The National Transportation Safety Board collects data by state (including the District of Columbia) on traffic fatalities. Part of this data is shown in the following table, along with potentially related factors including population, number of licensed drivers, number of registered vehicles, and total number of vehicle miles driven. You have been asked to develop a model to help explain the factors that underlie traffic fatalities.

a. Build a linear model to predict traffic fatalities based on all four potential explanatory variables as they are measured in the table. Evaluate the model in terms of overall goodness-of-fit. Evaluate the results for each regression parameter: Are the signs appropriate? Are the values different from zero?

b. Can you improve the model in (a) by removing one or more of the explanatory variables from the regression? If so, compare the advantages and disadvantages of the resulting regression from the one in (a).

c. Can you improve the models in (a) or (b) by transforming one or more of the explanatory variables from the regression? If so, compare the advantages and disadvantages of the resulting regression from the ones in (a) and (b).

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Traffic State fatalities AL AK AZ AR CA CO 5882 CT DE DC FL 1,083 85 903 610 4,226 585 310 112 69 2,687 Population (thousands) 4,219 606 4,075 2,453 31,431 3,656 3,275 706 570 13,953 Licensed drivers (thousands) 3,043 443 2,654 1,770 20,359 2,620 2,205 512 366 10,885 Registered vehicles (thousands) 3,422 508 2,980 1,560 23,518 3,144 2,638 568 270 10,132 Vehicle miles traveled (millions) 48,956 4,150 38,774 24,948 271,943 33,705 27,138 7,025 3,448 121,989