Hi I'm trying to find the value of $R^2$ but I think that I'm missing something. I've been given the values of the following sums: $$\sum_{i=1}^n x_i\ \ \ \ \ \ \ \ \ \ \ \ \ \ \sum_{i=1}^n y_i\ \ \ \ \ \ \ \ \ \ \ \ \ \ \sum_{i=1}^n x_i^2\ \ \ \ \ \ \ \ \ \ \ \ \ \ \sum_{i=1}^n x_iy_i$$ Where $x_i$ is the independent variable and $y_i$ the dependent variable of mi linear model.
I'm supossed to find the value of the determination coefficient $R^2$. I've try with several formulas of it but I always miss something I think that I need $\sum_{i=1}^{n} y_i$ but I'm not sure.
I have this formulas for $R^2$
$R^2=\hat{\beta}^2\frac{\sum(x_i-\bar{x})^2}{\sum(y_i-\bar{y})^2}$
$R^2=\frac{\sum(\hat{y}_i-\bar{y})^2}{\sum(y_i-\bar{y})^2}$
$R^2=\frac{(\sum(y_i-\bar{y})(x_i-\bar{x}))^2}{\sum(y_i-\bar{y})^2\sum(x_i-\bar{x})^2}$
The model is $y_i=\hat{\alpha}+\hat{\beta}x_i+e_i$ Where $e_i$ is an error of mean 0
If someone can help me I'll be very grateful. Thanks!