Consider the following sample regressions for the linear, quadratic, and the cub
ID: 3156985 • Letter: C
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..