Continuous Responses

When the response column (column assigned the Y role) is continuous, JMP fits the value of the response directly. The basic model is that for each observation,

Y = (some function of the X’s and parameters) + error

Statistical tests are based on the assumption that the error term in the model is normally distributed.

Fitting Principle for Continuous Response

The Fitting principle is called least squares. The least squares method estimates the parameters in the model to minimize the sum of squared errors. The errors in the fitted model, called residuals, are the difference between the actual value of each observation and the value predicted by the fitted model.

The least squares method is equivalent to the maximum likelihood method of estimation if the errors have a normal distribution. This means that the analysis estimates the model that gives the most likely residuals. The log-likelihood is a scale multiple of the sum of squared errors for the normal distribution.

Base Model for Continuous Responses

The simplest model for continuous measurement fits just one value to predict all the response values. This value is the estimate of the mean. The mean is just the arithmetic average of the response values. All other models are compared to this base model.