Question: Models with interactions. Suppose that x1 is an indicator variable with the value 0 for Group A and 1 for Group B, and x2 is

Models with interactions. Suppose that x1 is an indicator variable with the value 0 for Group A and 1 for Group B, and x2 is a quantitative variable. Each of the models below describes a relationship between μy and the explanatory variables x1 and x2.

For each model, substitute the value 0 for x1 and write the resulting equation for μy in terms of x2 for Group A. Then substitute x1 = 1 to obtain the equation for Group B and sketch the two equations on the same graph. Describe in words the difference in the relationship for the two groups.

(a) μy = 70 + 30x1 + 6x2 + 6x1x2

(b) μy = 60 − 8x1 + 7x2 − 5x1x2

(c) μy = 130 + 10x1 − 7x2 + 14x1x2

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