Question

Example 7.3 is included.

It wants me to develop a formulation of the piecewise linear regression model using indicator variables. It wants us to also assume that the function is continuous at point t.

8.7 Piecewise Linear Regression. In Example 7.3 we showed how a linear regres- sion model with a change in slope at some pointt(xmint t, the model is POLYNOMIAL MODELS IN ONE VARIABLE 235 +B11 10 Boo Pol Figure 7.9 Piecewise linear regression: (a) discontinuity at the knot: (b) continuous piece- wise linear regression model. That is if x s t, the model has intercept Bo and slope Pai, while if x > t, the intercept is Ao + βο-A11 and the slope is An + βι. The regression function is shown in Figure 7.9a. Note that the parameter pro represents the difference in mean response at the knot t. A smoother function would result if we required the regression function to be continuous at the knot. This is easily accomplished by deleting the term Ao(-1): from the original model, giving Now if x s t, the model is and if x >t, the model is The two regression functions are shown in Figure 7.9b

Answer 1

The solution is as follows:

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