5 points] For a new randomly sampled day when the high temperature is known to be X = 58 . 1, what is the approximate probability that the number of bowls sold will be within the interval in part (c), assuming all assumptions are correct? e) [5 points] Provide the best set of transformations on Y = soup and X = temp to make a better regression model. Justify briefly.

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