HW: Statistical Inferences Assignment

Note: This assignment uses the exact same three datasets as the previous assignment. Also similar to the previous assignment, most questions are near identical (primary differences exist in parts f and g).

Q1: For Dataset 1, use appropriate R functions, including lm, to provide the requested information.

a) What is the MS_Res (note: the sigma function in R gives the square root of the MS_Res for a linear model data frame)

b) We wish to test the following hypotheses at the 95% confidence level H₀: ?₀ = 0 vs. H₁: ?₀ ? 0.

i) What conclusion is drawn regarding H₀? (Highlight answer) Reject Fail to reject

ii) What is the associated p value?

c) We wish to test the following hypotheses at the 95% confidence level H₀: ?₁ = 0 vs. H₁: ?₁ ? 0. (This is also the significance of the regression, as we only have one regressor)

i) What conclusion is drawn regarding H₀? (Highlight answer) Reject Fail to reject

ii) What is the associated p value?

d) What is the confidence interval for ?₀?

e) What is the confidence interval for ?₁?

f) What is the confidence interval for E(Y|x) = ?_Y|x if x = 60?

g) What is the prediction interval for Y if x = 60?

\f