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Correlation Coefficient (small r)

PortoMarco79

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Hi @David Harper CFA FRM

Love the videos.

Am on video Stock & Watson 4 &5.

Your first question, find small r.

I had it 98% of the way.

One thing threw me off: you mention in the question that the TSS = 90.625 dollars ^2

--- what does the ^2 part mean in the TSS? Do I have to square the 90.625 in the denominator to calculate the R^2? If not, why mention the ^2 at all?

Thanks

Again -- love the videos. Have added so much colour and quality to my studying.
 

David Harper CFA FRM

David Harper CFA FRM
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Hi @PortoMarco79 Thank you, you are too kind :)

btw, the source question is here @ https://www.bionicturtle.com/forum/...ression-sums-of-squares-ess-ssr-and-tss.5408/

While admittedly many questions would omit the ^2, I included it because the proper units of TSS are dollars-squared; the 90.625 requires no adjustment. In this way, please note that TSS is like "variance" where if we have a set of dollar amounts, the variance has units of dollars^2, then sqrt(variance) produces a standard deviation with units of dollars.

In fact, in the equality given by TSS = ESS + RSS, the units of all three of these terms are squared (e.g., dollars-squared, or whatever-squared). Technically, TSS is a variation; and a variation divided by (df) is a variance. TSS = sum of: (each Y observation - mean Y)^2, the squaring of dollars implies dollar^2. Then TSS/df is actually the variance, but the units are still dollars^2. Finally, sqrt(TSS/df) = sqrt[TSS/(n-1)] = sample standard deviation, which has units of dollars. I hope that helps!
 
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