Interpret all statistics for Predict for Binary Logistic

Find definitions and interpretation guidance for every statistic that is provided with the prediction analysis.

Regression Equation for Binary Logistic Regression

For binary logistic regression, Minitab shows two types of regression equations. The first equation relates the probability of the event to the transformed response.

The second equation relates the predictors to the transformed response. If the model contains both continuous and categorical predictors, the second equation can be separated for each combination of categories.

Interpretation

Use the equations to examine the relationship between the response and the predictor variables.

For example, a model to predict whether a customer buys a product has these terms:
• Customer's income
• Whehter the customer viewed the ad

The first equation shows the relationship between the probability and the response.

The second set of equations show how income and whether the individual viewed the cereal ad relate to the response. The coefficient for income is about 0.02, whether or not the customer views the ad. For these equations, the more income a customer has, the more likely they are to buy the product.

 Regression Equations
 P(1) = exp(Y')/(1 + exp(Y'))
 ViewAd No Y' = −2.4148 + 0.02656 Income Yes Y' = −1.2946 + 0.02656 Income

Variable settings

Minitab Express uses the regression equation and the variable settings to calculate the fit. If the variable settings are unusual compared to the data that was used to estimate the model, then a warning is displayed below the prediction.

Use the variable settings table to verify that you performed the analysis as you intended.

Fitted probability

The fitted probability is also called the event probability or predicted probability. Event probability is the chance that a specific outcome or event occurs. The event probability estimates the likelihood of an event occurring, such as drawing an ace from a deck of cards or manufacturing a non-conforming part. The probability of an event ranges from 0 (impossible) to 1 (certain).

Interpretation

In binary logistic regression, a response variable has only two possible values, such as the presence or absence of a particular disease. The event probability is the likelihood that the response for a given factor or covariate pattern is 1 for an event (for example, the likelihood that a woman over 50 will develop type-2 diabetes).

Each performance in an experiment is called a trial. For example, if you flip a coin 10 times and record the number of heads, you perform 10 trials of the experiment. If the trials are independent and equally likely, you can estimate the event probability by dividing the number of events by the total number of trials. For example, if you flip 6 heads out of 10 coin tosses, the estimated probability of the event (flipping heads) is:

Number of events ÷ Number of trials = 6 ÷ 10 = 0.6

SE Fit

The standard error of the fit (SE fit) estimates the variation in the estimated probability for the specified variable settings. The calculation of the confidence interval for the prediction uses the standard error of the fit. Standard errors are always non-negative.

Interpretation

Use the standard error of the fit to measure the precision of the estimate of the mean response. The smaller the standard error, the more precise the predicted mean response. With the fitted value, you can use the standard error of the fit to create a confidence interval for the fitted probability.

Confidence Interval for fit (95% CI)

These confidence intervals (CI) are ranges of values that are likely to contain the fitted probability for the population that has the observed values of the predictor variables that are in the model.

Interpretation

Use the confidence interval to assess the estimate of the fitted value for the observed values of the variables.

For example, with a 95% confidence level, you can be 95% confident that the confidence interval contains the event probability for the specified values of the variables in the model. The confidence interval helps you assess the practical significance of your results. Use your specialized knowledge to determine whether the confidence interval includes values that have practical significance for your situation. If the interval is too wide to be useful, consider increasing your sample size.

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