EXAMPLE 11.19 Quadratic Regression of Price on Square Feet

CASE 11.3 To predict price using a quadratic function of square feet, first create a new variable by squaring each value of SqFt. Call this variable SqFt2. Figure 11.15 displays the output for multiple regression of Price on SqFt and SqFt2. The fitted model is

This model explains 38.6% of the variation in Price, little more than the 37.3% explained by simple linear regression of Price on SqFt. The coefficient of SqFt2 is not significant ($t=0.84$, $\text{df}=34$, $P=0.41$). That is, the squared term does not significantly improve the fit when the SqFt term is present. We conclude that adding SqFt2 to our model is not helpful.