The data in the file Demographics were obtained from a random sample of 20 states of the US.

VariableDescriptionyLife Expectancy (LIFE.EXP):Life Expectancy in years.x₁Population (POPULATION):Population size.x₂Murder Rate (MURDER):Murder rate per 100,000.x₃HS Graduation Rate (HS.GRAD):High school graduation rate as a percent.x₄Illiteracy Rate (ILLITERACY):Illiteracy rate per 100,000.

(a) Test the overall fit of the regression model constructed using just those variables outlined above. Use a 10% level of significance.

State the hypotheses to be tested.

H₀:₁=₂=₃=₄= 0

H_a: At least one of the coefficients is not equal to 0.

H₀:₁=₂=₃=₄= 0

H_a: None of the coefficients are equal to zero.

H₀: At least one of the coefficients is not equal to 0.

H_a:₁=₂=₃=₄= 0

H₀: None of the coefficients are equal to zero.

H_a:₁=₂=₃=₄= 0

State the test statisticF. Round your answer to three decimal places.

F=

State your decision at the 0.05 level of significance.

Do not rejectH₀. The coefficients are all equal to zero: None are useful in explaining the variation in life expectancy.

RejectH₀. At least one of the coefficients is not equal to zero: At least one variable is useful in explaining the variation in life expectancy.

Do not rejectH₀. At least one of the coefficients is not equal to zero: At least one variable is useful in explaining the variation in life expectancy.

RejectH₀. The coefficients are all equal to zero: None are useful in explaining the variation in life expectancy.

According to this analysis, which variable(s) is/are significant in this current model at explaining life expectancy at the 0.05 level of significance? Select all that apply.

HS.GRAD

ILLITERACY

MURDER

POPULATION

(b) If you were to attempt to refine this regression model further, what would be the next step?Note, you should not use any formal model building procedures here - instead consider the next logical step to refine the model, based on the output for the full model with the four previously listed explanatory variables.

Drop MURDER from the model and then re-run the analysis

Drop multiple explanatory variables from the model immediately and then re-run the analysis

Drop ILLITERACY from the model and then re-run the analysis

Drop HS.GRAD from the model and then re-run the analysis

Do nothing - leave the regression model as it currently is