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Modeling and Multivariate Methods - SAS

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264 Performing Nonlinear Regression Chapter 9<br />

Fit a Custom Model<br />

Save Std Error of Individual saves the st<strong>and</strong>ard error for an individual prediction. This is the st<strong>and</strong>ard<br />

error for predicting an individual Y value for a given X value. The formula is of the form<br />

Sqrt(VecQuadratic(matrix1,vector1)+mse). matrix1 is the covariance matrix associated with<br />

the parameter estimates, vector1 is a composition of the partial derivatives of the model with respect to<br />

each parameter, <strong>and</strong> mse is the estimate of error variance.<br />

Save Residual Formula saves the formula for computing the residuals.<br />

Save Pred Confid Limit Formula saves the formula to calculate the confidence interval for a model<br />

prediction. This is a confidence interval for the average Y for a given X.<br />

Save Indiv Confid Limit Formula saves the formula to calculate the confidence interval for an<br />

individual prediction. This is a confidence interval for an individual Y for a given X.<br />

Save Inverse Prediction Formula saves formulas for the inverse of the model, the st<strong>and</strong>ard error of an<br />

inverse prediction, <strong>and</strong> the st<strong>and</strong>ard error of an individual inverse prediction.<br />

Save Specific Solving Formula is equivalent to Save Inverse Prediction Formula in simple cases.<br />

However, this comm<strong>and</strong> allows the formula to be a function of several variables <strong>and</strong> allows expressions<br />

to be substituted. This feature only works for solving easily invertible operators <strong>and</strong> functions that occur<br />

just once in the formula.<br />

After selecting this comm<strong>and</strong>, a dialog appears that enables you to select the variable to solve for. You<br />

can also edit the names of the columns in the resulting table. You can also substitute values for the names<br />

in the dialog. In these cases, the formula is solved for those values.<br />

Note: The st<strong>and</strong>ard errors, confidence intervals, <strong>and</strong> hypothesis tests are correct only if least squares<br />

estimation is done, or if maximum likelihood estimation is used with a proper negative log likelihood.<br />

Show Prediction Expression<br />

Shows the prediction model or the loss function at the top of the report.<br />

Use the Model Library<br />

The Model Library can assist you in creating the formula column with parameters <strong>and</strong> initial values. Click<br />

the Model Library button on the Nonlinear launch window to open the library (Figure 9.14).

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