Suppose X1 is a numerical variable and X2 is a dummy variable with two categorie

Question

Suppose X1 is a numerical variable and X2 is a dummy variable with two categories and the regression equation for a sample of n=18 is Y^ i =6+ 3X1i- 2X2i.

a. Interpret the regression coefficient associated with variable X1.

b. Interpret the regression coefficient associated with variable X2.

c. Suppose that the tSTAT test statistic for testing the contribution of variable X2 is negative 1.66 . At the 0.05 level of significance, is there evidence that variable X2 makes a significant contribution to the model?

Explanation / Answer

Answer:

Suppose X1 is a numerical variable and X2 is a dummy variable with two categories and the regression equation for a sample of n=18 is Y^ i =6+ 3X1i- 2X2i.

a. Interpret the regression coefficient associated with variable X1.

When x1 increases by 1, y increases by 3.

b. Interpret the regression coefficient associated with variable X2.

When the variable x2 is present, y is decreases by -2.

c. Suppose that the tSTAT test statistic for testing the contribution of variable X2 is negative 1.66 . At the 0.05 level of significance, is there evidence that variable X2 makes a significant contribution to the model?

Critical value of t with 15 df is 2.131

Rejection region: Reject Ho if t <-2.131 or t > 2.131

Calculated t value not in the rejection region.

There is no evidence that variable X2 makes a significant contribution to the model.

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