Is it correct to say that if the significance of a variable is very high (p<0.001) and the coefficient is very large that the variable is important in a general sense?
If not can you give an example?
Thank you
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"Important in a general sense" is hard to define, but if your interest is in trying to make causal inferences you will have a problem if a particular variable just happens to correlate with a truly "important" variable.
The answer from @TheJiminySea on this Cross Validated page has an amusing example with predictor variables "Years of work experience" and "Number of carrots eaten in one's lifetime". These 2 variables are likely to be highly correlated, but for predicting things like income "Years of work experience" is presumably the "important" variable. Nevertheless, if you did analyses with "Number of carrots ..." as the predictor of income you might still get highly significant p-values and large coefficients.
So you have to be careful in what you mean by "important".
