STAT 3300 Homework #7 Due Thursday, 05/26/2020

Note: Answer these questions on a separate piece of paper. In the top right corner, include your name, SMU ID, and course number. Please include a title for the assignment so that it is clear to the graders. If you miss class the day the assignment is turned in, submit this before class in order to receive credit.

Question 1 (60 points total) In Homework #5, data on the number of tornadoes in the United States between 1953 and 2014 were analyzed to see if there was a linear trend over time. Some argue that it’s not the number of tornadoes increasing over time, but rather the probability of sighting them because there are more people living in the United States. Let’s investigate this by including the U.S. census count (in thousands) as an additional explanatory variable (the data can be found in the file “EX11-24TWISTER.csv”).

a) (12 points) Using numerical and graphical summaries, describe the relationship between each pair of variables.

b) (16 points) Fit one SLR model with year as the predictor and another SLR model with census count as the predictor. Write down the two models. Are year and census count significant, respectively?

c) (12 points) Perform a multiple regression using both year and census count as explanatory variables. Write down the fitted model. Are year and census count, respectively, significant in the MLR model?

d) (12 points) Is the MLR model in part (c) useful in predicting the response variable? Interpret the estimated regression coefficient ??year. Does this make sense? Explain.

e) (8 points) What do you suggest to do next?

Question 2 (40 points total, 8 points per model and 16 for the justification) This data set of size n = 15 (found in “Yield.csv”) contains measurements of yield from an experiment done at five different temperature levels. The variables are y = yield and x = temperature (in degrees Fahrenheit). Fit a simple linear model, a quadratic regression model, and a cubic regression model, respectively. Which one do you choose as the final model? List your justifications, which should include some kind of statistical test.

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Question 1 (60 points total)
Question 2 (40 points total, 8 points per model and 16 for the justification)