Curve Estimation

The Curve Estimation procedure produces curve estimation regression statistics and related plots for 11 different curve estimation regression models. A separate model is produced for each dependent variable. You can also save predicted values, residuals, and prediction intervals as new variables.

Example. An Internet service provider tracks the percentage of virus-infected e-mail traffic on its networks over time. A scatterplot reveals that the relationship is nonlinear. You might fit a quadratic or cubic model to the data and check the validity of assumptions and the goodness of fit of the model.

Statistics. For each model: regression coefficients, multiple R, R 2, adjusted R 2, standard error of the estimate, analysis-of-variance table, predicted values, residuals, and prediction intervals. Models: linear, logarithmic, inverse, quadratic, cubic, power, compound, S-curve, logistic, growth, and exponential.

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Curve Estimation Data Considerations

Data. The dependent and independent variables should be quantitative. If you select Time from the active dataset as the independent variable (instead of selecting a variable), the Curve Estimation procedure generates a time variable where the length of time between cases is uniform. If Time is selected, the dependent variable should be a time-series measure. Time-series analysis requires a data file structure in which each case (row) represents a set of observations at a different time and the length of time between cases is uniform.

Assumptions. Screen your data graphically to determine how the independent and dependent variables are related (linearly, exponentially, etc.). The residuals of a good model should be randomly distributed and normal. If a linear model is used, the following assumptions should be met: For each value of the independent variable, the distribution of the dependent variable must be normal. The variance of the distribution of the dependent variable should be constant for all values of the independent variable. The relationship between the dependent variable and the independent variable should be linear, and all observations should be independent.

To Obtain a Curve Estimation

  1. From the menus choose:

    Analyze > Regression > Curve Estimation...

  2. Select one or more dependent variables. A separate model is produced for each dependent variable.
  3. Select an independent variable (either select a variable in the active dataset or select Time).
  4. Optionally:
  • Select a variable for labeling cases in scatterplots. For each point in the scatterplot, you can use the Point Selection tool to display the value of the Case Label variable.
  • Click Save to save predicted values, residuals, and prediction intervals as new variables.

The following options are also available:

  • Include constant in equation. Estimates a constant term in the regression equation. The constant is included by default.
  • Plot models. Plots the values of the dependent variable and each selected model against the independent variable. A separate chart is produced for each dependent variable.
  • Display ANOVA table. Displays a summary analysis-of-variance table for each selected model.

This procedure pastes CURVEFIT command syntax.