Cubic regression is another form of regression where the parameters in a linear regression model are increased up to one or two levels of polynomial calculation. Using the Cars93_1.csv dataset, let's understand the cubic regression:

> fit.6<-lm(MPG.Overall~ I(Price)^3+I(Horsepower)^3+I(RPM)^3+

+ Wheelbase+Width+Turn.circle, data=Cars93_1[-c(28,42,39,59,60,77),])

> summary(fit.6)

Call:

lm(formula = MPG.Overall ~ I(Price)^3 + I(Horsepower)^3 + I(RPM)^3 +

Wheelbase + Width + Turn.circle, data = Cars93_1[-c(28, 42,

39, 59, 60, 77), ])

Residuals:

Min 1Q Median 3Q Max

-5.279 -1.901 -0.006 1.590 8.433

Coefficients:

Estimate Std. Error t value Pr(>|t|)

(Intercept) 57.078025 12.349300 4.622 1.44e-05 ***

I(Price) -0.108436 0.065659 -1.652 0.1026

I(Horsepower) -0.024621 0.015102 -1.630 0.1070

I(RPM) 0.001122 0.000727 1.543 0.1268

Wheelbase -0.201836 0.079948 -2.525 0.0136 *

Width -0.104108 0.198396 -0.525 0.6012

Turn.circle -0.095739 0.158298 -0.605 0.5470

---

Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 2.609 on 80 degrees of freedom

Multiple R-squared: 0.6974, Adjusted R-squared: 0.6747

F-statistic: 30.73 on 6 and 80 DF, p-value: < 2.2e-16

> vif(fit.6)

I(Price) I(Horsepower) I(RPM) Wheelbase Width Turn.circle

4.121923 7.048971 2.418494 3.701812 7.054405 3.284228

> coefficients(fit.6)

(Intercept) I(Price) I(Horsepower) I(RPM) Wheelbase Width

57.07802478 -0.10843594 -0.02462074 0.00112168 -0.20183606 -0.10410833

Turn.circle

-0.09573848

Keeping all other parameters constant, one unit change in the independent variable would bring a multiplicative change in the dependent variable and the multiplication factor is the cube of the beta coefficients.