co effiecient of determination help!!!!

CFA Level I
#1

Can someone please confirm if I have this right. unexplained variation is the variation of the independent variable. therefore sqrt(unexplained variation) = standard deviation of independent variable sqrt(unexplained variation/n-2) = standard error of indep total variation is the variation of the dependent variable therefore sqrt(total variation) = standard deviation of dependent variable sqrt(total variation/n-2) = standard error of dep thanks in advance. i had totally missed this stuff and came across last night in CFA #3. cheers, otaw

#2

Nope. The independent variable doesn’t even have to be random and even if it is, regression is not trying to explain anything about the independent variable. "total variation is the variation of the dependent variable "

#3

I think the relevant concepts are as follows: Sum of Squared Total Variation (SST): the sum of the squared differences from the mean of the observations to each observation. Note this amount has nothing to do with the regression line, it is just a measure of variation. Sum of Squared Errors (SSE): the sum of the squared differences from the regression line to each observation. This is the amount of the variation that is unexplained. Sum of Squared Regression (SSR): calculated by subtracting SSE from SST. If you think about this, what you are doing is subtracting the unexplained variation from the total variation, so you are left with the explained variation. Coefficient of Determination: the percentage of variation that is explained. Hence, SSR/SST, or alternatively (SST-SSE)/SST or alternatively, for single variable regression, the correlation coefficient squared. Standard Error of Estimate: Square root of (SSE/n-2). A standardized version of the sum of squared errors that could be compared between different regressions (note how the SSE itself is a gross figure).

#4

thanks guys. didn’t think that independent variable variations made much sense. i think I’ve got my sst’s and sse’s in the right order!!!lol cheers otaw

#5

Also, to test the significance of the correlation in a one variable linear regression: H0: r=0 Ha: r<>0 t= r * sqrt(n-2)/sqrt(1-r^2)