In Linear regression there is listed following Mutliple R 0.5549 R-squared as 0.3079 I understood that R-squared as coefficient of determination obtained by squaring of multiple R. What is Mutliple R means? Why are they listed coefficient of determination as R-squared. It is confusing for me. Appreciate for any help.
It’s actually the other way around; multiple R is the square root of r^2. r^2 is the percentage of variability explained by the regression (SSR/SST). The idea is that multiple r is the analogue of the usual correlation coefficient when there are multiple independent variables. Anyway, you calculate r^2 first then get multiple r from it.
Joey, Thanks for quick reply and you had answered lot of questions in L1. I am glad to see you in L2 forum. Now I understood little better on R squared. So, basically, R squared is determined first and then square root of it will give multiple R. You said following “The idea is that multiple r is the analogue of the usual correlation coefficient when there are multiple independent variables” I read that square root of coefficient of determination gives correlation coefficient only in case of one independent variable in regression equation. Could you please explain above sentence little more. I guess R^2 is just symbol for coefficient of determination. I am not clear on word MULTIPLE in “multiple R”. Appreciate for your time.
"I read that square root of coefficient of determination gives correlation coefficient only in case of one independent variable in regression equation. Could you please explain above sentence little more. " That’s right, so you can’t do a regression with multiple independent variables and take the results of that regression and get the correlation coefficient of any single independent variable with the dependent variable. But in the case of 1 i.v. the sqrt of r^2 is the correlation coefficient so in the case of multiple i.v’s it is the “multiple r”. It’s not really very comparable with the correlation coefficient and contains just the same info as r^2 but I guess some people like it (not me).
Joey, Excellent. Thanks for explaining very well chinni