If the value of correlation is insignificant or negligible. Whether We should run regression analysis or not. Obviously it will be insignificant, is it necessary to mention in article?
Hello Annu,
If you're asking, for a single candidate IV, if it shows a nonsignificant correlation with the target dependent variable (DV), should you then proceed with a bivariate regression (1 IV, 1 DV)? No, because you've already tested whether there is a nonzero slope for the best fitting regression line by evaluating whether the Pearson correlation is nonzero.
If you are screening a set of potential IVs for subsequent inclusion in a regression model, and only retaining those which show a significant bivariate relationship with the chosen DV, then:
1. Yes, you would mention all candidate IVs in your documentation;
2. Please recognize that this process is in no way guaranteed to yield the best ensemble of IVs for explaining differences in DV scores. As one simple example, the method above will almost assuredly omit possible suppressor variables.
Good luck with your work.
"Significance" is not what should concern you. It is a function of sample size, and even if you compare x-variables with the same sample size in a multiple regression, issues such as collinearity could foul such comparisons. Of course if your sample size is too small, you won't be able to discover much of anything. But you might try plotting the points with a regression "line," and put curves around it using the estimated variance of the prediction error. Don't forget heteroscedasticity. I know SAS does a good job of this. You could put predicted-y on the x-axis and the y-values on the y-axis (or estimated residuals on the y-axis when looking for heteroscedasticity, which is natural, associated with the predicted-yi as a size measure).
Penn State has some good introductory material on this, though they did not include heteroscedasticity, the last time I looked. You can find information from Penn State by searching on a term, and including "Pennsylvania State University" in the search.
Best wishes.
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