Statistics/Econometrics HELP PLEASE

[Al B. Sure!]

I had to work so I cut class today and I started to do the homework due Monday and I'm confused about something.

I am giving the following information about a sample with 33 observations following a y= b1+b2x2+b3x3+e equation:

Standard Error of Regression: 46.948
Sum of Squared Residuals: 59513
Mean dependent var: 125.527
S.D. dependent var: 90.713

I need to find R^2. This is pretty basic stat but I can't remember how to solve for it given this info. R^2 = 1- sum of squared residuals/????.

thanks

[AnnC]

Ok, I assume you're doing an Ordinary Least-Squares (OLS) regression and the error terms (residuals) are normally distributed.

The coefficient of determination, R^2, is 1-SSR/SST where SSR is the sum of square residuals and SST is the total sum of squares.

R^2 is always between 0 and 1 (inclusive) so if you get a number outside of that range, you've done something wrong.

[Al B. Sure!]

in our nomenclature, the sum of squared residuals is SSE, SSR being the sum of squares whose variation is explained by the regression model.

and i know the formula... what i'm lost about is how to derive SST or SSR (explained by regression) from the given information. we just use notation in class so I don't know how the mean dependent variable and what not relate to R^2. the professor never refers to them by any other name but the notation (let's say y bar instead of the mean of y, y dot or y with the ^ mark over it, etc.)

[AnnC]

I use SSE for 'explained sum of squares' which is the sum of the differences between the fitted values and the mean, namely:

> Sum of (fitted y - mean y) ^2

Whereas SSR is the sum of the square residuals, namely the error terms. You're given that number btw but it appears that a decimal is missing - it ought to be 0.59513 <--- actually, I take that back. If you've got really scattered data, you might have a huge SSR.

The total sum of squares (SST) is:

> Sum of (sampled y - mean y)^2

An alternative formula for R^2 is SSE/SST.

[Al B. Sure!]

but how would i get the sampled y? what is S.D. dependent var? it's not standard deviation, is it? it's so large... but it also should be greater than Sum of Squared Residuals which is apparently 59,513. it can't be a typo because the following problem uses the same data but has it reestimated after adding squares and cubes of predictions... and that sum of squared residuals is 37,130.

[JimmyCracksCorn]

AnnC, where is "State"?

[Al B. Sure!]

i know it sounds real stupid but what is the relationship between the given data and R^2? I think he went over this stuff on a day I worked late and I was sleepy. i can tell it's supposed to be easy but I don't know what S.D. of y has to do with R^2.

[AnnC]

My nomenclature: "sampled y" is the observed value of y - it's the data you're given, "fitted y" is y-hat, and "mean y" is y-bar.

As for the information you're given, those values appear to be the output of a statistics program so their meaning depends upon the software. But here's what it looks like to me:

Mean dependent var <--- looks like y-bar

S.D. dependent var <--- looks like standard deviation of y

Most of the time, "standard error of regression" is the square root of SSR/(n-2).

[AnnC]

Originally posted by JimmyCracksCorn
AnnC, where is "State"?

It's not in Canada (if that's what you were thinking).

[Al B. Sure!]

I know SSE is sum of (y-fitted)^2 but how would i calculate that based on the standard deviation of y?

[Stuie]

Speer!!! Good to see you're not lying dead in a gutter in North Philly. Long time no see. I'm not answering your question obviously, but just saying take care of yourself, ok?

[AnnC]

'S.D. dependent var' is probably the square root of SST, but it depends upon the software - I recommend you look at the documentation and verify that.

And that SSR number just doesn't look right to me - there's gotta be a decimal point somewhere in that number.

[Al B. Sure!]

SD dependent couldn't be the sqrroot of SST because then with an SD of 90.713, SST would be 8228.84, which would be less than the sum of squared residuals.

[AnnC]

You're right, which is why that SSR number appears to be incorrect. Could it possibly be 595.13 or 5951.3?

[Al B. Sure!]

ah! SD is the sqrroot of (SST/(T-k))!