Consider the following sample regressions for the linear, quadratic, and the cub

Question

Consider the following sample regressions for the linear, quadratic, and the cubic mod-els along with their respective R2 and adjusted R2

Linear Quadratic Cubic

Intercept 19.80 20.08 20.07

X 1.35 1.50 1.58

X2 NA -.031 -.27

X3 NA NA -.03

R2 .640 .697 .698

Ajusted R2 .636 .691 .689

(a) Write out the linear, quadratic, and cubic population regression equations.
(b) Write out the linear, quadratic, and cubic estimated sample regression equations.
(c) Predict Y for x = 2 and 3 with each of the estimated models.
(d) Select the most appropriate model. Explain.

Explanation / Answer

a) Linear=Y=a+bX, Quadratic:Y=aX^2+bX+c, Cubic:Y=aX^3+bX^2+cX+d

b) Linear:Y=19.80+1.35X, Quadratic: Y=-0.31X^2+1.50X+20.08 Cubic:Y=-0.03X^3-0.27X^2+1.58X+20.07

c) For X=2, substitute X with 2 in all preceding equaltion, Y1=22.25, Y2=21.84, Y3=21.91

For X=3, Y1=23.85, Y2=21.79, Y3=21.57

d) Linear model seems to be best fit..

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