A bit of a stupid question…
If you have a regression output with a high r-squared/F-stat, but one of the coefficients is insignificant (slope or intercept), can the output still be used? Or would you have to make any adjustments? Assuming multicollinearity is not an issue of course.
yes, the regression equation can still be used. you don’t drop a variable from the equation just because the beta isn’t significant.
If you have spotted an statistically insignificant coefficient on your model, it is advised to remove it in order to reduce error variance and also to check if the other variables are still significant after removing the rotten variable. Why would a researcher use her model before doing this step?
You don’t need to remove the variable if it is theoretically or empirically (mountains of prior research) justified. In fact, it is unwise to conduct significance testing on these kinds of variables because it is nonsensical. If you KNOW that interest rates effect prices, why test the coefficient of interest rate for the regression of price? It’s theoretically justified as a variable and there is great research to justify it. A nonsignificant coefficient more likely represents data artifact. Blindly following p-values is a recipe for disaster.