8. (7 points) I have 30 sets of observations ((ri, yi), i = 1,..., 30) and wish to study the rela- tionship between the

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8 7 Points I Have 30 Sets Of Observations Ri Yi I 1 30 And Wish To Study The Rela Tionship Between The 1 (84.31 KiB) Viewed 20 times

8. (7 points) I have 30 sets of observations ((ri, yi), i = 1,..., 30) and wish to study the rela- tionship between the two variables, X and Y. I fit a simple linear regression model in R. and obtain the following regression output. Answer the questions below. Provide explanation or show your work. > summary (model) Call: 1m (formula y ~ x) Residuals: Min 1Q Median 3Q Max -5.151 -1.523 -0.012 1.900 5.616 Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) 1.540 0.469 3.284 0.00275 X 2.557 0.452 5.657 4.62e-06 (a) Write the estimated regression line. (b) How do you obtain the results of "t value", 3.284, and "Pr(> [t])", 0.00275, respectively, based on the output? (c) Construct a 90% confidence interval for the slope of the regression line, B₁. Interpret your confidence interval. (d) I would like to test whether the slope is equal to 3, i.e., Ho: B₁ = 3. Is the number in the output, 4.62e-06, the p-value of this test? If not, compute the correct p-value.