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

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 29.79 31.64 37.85

x 0.16 0.99 6.11

x2 NA 0.07 1.09

x3 NA NA 0.06

R2 0.010 0.023 0.090

Adjusted R2 0.016 0.030 0.014

a. Predict y for x = 2 and 6 with each of the estimated models. (Round your answers to 4 decimal places.)

Linear Quadratic Cubic

x = 2

x = 6

b. Select the most appropriate model.

Cubic model

Quadratic model

Linear model

Explanation / Answer

Equations:

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

a) x = 2

Linear : Y=a+bX

y = 29.79 - 0.16 * 2 = 29.47

Quadratic:

y = 0.07 * x^2 - 0.99 * x + 31.64

y = 0.07 * 2^2 - 0.99 * 2 + 31.64

y = 29.94

Cubic:

y = - 0.06 * x^3 + 1.09 * x^2 - 6.11 * x + 37.85

y = - 0.06 * 2^3 + 1.09 * 2^2 - 6.11 * 2 + 37.85

y = 29.51

x = 6

y = 29.79 - 0.16 * 6 = 28.83

Quadratic:

y = 0.07 * x^2 - 0.99 * x + 31.64

y = 0.07 * 6^2 - 0.99 * 6 + 31.64

y = 28.22

Cubic:

y = - 0.06 * x^3 + 1.09 * x^2 - 6.11 * x + 37.85

y = - 0.06 * 6^3 + 1.09 * 6^2 - 6.11 * 6 + 37.85

y = 27.47

b) R^2 value for cubic is highest

So, cubic is the best odel

Related Questions

Navigate

• Browse (All)
• Browse C
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.