EXAMPLE 11.19 Quadratic Regression of Price on Square Feet
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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
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Figure 11.15: FIGURE 11.15 Quadratic regression output for predicting price using square feet, Example 11.19.
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 (, , ). 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.