Example: A Second Order Model with One Explanatory Variable

The effectiveness of a new overdrive gear in reducing gas consumption was studied in 12 trials with a light truck equipped with this gear.

The plot of the data is below. There appears to be a quadratic relationship.

To see that it would be inappropriate to fit a straight line to this data, the least squares line calculated by Minitab is plotted with the data below. Clearly it is a poor description of the relationship.

To fit a quadratic model in Minitab, the first thing we would have to do is use the Calc selection on the menu to create a new variable, labelled Speedsq below, which contains the squared values of Speed.

Regression Analysis: Mileage versus Speed, Speedsq

The regression equation is

Mileage = - 183 + 8.98 Speed - 0.0911 Speedsq

Predictor Coef SE Coef T P

Constant -182.58 17.68 -10.33 0.000

Speed 8.9832 0.7616 11.80 0.000

Speedsq -0.091071 0.007993 -11.39 0.000

S = 1.727 R-Sq = 94.7% R-Sq(adj) = 93.6%

Analysis of Variance

Source DF SS MS F P

Regression 2 483.17 241.58 81.03 0.000

Residual Error 9 26.83 2.98

Total 11 510.00

Source DF Seq SS

Speed 1 96.11

Speedsq 1 387.05