I am searching for the formula to calculate the correlation coefficient in case of multiple linear regression. Please help me out!
-Nath
I have 2 independent variables: $X1$ and $X2$ and 1 dependent variable $Y$. I want to study whether there is correlation between the 3 parameters.
The model is
$$ Y = aX1 + bX2 + c $$
I was able to calculate $a$, $b$, and $c$. Now I need to 'analyze' whether there is a correlation. In case of linear regression $x$ and $y$, the formula is:
$$ r = \frac{cov(x,y)}{ \sqrt{var(x)var(y)} } $$
What is the formula in case of $x1$, $x2$, and $y$.
Is it called multiple correlation?
Best Answer
Multiple correlationIS what you are looking for. It is a measure of how well the dependent variable can be predicted by a set of independent variables. The symbol is $R$ and it should be $R>0$.Assuming your independent variables are $x$ and $y$. The dependent variables is $z$, then the
multiple correlation coefficientis given by$$ R_{z,xy} = \sqrt{ \frac{r_{xz}^2 + r_{yz}^2 - 2r_{xz}r_{yz}r_{xy} }{ 1-r_{xy}^2 } }$$
where $r_{xz}$, $r_{yz}$, and $r_{xy}$ are defined as the correlation coefficient between 2 variables. The formula to each is the one you stated above.