11.24 Is the number of tornadoes increasing? In Exercise 10.19, 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 as an additional explanatory variable.

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

  2. (b) Perform a multiple regression using both year and census count as explanatory variables. Write down the fitted model.

  3. (c) Obtain the residuals from part (b). Plot them versus the two explanatory variables and generate a Normal quantile plot. What do you conclude?

  4. (d) Test the hypothesis that there is a linear increase over time. State the null and alternative hypotheses, test statistic, and P-value. What is your conclusion?