A researcher is investigating possible explanations for deaths in traffic accidents. He examined data from 1991 for each of the 50 states plus Washington, DC. 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 multiple regression model,
Deaths = b0 + b1(Children) + b2(Income) + ei,
where the deviations ei were assumed to be independent and Normally distributed with a mean of 0 and a standard deviation of s. This model was fit to the data using the method of least squares. The following results were obtained from statistical software.
Source Sum of squares df
Model 48362278 2
Error 3042063 48
Variable Coefficient Standard error
Constant 593.829 204.114
Children 90.629 3.305
Income –0.039 0.015
The researcher also ran the simple linear regression model
Deaths = b0 + b2(Income) + ei.
The following results were obtained from statistical software:
Source Sum of squares df
Model 711680 1
Error 50692661 49
Variable Coefficient Standard error
Constant 292.518 823.505
Income 0.050 0.060
Based on the above results, the researcher tested the hypotheses H0: b2 = 0 versus
Ha: b2 ¹ 0.What do we know about the P-value of the test?