After running a linear regression using the Fit Model platform, JMP displays P value (as P), RSq and RMSE on the bottom of the a Actual by Predicted Plot. I would like to understand how P value is calculated and what it means.
I ask this because in a simple Y =aX+b case, the p value is identical to the p value of the X but if there are more Xs (e.g. Y = aX1+ bX2 + c) then, p value is something else. I would like to know the meaning and calculation of p value of Actual by Predicted Plot in multiple regression situations. Any comments would be very welcomed.
The p-value underneath the Observed vs Predicted plot is the p-value from the overall analysis of variance report. This report is the overall test to determine the significance of the entire model. For example, if the model is Y=B0 + B1*X1 + B2*X2, the null hypothesis for the overall ANOVA would be Ho: B1=B2=0. So this is testing if the proposed model does better at explaining the variance in the response than the overall mean.
The calculation of the p-value is more difficult to describe in this brief response, but it is the probability of seeing the associated observed F-statistic under the null hypothesis. You calculate the p-value by finding the area under the F-distribution with the proper degrees of freedom to the right of your observed F-statistic. Thus, if the p-value is low, there is a small chance of observing the data we have. That implies that the null hypothesis is unlikely to be true.
You may wish to look into some regression books for more specific details.
I hope this helps.