Generate a bivariate sample of size 50 as in Problem 33 with correlation coefficient .8....

Generate a bivariate sample of size 50 as in Problem 33 with correlation coefficient .8. Find the estimated regression line and the residuals. Plot the residuals versus X and the residuals versus Y . Explain the appearance of the plots.

Reference

a. Let X ∼ N(0, 1) and E ∼ N(0, 1) be independent, and let Y = X + βE. Show that

b. Use the results of part (a) to generate bivariate samples (x_i , y_i ) of size 20 with population correlation coefficients −.9, −.5, 0, .5, and .9, and compute the sample correlation coefficients.

c. Have a partner generate scatterplots as in part (b) and then guess the correlation coefficients.