Question: Consider the simple linear regression Y = Bo + X.B. + where X, takes value 0 and 1, so that X = 1 if the

Consider the simple linear regression Y = Bo + X.B. + where X, takes value 0 and 1, so that X = 1 if the ith subject is in group 1, and X = 0 if the ith subject is in group 2. 1. Using the OLS formula for , and Bo, show that Bo is the sample average for group 2 and , is the difference of the sample averages for group 1 and group 2. (8 points) 2. Show that the test for 8, is as the same as the two sample t-test with pooled variance, (ie, when equal variance is assumed). Hint: show that the formula of the variance for B, is equivalent to the formula of the pooled sample variance. (12 points)

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