a Generate 500 data sets, each with 30 pairs of observations (xi,yi). Use a bivariate normal distribution with means 0, standard deviations 1, and correlation 0.5 to generate each pair (xi,yi). For each data set, calculate ¯ y and ˆ ¯ yreg, using ¯ xU = 0.Graphahistogramofthe500valuesof ¯ y andanotherhistogramofthe500values of ˆ ¯ yreg.What do you see?
b Repeat part (a) for 500 data sets, each with 60 pairs of observations.