An independent researcher in district W wants to study the monthly electricity consumption of households (E, measured in kilowatt hours) in the district. For his study, he selects a random sample of 100 households from the district and estimates the following regression function:
E^ = 102.5 + 1.75N - 0.0122N^2,
(3.5457) (0.6954) (0.0061)
where N denotes the number of members in the household and standard errors appear in parentheses.
The researcher wants to test the hypothesis that the relationship between number of members in the house and the electricity consumption by households is linear, against the alternative that it is nonlinear.
Suppose β2, denotes the population slope coefficient on the regressor N. The researcher conducts the test H0:β2 = 0 vs. H1:β2 /= 0.
a) The test statistic associated with the test the researcher wants to conduct is . (Round your answer to two decimal places. Enter a minus sign if your answer is negative.)
b) At the 5% significance level, the researcher will the hypothesis that the relationship between number of members in the house and the electricity consumption by households is linear.