How to calculate R-square from adjusted r-square, n, and p? Let $\bar{R}^2$ denote the adjusted coefficient of determination.
I have $\bar{R}^2 = 0.9199$ with 15 cases. Now I am trying to find $R^2$ given the results below. 
I found the formula for $R^2$ but did not understand it. How do you calculate $R^2$ from $\bar{R}^2$?

$\bar{R}^2 = 1-\dfrac{(n-1)(1- R^2)}{n-p-1}$


 A: Given the equation for $\bar{R}^2$ you have:
$\bar{R}^2 = 1-\dfrac{(n-1)(1- R^2)}{n-p-1}$
You have $3$ regressors and a sample of $15$, thus substituting these and $\bar{R}2$ into the equation yields:
$0.9199 = 1 - \dfrac{(15-1)(1-R^2)}{15-3-1}$
Rearranging this expression and solving for $R^2$ gives:
$R^2 = 0.9371$
A: Well, I think there is a little mistake in the equation. 
$p$ stands for the number of parameters, which means the number of predictors plus one for the constant.
$k$ stands for the number of predictors.
Thus, 
\begin{align}
p=k+1\tag{1}.
\end{align}
The equation using $p$ is as follows:
\begin{align}
1-\frac{(n-1)(1-R^2)}{n-p} \tag{2}.
\end{align}
If you substitute equation $(1)$ in $(2)$ you got
$$ 
1-\frac{(n-1)(1-R^2)}{n-(k+1)}=1-\frac{(n-1)(1-R^2)}{n-k-1}.
$$
The equation using $k$ is as follows:
$$
1-\frac{(n-1)(1-R^2)}{n-k-1}.
$$
I know it is very common mistake. The degree of freedom for the SSR is $p-1$. For simple regression, the $\mathrm{df}$ of SSR is either $k=p-1=1$. 
A: As was stated above, the answer by GovEcon is wrong.
Wiki defines p in the above formula as: "where p is the total number of explanatory variables in the model (not including the constant term), and n is the sample size."
The parameters three parameters. Excluding the intercept (constant/beta0) p = 2.
That being said it would be easier to calculate $R^2$ as follows.
The formula for $R^2$ adjusted can be given as:
$R^2_{adj} = 1 - (n-1){MSE \over SST}, MSE = {SSE \over (n-p-1)}$
$= 1 - (n-1)[({SSE \over n-p-1})/SST] = 1 - [{(n-1)\over(n-p-1)}]*({SSE \over SST})$
If you recall from the definition that $R^2$ adjusted controls for increase in $R^2$ due to  increase in parameters then it makes sense that removing [{(n-1) \over (n-p-1)}$] should give you $R^2$
$R^2 = 1 - {SSE \over SST}$
Check by plugging in:
${SSE \over SST} = 1 - R^2$
Original formula: 
$R^2_{adj} = 1 - [(n-1)/(n-p-1)]*(1-R^2)$ = original formula 
Then, $R^2_{adj} = 1 - (n-1)*(MSE/SST) = 1- (15-1)(8224/1436706) = ~.9198 $
$R^2 = 1- SSE/SST = 1- 98690/1436706 = ~.931$ NOT $.9371$
Note: the anova table is already rounded MSE = SSE/ (n-p-1) = 98690/(15-2-1) = 8224.16666 = ~8224. So discrepancies with table arise from here.
Aside: I don't know how to format equations and don't have time to do it now, but I do not want the current answer to mislead more people.
A: You must also take into consideration what does constant mean. If it is Intercept, then you have two independent variables, which means $k=2$, not $3$.
