Consider a linear regression model where y represents the response variable and

Question

Consider a linear regression model where y represents the response variable and x and d are the explanatory variables; d is a dummy variable assuming values 0 or 1. A model with the dummy d and the interaction xd variables is estimated as y-hat = 5.8 + 0.99x + 1.1d + 0.22xd.

Compute y-hat for x = 11 and d = 1

Compute y-hat for x = 11 and d = 0

Consider a linear regression model where y represents the response variable and x and d are the explanatory variables; d is a dummy variable assuming values 0 or 1. A model with the dummy d and the interaction xd variables is estimated as y-hat = 5.8 + 0.99x + 1.1d + 0.22xd.

Explanation / Answer

y-hat = 5.8 + 0.99x + 1.1d + 0.22xd.

a. we have to compute y-hat for x = 11 and d = 1

so putting value in the model

y - hat = 5.8 + 0.99 * 11 + 1.1 * 1 + 0.22 * 11 *1 = 20.21

b. we have to compute y-hat for x = 11 and d = 0

so putting value in the model

y - hat = 5.8 + 0.99 * 11 + 1.1 * 0 + 0.22 * 11 *0 = 16.69

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