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A regression formula that gives a parabolic shape instead of

A regression formula that gives a parabolic shape instead of a straight line for the relationship between two variables is μy = α + β1x + β2 x2.

a. Explain why this is a multiple regression model, with x playing the role of x1 and x2 (the square of x) playing the role of x2.

b. For x between 0 and 5, sketch the prediction equation (i) = 10 + 2x + 0.5x2 and (ii) = 10 + 2x - 0.5x2.This shows how the parabola is bowl-shaped or mound-shaped, depending on whether the coefficient x2 is positive or negative.

a. Explain why this is a multiple regression model, with x playing the role of x1 and x2 (the square of x) playing the role of x2.

b. For x between 0 and 5, sketch the prediction equation (i) = 10 + 2x + 0.5x2 and (ii) = 10 + 2x - 0.5x2.This shows how the parabola is bowl-shaped or mound-shaped, depending on whether the coefficient x2 is positive or negative.

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