Consider the simple linear regression Y; = Bo + X;B1 + ;, where X; takes value...

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Consider the simple linear regression Y; = Bo + X;B1 + €;, 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 B1 and Bo, show that Bo is the sample average for group 2 and B1 is the difference of the sample averages for group 1 and group 2. 2. Show that the test for B1 is as the same as the two sample t-test with pooled variance, (i.e., when equal variance is assumed). Hint: show that the formula of the variance for B1 is equivalent to the formula of the pooled sample variance. Consider the simple linear regression Y; = Bo + X;B1 + €;, 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 B1 and Bo, show that Bo is the sample average for group 2 and B1 is the difference of the sample averages for group 1 and group 2. 2. Show that the test for B1 is as the same as the two sample t-test with pooled variance, (i.e., when equal variance is assumed). Hint: show that the formula of the variance for B1 is equivalent to the formula of the pooled sample variance.