Question: A researcher is investigating possible explanations for deaths in traffic accidents. He examined data from 1991 for each of the 50 states plus Washington, D.C. The data included information on the following variables:

Deaths: The number of deaths in traffic accidents

Income: The average income per family

Children: The number of children (in multiples of 100,000) between the ages of 1 and 14 in the state

As part of his investigation he ran the following multiple regression model:

where the deviations \({{\varepsilon }_{i}}\) were assumed to be independent and Normally distributed with mean 0 and standard deviation σ. This model was fit to the data using the method of least squares. The following results were obtained from statistical software:

a) Suppose we wish to test the hypotheses H0: β1 = β2 = 0 versus Ha: at least one of the

βj is not 0 using the ANOVA F test. What is the value of the F statistic?

b) What can we say about the P-value for the ANOVA F test?

c) What is a 99% confidence interval for β2, the coefficient of the variable income? Show work.

d) What proportion of the variation in the variable deaths is explained by the explanatory variables children and income? Explain.