Using 20 observations, the following regression output is obtained from estimati

Question

Using 20 observations, the following regression output is obtained from estimating y = beta _0 + beta _1 x + beta _2 d + beta _3 xd + epsilon. Compute ycirc for x = 9 and d = 1; then compute ycirc for x = 9 and d = 0. (Round your final answers to 2 decimal places.) Is the dummy variable d significant at the 5% level? Yes, since we reject the relevant null hypothesis. Yes, since we do not reject the relevant null hypothesis. No, since we reject the relevant null hypothesis. No, since we do not reject the relevant null hypothesis. Is the interaction variable xd significant at the 5% level? Yes, since we reject the relevant null hypothesis. Yes, since we do not reject relevant null hypothesis No, since we reject the relevant null hypothesis.

Explanation / Answer

a) From the given table ( coefficient column ) , we get the regression equation as:

y = 14.95 + 3.04x -6.72d +2.46xd

Now for x = 9 and d= 1, we get:

y = 14.95 + 3.04*9 -6.72 + 2.46*9 = 57.73

Therefore the predicted y value here is 57.73

Now for x = 9 and d= 0, we get:

y = 14.95 + 3.04*9 -6.72*0 + 0 = 42.31

Therefore the predicted y value here is 42.31

b-1) As the p-value for d from the table is 0.0519 > 0.05, therefore the dummy variable is not significant and we do not reject the null hypothesis. Therefore d is the correct answer here

b-2) As the p-value for xd from the table is 0.0085 < 0.05, therefore the variable here is significant and we reject the null hypothesis. Therefore a is the correct answer here

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