Hello. I’ve been doing well on the EOC’s for Quant but poorly on Q bank and Mock’s. I get what correlation is. I get how the equation is set up with the intercept and then the amount of the change in the dependent variable for the amount of change in the independent variable and I know how to calculate everything on the Anova table. I get that the SSR is the amount of change the model explains and the SSE is the amount of change it doesn’t. What I’m having problems with is putting it all together. Can someone help me out with how it is all interconnected? I’m looking at these problems where they throw out half an anova table and the correlation and they are getting all these things from it. Can someone try to explain to me how the correlation relates to the anova table?
Here is what i know. For a regression with 1 independent variable, the R2 = correlation^2 = SSR / TSS, Therefore the Square root of SSR / TSS is the correlation. For regressions with more than 1 independent variables, this relationship does not work.
thanks phrenchy, any idea what value from the Anova table they are using when doing the T Test? is it SEE?
I don’t know that you do t-tests from the ANOVA table output. I think it’s used for F-Test, R2 and other global tests-- it’s more of a tool for analyzing the entire regression formula. T-tests are performed on the coefficients themselves. Can anyone else add anything–am I totally wrong?
Fraser Wrote: ------------------------------------------------------- > thanks phrenchy, any idea what value from the > Anova table they are using when doing the T Test? > is it SEE? Yes! SEE is used in the denominator for doing the T-Test.
Ignore my previous statement. Freecmorgan you are right! SEE as given in ANOVA table can not be used for T-Test as that standard error is calculated for whole regression equation and not of a single coefficient.
That’s the exact issue I’m having with almost all of reading in CFAI books, putting it all together. The explanation might be long, but… First, there is a predicition. Second, there is an estimation of variance. Thirds, there is a prediction interval. Imgaine you have an economic forecast (X - indep var) and a stock price (Y - dep var). You want to know, whether you can build a linear model, which you could use to predict the stock price using the economic forecast. Before building a model, you test whether the relation exists. For this, you find the correlation and test it with a T-stat (for single slope) and F-stat (for multiple slopes). In our case we keep the t-stat. If the correlation is significantly different from zero, you may build a simple model Yi = b0 + b1Xi + e. The first step is completed. Now, there is variance of the dependent variable. Don’t forget that we are still in the scope of predictions (future), for which we are using the past (statistical) data). For estimation of variation you use ANOVA. With ANOVA you may identify which level of Y’s FUTURE variation will be explained by the FUTURE variation of X. Here is where of all these total variation, sum of squared errors, RSS, come into play. You know how to do calculation using the ANOVA table. The last thing, usually you are not interested in predicting the exact value of Y, but instead building a confidence interval of prediction (I say the future value of Y will be between A and B, whith a C level of confidence). That’s why you build a confidence interval. In summary, that’s all what the reading about is.