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 (xi , yi ) 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.
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