A regression formula that gives a parabolic shape instead of a straight line for the relationship between two variables is Icirc frac14 y Icirc plusmn Icirc sup2 1x Icirc sup2 2 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 ...

a This is a multiple regression model ...

A regression formula that gives a parabolic shape instead of a straight line for the relationship between

Question:

A regression formula that gives a parabolic shape instead of a straight line for the relationship between two variables is Î¼y = Î± + Î²1x + Î²2 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.