Normal Regression with a Log Link

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Fitting Linear Models • Generalized Linear Models • Additional Examples of the Generalized Linear Models Personality • Normal Regression with a Log Link

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This example uses the Nor.jmp data table, where X is an explanatory variable and Y is the response variable. First, you explore the relationship between X and Y to determine the appropriate link function to use in the Generalized Linear Model personality of the Fit Model platform.

Select Help > Sample Data Library and open Nor.jmp.

Select Analyze > Fit Y By X.

Select Y and click Y, Response.

Select X, click X, Factor, and then click OK.

Figure 11.8 Y by X Results for Nor.jmp

You can see that Y varies nonlinearly with X and that the variance is approximately constant. Therefore, a normal distribution with a log link function is appropriate to model these data; that is, log(μi) = xi'β so that μi = exp(xi'β).

Select Analyze > Fit Model.

In the Personality list, select the Generalized Linear Model.

In the Distribution list, select Normal.

In the Link Function list, select Log.

Select Y and click Y.

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Select X and click Add.

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Click Run.

Figure 11.9 Nor Results

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Help created on 10/11/2018