Question

Suppose the following are the results of a linear regression with the voter turnout rate in a county as a percentage in decimal form as the dependent variable and the unemployment rate and the amount of rain on election day in inches as the independent variables. The unemployment rate is a percentage in decimal form. The coefficient on the unemployment rate is 4.132 with a p-value of 0.003. The coefficient on the amount of rain on election day in inches is −0.0258 with a p-value of 0.043. The F-Statistic for the regression is 20.958 with a p-value less than 0.001. At a 5% Level of Significance, what can be said about the coefficient on the unemployment rate?

Group of answer choices

The coefficient on the unemployment rate isn’t statistically significant because the F-Statistic has a p-value less than 5%

The coefficient on the unemployment rate is statistically significant because it’s p-value of 0.003 is less than the Level of Significance of 5%

Based on the p-value of the coefficient on the unemployment rate, the coefficient on the unemployment rate isn’t statistically significant

There isn’t enough information to determine the statistical significance of the coefficient on the unemployment rate

Answer 1

Level of significance = 5% = 0.05 = a

p-value of unemployment =0.003

p-value of rain = 0.043

H0:- coefficient of unemployment = 0

Ha:-not H0

=> two tailed test is required here.

rule of p-value for two tailed test:--- if p-value is less than a/2 then reject the null hypothesis & if p-value is greater than a/2 then fail to reject the null hypothesis.

here. a/2 = 0.05/2 = 0.025

since 0.003 < 0.025 => p-value < a/2

hence reject the null hypothesis.

hence the coefficient of the unemployment is statistically significant.

hence correct option is The coefficient on the unemployment rate is statistically significant because it’s p-value of 0.003 is less than the Level of Significance of 5%