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

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.