Improve the accuracy of predictions with advanced regression procedures

IBM® SPSS® Regression software enables you to predict categorical outcomes and apply a range of nonlinear regression procedures. You can apply the procedures to business and analysis projects where ordinary regression techniques are limiting or inappropriate—such as studying consumer buying habits, responses to treatments or analyzing credit risk.

With SPSS Regression software, you can expand the capabilities of IBM SPSS Statistics Base for the data analysis stage in the analytical process.

**Predict categorical outcomes**with more than two categories using multinomial logistic regression (MLR).**Easily classify your data**into groups using binary logistic regression.**Estimate parameters of nonlinear models**using nonlinear regression (NLR) and constrained nonlinear regression (CNLR).**Meet statistical assumptions**using weighted least squares and two-stage least squares.**Evaluate the value of stimuli**using probit analysis.

## SPSS Regression Screenshots

**Binomial regression parameter estimates**

The parameter estimates table summarizes the effect of each predictor. The ratio of the coefficient to its standard error, squared, equals the Wald statistic. If the significance level of the Wald statistic is small (less than 0.05) then the parameter is useful to the model. The predictors and coefficient values shown in the last step are used by the procedure to make predictions.

**Multinomial regression parameter estimates**

The parameter estimates table summarizes the effect of each predictor. The ratio of the coefficient to its standard error, squared, equals the Wald statistic. If the significance level of the Wald statistic is small (less than 0.05) then the parameter is different from 0. Parameters with significant negative coefficients decrease the likelihood of that response category with respect to the reference category. Parameters with positive coefficients increase the likelihood of that response category.

**Multinomial regression classification**

The classification table shows the practical results of using the multinomial logistic regression model. For each case, the predicted response category is chosen by selecting the category with the highest model-predicted probability. Cells on the diagonal are correct predictions. Cells off the diagonal are incorrect predictions.

**Nonlinear regression parameter estimates**

The parameter estimates table summarizes the model-estimated value of each parameter. Parameters in a nonlinear regression model usually do not have the same interpretation as linear regression coefficients, and often vary from model to model. In this example, b1 represents the maximum possible sales, even if infinite advertising money were available. Its small standard error with respect to the value of the estimate suggests that you can be confident in the estimate. b2 is the difference between maximum possible sales and sales when no advertising money is spent. Its standard error is large and confidence interval is wide compared to the value of the estimate, so there is some uncertainty here. b3 controls the rate at which the maximum is reached, the so-called "rate constant". Like b2, there is some uncertainty in the estimate.

**Predict categorical outcomes**

- Using MLR, regress a categorical dependent variable with more than two categories on a set of independent variables. This helps you accurately predict group membership within key groups.
- Use stepwise functionality, including forward entry, backward elimination, forward stepwise or backward stepwise, to find the best predictor.
- For a large number of predictors, use Score and Wald methods to help you quickly reach results.
- Assess your model fit using Akaike information criterion (AIC) and Bayesian information criterion (BIC).

**Easily classify your data**

- Using binary logistic regression, build models in which the dependent variable is dichotomous; for example, buy versus not buy, pay versus default, graduate versus not graduate.
- Predict the probability of events such as solicitation responses or program participation.
- Select variables using six types of stepwise methods. This includes forward (select the strongest variables until there are no more significant predictors in the data set) and backward (at each step, remove the least significant predictor in the data set).
- Set inclusion or exclusion criteria.

**Estimate parameters of nonlinear models**

- Estimate nonlinear equations using NLR for unconstrained problems and CNLR for both constrained and unconstrained problems.
- Using NLR, estimate models with arbitrary relationships between independent and dependent variables using iterative estimation algorithms.
- With CNLR, use linear and nonlinear constraints on any combination of parameters.
- Estimate parameters by minimizing any smooth loss function (objective function), and compute bootstrap estimates of parameter standard errors and correlations.

**Meet statistical assumptions**

- If the spread of residuals is not constant, use weighted least squares to estimate the model. For example, when predicting stock values, stocks with higher share values fluctuate more than low-value shares.
- Use two-stage least squares to estimate the dependent variable when the independent variables are correlated with regression error terms. This allows you to control for correlations between predictor variables and error terms.

**Evaluate the value of stimuli**

- Use probit analysis to estimate the effects of one or more independent variables on a categorical dependent variable.
- Evaluate the value of stimuli using a logit or probit transformation of the proportion responding.

### SPSS Regression resources

- Data sheet: IBM SPSS Regression (534KB)
Learn how to apply more sophisticated models to your data using a wide range of nonlinear regression procedures.

- Trial software: IBM SPSS Statistics Desktop
Identify your best customers, forecast future trends, and perform advanced analysis.

- White paper: Seven Reasons You Need Predictive Analytics Today
Learn about the seven strategic objectives that can be attained by employing predictive analytics.

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