Question

This question asks you to compute the sample correlation coefficient (?_xy ) and estimate the regression coefficients with ordinary least squares (OLS) “by hand” for the model (Y_i = ?₁ + ?₂X_i +u_i) using the data below, but without using R (except to get critical values or p‐values, and to check your work)

y	x
1	2
5	6
4	4
4	6
1	2

A. Compute and report the sample correlation coefficient

B. Can you reject the null hypothesis that the true population correlation coefficient is zero at the 5‐percent level of significance?  Can you reject the null at the 1‐percent level of significance?  Show your work and explain.

C. Show all of your work in computing the OLS estimates ?₁ and ?₂.

D. Show all of your work in computing the coefficient of determination (R2) and interpret its meaning.

E. At the 5‐percent level of significance, can you reject the null hypothesis that ?₂ = 0?  Can you reject the null hypothesis at the 1‐percent level of significance?  Show your work and explain.

F. What is the 99‐percent confidence interval for ?₂?  Can you reject the null hypothesis that ?₂ = 2 at the 1‐percent level of significance?  Show your work and explain.

Answer 1