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I am doing multiple regression analysis. I was looking for help in interpreting a special case of output. In my regression, the overall p value for the test is less than 0.05 and the variables are also significant. But the P value for the constant is not significant and is above 0.05.
How does this condition impact the interpretation of results. The residual analysis also does not indicate much issue.
The p values in the regression refer to the significance of the terms in the regression model. For any particular X a lack of significance with respect to Y means that the slope of the regression line relating that X and Y has not tested as being significantly different from 0. For the constant an insignificant p-value means the interecept is not significantly different from 0.
To see this run the following regression
Now run the regression again only add 2 to every value of Y.
In the first case you will have a p value of .36 for the intercept and in the second case you will have a p value of <.0001
As for impacting the rest of the regression – not much – look at the various summary statistics for the above to examples – no changes in R2 or RMSE and, as you noted, no changes in the residual patterns.
Given that we are talking about significance of intercepts and not significance of slopes this really isn’t too surprising.
in layman terms: the regression multi-plane is calculated to meet Y=Constant on location (0,…,0) for the X’s. But that Constant is calculated from the data from the sample. The high p-value for Constant means that the Confidence Interval of that Constant contains 0 so that it is possible that the multi-plane goes through the origin (Y=0) instead of through Y=Constant.
The high p-value for Constant happens often when the area of interest fr the X’s is ‘far from the origin’ (for example: temperatures are varied from 400-660 C, then the prediction of the model for 0 C has a large Confidence Interval).
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