My hypothesis is: Company size (CSIZE) is positively correlated with Return on Assets (ROA).
I create a Pearson correlation matrix in Stata using
pwcorr csize roa and it returns a correlation of
0.2 with a 5% significance level.
Now I also want create a multiple regression to test Company Age (CAGE) and Company Size (CSIZE) on Return on Assets (ROA).
I create a linear regression model in Stata using
regress roa cage csize
I returns low
R^2=0,007 and low F-statistic
1,08. Neither independent variable had significant T-statistic either.
My question is how to interpret such a result: The low R^2 means my model does not explain much of the variation. Plus it is not significant. But is that only for the combined effect of both independent variables (CAGE+CSIZE) on the dependent variable (ROA)? The individual t-test was also insigificant, so what about the result from my Pearson correlation?
I am having a hard time seeing how linear regression and Pearson correlation relates to each other, and what implications the results of both have on my hypothesis.