# Is there a way to calculate the coefficient determination if the values of x and y are not given?

so I am having a problem to calculate the r-squared because the values of the variable (y and x) are not given in the question. All I have is the mean and the standard deviation of each variable as well as the scatter plot with pearson correlation value.

In linear least squares regression with an estimated intercept term, $R^2$ equals the square of the Pearson correlation coefficient between the observed $y$ and modeled (predicted) $f$ data values of the dependent variable. In a univariate linear least squares regression, this is also equal to the squared Pearson correlation coefficient of the dependent $y$ explanatory $x$ variables.
So square your Pearson correlation to get the $R^2$ value if you have simple linear regression, which I assume you do.