Q3: For Dataset 3, 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 = 30?

g) What is the prediction interval for Y if x = 30?

Q4: Paste all R code used to generate the above here. Use an 8pt fixed width font (ideally Courier New or Consolas).

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