Let X = {0, 1} and Y be two random variables and let S denote a random sample of size n = 5 from the population. The observations for each individual i in the sample is given by the following table

Table 1: Observations of X and Y in S

I X Y

1 1 20.03

2 0 16.76

3 1 19.97

4 0 17.13

5 0 17.98

a. Estimate the model Y = β0 + β1X + u using OLS.

b. Interpret the coefficient for X from your regression in a.

c. Calculate the R2 from the regression in a (not the adjusted R2 ).

d. State the null hypothesis that X is irrelevant in explaining the variation in Y.

e. Test the null hypothesis in d by: i. t-test [5 Marks] ii. F-test