Is it possible to tweak the statistical significance of variables in a regression? my regression gives me a p-value of 0.03039 for my coefficient (beta) and 0.22488 for my intercept (alpha). I am mostly interested in my alpha and want to improve its statistical significance. Is this possible without adding any new data? I already used all the data available. The standard errors are robust.
I used the lm funtion of r.
 A: The answer is yes and no. Yes, there are ways to do that (including faking data and other kinds of cheating and manipulation). No, none of them is valid. In particular, the theory of significance tests assumes that they are run unconditionally, meaning that they become invalid if they are only chosen because some other analysis of the same data before gave a certain result (the only exception is if it was specified before analysing the data what exactly you do in what case, as in sequential analysis). But this is now the situation in which you are. So assuming that the first test you ran was correct, every further one that you apply because this one didn't give you significance will be invalid.
To add some more, a significance test gives you information about your data. This information can turn out one way or another. If it were not like this, it wouldn't be informative. This in particular means that you should accept the results as they are. If you are guided by the idea that a significant result is better and should be achieved (which is implied by your use of the word "improved"), you are engaged in wishful thinking rather than science.
A: I would add to Lewian's response that insignificance does not mean you have to strike the variable out of the estimation. For example, if you include a variable which has a p-value of 0.055, it won't be significant at the 5% level. However, if by including the variable it affected the model's explanatory power positively, and reduced omitted variable bias which can be seen through the coefficients of other variables, then it would be rather arbitrary to exclude it just because it isn't significant at a certain level. When conducting multivariate regressions, in essence you want to be maximizing explanatory power, not individual significance of variables. Unfortunately, in my experience at different levels of educations, this emphasis on significance teaches students the opposite.
A: Your emphasis on the "significance" of the intercept might be misplaced.
In a regression, the intercept is the estimated value of the outcome when all continuous predictors have values of 0 and (under standard treatment coding) all categorical predictors are at their reference levels. The "significance" of an intercept is how reliably its value can be distinguished from 0.
So things as simple as changing the centering a continuous predictor or re-coding a categorical predictor can change the value and thus the "significance" of the intercept. Unless the nature of your study requires a specific centering of continuous predictor values and particular coding of categorical predictors, there isn't much practical significance to the statistical "significance" of an intercept.
