# quant: multiple R-squared

curriculum page 395. question 20.

the correct answer is C. it takes square root of multiple R-squared to get correlation.

but its written in reading 11, page 293 that above relation is true when there is one independent variable.

in question 20 we have four independent variables, then how could we use this relation.

just cant figure out what am i missing. can anyone help.

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There are some ideas being confused here.

There is no such thing as

multiple R²; there is, and, in a multiple regression, there isR², but there is nomultiple Rmultiple R².In a simple regression, there is a correlation coefficient between the (single) independent variable and the dependent variable: ρ. It can range from -1 to +1.

In a multiple regression, there is no correlation coefficient between the (multiple) independent variables (taken as a group) and the dependent variable: correlation is calculated between exactly two variables.

In a simple regression, R = √R², and ρ = ±R. In a multiple regression, multiple-R = √R², and that’s that; note that multiple-R is never negative.

If anyone tells you that for a multiple regression, ρ = ±√R², they’re wrong.

Simplify the complicated side; don't complify the simplicated side.

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On the same item set, but Q18, can you tell me why they use 1.96 as the critical t-value in their calculations? You are asked to work out the 95pc CI, but it looks to me like a one sided test so I used a critical t-value of 1.645.

Btw I know you haven’t got the CFAI books S2000, but it actually uses the phrase “multiple R-squared” in Q20 to which the OP refers.

Sloppiness.

Simplify the complicated side; don't complify the simplicated side.

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Sloppiness indeed.

BTW, I think you meant R = ABS(√R²), and ρ = ±R above right? (tongue-in-cheek)

Be true

√

xis defined as the nonnegative square root ofx; the ABS is superfluous.Simplify the complicated side; don't complify the simplicated side.

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I’m bumping this because this question really threw me off and it’s still being used in the CFA EOC questions. Still question 20, no less.

I’ve combed through both CFAI regression chapters and this term is never presented… we either get Multiple R or R-squared. But yet in the ANOVA table, there it is…

Multiple R-squared = 0.36, and we’re asked to give the most appropriate interpretation of this! How ridicuous.Edit: didn’t realize how old this was…but yeah, it’s a shame they haven’t fixed this typo (multiple R-squared isn’t a concept in any statistics/econometrics course)…