Question

Consider the following sample regressions for the linear, the quadratic, and the cubic models along with their respective R2 and adjusted R2.

Linear Quadratic Cubic
Intercept 29.83 29.35 26.88
x −0.04 0.16 2.11
x2 NA −0.02 −0.38
x3 NA NA 0.02
R2 0.001 0.001 0.008
Adjusted R2 −0.026 −0.053 −0.075
a. Predict y for x = 1 and 2 with each of the estimated models.
b. Select the most appropriate model.
1. Linear model
2. Cubic model
3. Quadratic model

Answer 1

Kindly check explanation

Explanation:

From the given information :

Linear model : y = - 0.04x + 29.83

Quadratic model : y = - 0.02x² + 0.16x + 29.35

Cubic model : y = 0.02x³ - 0.38x² + 2.11x + 26.88

Predicted y value for X = 1 ; X = 2

Linear model :

y = - 0.04(1) + 29.83 = 29.79

y = - 0.04(2) + 29.83 = 29.75

Quadratic model :

X = 1

y = - 0.02(1)^2 + 0.16(1) + 29.35 = 29.49

X = 2

y = - 0.02(2)^2 + 0.16(2) + 29.35 = 29.59

Cubic model :

X = 1

y = 0.02(1)^3 - 0.38(1)^2 + 2.11(1) + 26.88 = 28.63

X = 2

y = 0.02(2)^3 - 0.38(2)^3 + 2.11(2) + 26.88 = 28.22

Based on the R² value of the models given :

Linear ; R² = 0.001 ; R = sqrt(0.001) = 0.0316

Quadratic ; R² = 0.001 ; R = sqrt(0.001) = 0.0316

Cubic ; R² = 0.008 ; R = sqrt(0.008) = 0.089

Hence, the model which best fits the data is Cubic model.