# Minitab Help: Poisson & Nonlinear Regression

Minitab Help: Poisson & Nonlinear Regression
## Hospital recovery (exponential regression)

- Select Calc > Calculator to create a log(prog) variable.
- Obtain starting values for nonlinear model parameters from fitting a simple linear regression model of log(prog) vs days.
- Select Stat > Regression > Nonlinear Regression to fit a nonlinear regression model to data using these starting values. Put prog in the "Response" box and type "Theta1 * exp(Theta2 * days)" into the box labeled "Edit directly." Before clicking OK, click "Parameters" and enter 56.7 as the starting value for Theta1 and -0.038 as the starting value for Theta2.
- A scatterplot of prog vs days with a fitted line based on the nonlinear regression model is produced by default.

## U.S. Census population (population growth nonlinear regression)

- Obtain starting values for nonlinear model parameters from observing features of a scatterplot of population vs year.
- Select Stat > Regression > Nonlinear Regression to fit a nonlinear regression model to data using these starting values. Put population in the "Response" box and type "beta1 / (1 + exp(beta2 + beta3 * (year - 1790) / 10))" into the box labeled "Edit directly." Before clicking OK, click "Parameters" and enter 56.7 as the starting value for Theta1 and -0.038 as the starting value for Theta2.
- A scatterplot of population vs year with a fitted line based on the nonlinear regression model is produced by default.
- Before clicking "OK" in the Regression Dialog, click "Graphs" and put the year in the "Residuals versus the variables" box.

## Poisson example (Poisson regression)

- Select Graph > Scatterplot to create a scatterplot of the data.
- Select Stat > Regression > Poisson Regression > Fit Poisson Model, put y in the "Response" box, and put x in the "Continuous predictors" box. Before clicking "OK," click "Results" and select "Expanded tables" for "Display of results."
- Before clicking "OK" in the Regression Dialog, click "Graphs" and select "Residuals versus Fits" to create residual plots using deviance residuals. To change to Pearson residuals, click "Options" in the Regression Dialog and select "Pearson" for "Residuals for diagnostics."

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