A regression model with a dummy variable d, a quantitative variable x , and an interaction variable xd is specified b y y 0 1x 2d 3xd We estimate this model to make predictions as (b0 b2) (b1 b3)x for d 1, and as b0 b1x for d 0 In addition, we can perform the t test to determine the significance of d or xd Similarly, we can implement the partial F test to determine the joint significance of d and xd

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Question: A regression model with a dummy variable d, a quantitative variable x , and an interaction variable xd is specified b y y =

A regression model with a dummy variable

d, a quantitative variable x , and an interaction variable xd is specified b y y = β 0 + β1x + β 2d + β 3xd + ε . We estimate this model to make predictions as ŷ = (b0 + b2) + (b1 + b3)x for d = 1, and as ŷ = b0 + b1x for d = 0. In addition, we can perform the t test to determine the significance of d or xd. Similarly, we can implement the partial F test to determine the joint significance of d and xd.

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