When running the regression analysis using a single column for X, I get a fairly low p-value (p < 0.05). When running multiple columns together (which all have p values lower than 0.05) however, the p-values strongly increase. What could be the cause of this?
Gino -
Larger data sets should have lower p-values. Maybe those data sets don't really belong together??
Do the columns represent different categories? Maybe they partially do represent different things if you look at the data source(s).
Graphical residual analyses might help.
Cheers - Jim
Hello Gino,
My guess would be that you have a pretty small sample size, such that (because of the degrees of freedom) you can get a significant result with one predictor, but not with a set of predictors (I presume you include the one that was significant by itself in the multiple regression).
As James R Knaub suggests, thinking about the variables and their meaning in the context of this analysis, as well as inspecting the errors of estimate (residuals) are both good ideas.
Good luck with your work!
Thanks for your help so far, I've been able to advance a bit.
To add to my question, is the p-value of the intercept value actually relevant?
You could look at the magnitude of the standard error compared to the intercept to consider the accuracy based on the given sample size, but I would not bother with the p-value.
If your subject matter tells you that y should be zero when x is zero, then the intercept should be set to zero by not having an intercept term. If you do use an intercept term in such cases, it should look small based on the comparison mentioned above, and there would be a loss of efficiency by using it.
Taking your original question and adding your new one, if the intercept is a large part of each prediction, that might be part of the confusion.
Try graphical residual analysis: Put predicted y on the x-axis. (If you put x there and have one predictor and no intercept term, that is going to be equivalent. It won't matter if you use x or a multiple of x like bx. But if there is a non-zero intercept, it might be better to interpret if you stay with predicted y as you would for multiple regression.) Put the estimated residuals on the y-axis. There is a good deal of information on the internet regarding interpretation of the resulting graph. You could do that for each data set you mentioned, and another one for all combined. That might help show you what is going on.
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