Use to model the relationship a continuous explanatory variable has with a categorical outcome variable. Useful for estimating the probability of the occurrence of an event for different values of the explanatory variable.
Logistic Regression Using Fit Y by X
- From an open JMP® data table, select Analyze > Fit Y by X.
- Click on a categorical variable from Select Columns, and click Y, Response (nominal variables have red bars, ordinal variables have green bars).
- Click on a continuous variable, and click X, Factor (continuous variables have blue triangles). Click OK.
By default, JMP will provide the following results:
- The logistic plot, with curves of cumulative predicted (fitted) probabilities.
- The whole model test for model significance.
- Parameter estimates for the fitted model, among others.
Note: Default output can be changed via Preferences (File > Preferences)
- When the response is nominal, a nominal logistic model will be fit. When the response is ordinal, as in this example, an ordinal logistic model will be fit.
- To color points and add a legend, right-click in the graph and select Rows > Row Legend.
- To save the probability formula or request other options, click on the top red triangle and select the option.
- To find the fitted probability for a given value of X, select the cross-hair tool (
) from the toolbar. Click on the graph dragging the cross-hair to the desired point on the curve.
Interpretation (for this example, X = buying age and Y = car size):
• The bottom curve represents the predicted probability that for a given age, someone will buy a large car.
• The second curve represents the probability that someone will buy a large or medium car.
• The distance between the two curves represents the probability that someone will buy a medium car.
• The distance between 1.00 and the top curve represents the probability that someone will buy a small car.
• The cross-hairs show that the predicted probability that someone aged 39 years will purchase a large car is 0.191.
Notes: Simple nominal and ordinal logistic regression can also be performed from Analyze > Fit Model.
Visit Basic Analysis > Logistic Analysis in JMP Help to learn more.
Audio Transcription of Video
In this video, we will explore one method for performing simple logistic regression. Logistic regression is useful to predict the probability of an occurrence or an event.
I'm using the Car Poll example data set available in the sample data directory to start our logistic regression. We'll go to analyze Fit Y by X. Fit Y by X is a contextual platform and the type of analysis run will depend on the variable types we provide for our Y response, which is what we're trying to predict.
I'm going to use an ordinal variable here, size, as a predictor. I'm going to use the age of the person in the survey. When I click, OK, JMP will produce the ordinal logistic regression. If our Y variable only had two levels, JMP would have produced a nominal logistic regression. By default, JMP will provide the logistic plot whole model test and parameter estimates. The logistic plot shows the predicted probabilities of falling into one of our categories, large medium or small car, on the basis of our predictor age. In this case, the lower line shows the predicted probability of owning a large car depending on the age of the individual. The upper line shows the predicted probability of owning a medium or large car on the basis of age.
Individual observations here are jittered within their space. This person, for instance, in row 256, does not have a value on the Y axis. Rather, this person indicated that they drove a medium car, and so they are placed into the medium section. This jittering is done to give a proper sense of the proportion of individuals falling into a particular category. To color our points, we can right click and select row legend. Here, I'll select size of car as my row legend and click OK. JMP will color the points on the basis of the size of cars. For statistical results on whether age is predictive of car size, we can scroll down to the parameter estimate section and look at the parameter estimate for age. Here we see that we have a statistically significant effect of age on the category membership of an individual.