I have a very simple question. I know that the R-squared is the proportion of the variance for a dependent variable that's explained by an independent variable or variables in a regression model.
I also know that the p-value is the probability of obtaining test results at least as extreme as the results actually observed, under the assumption that the null hypothesis is correct.
My question essentially is, is the value of the R-squared only dependent on the coefficients? Or also on the significance of the coefficients? In other words, does an increase in the p-value of a Beta estimate, ceteris paribus (everything else equal) affect the R-squared?