Quant question SS11

Pg 270, Q9 in CFAI, the shorter version- SST = 140.58 SSR = 60.16 SSE = 80.42 n =60 cruising along, r-sq = .427941, r = .654172, SEE = 1.199519 then it gets to part D which asks “compute the sample std deviation of monthly energy consumption” which here is the dependent variable… we’re explaining variation in energy consumption as a function of temperature. so answer on variance of dependent variable is sum (Yi - Ybar)^2/n-1 = total variation/n-1 2.3827 then you sq root for the std dev. = 1.544 cool, fine. my question- if they had asked me “compute the sample std deviation of temperature” which is the independent variable here, i’d think it’d be sum (Xi - Xbar)^2/n-1 so same formula but with X’s instead of Y’s, but is that numerator the same as SSR then so we’d get 60.16/59 = 1.019661 for variance and the sq root of that for std dev? Just want to make sure that if asked std dev of the INDEPENDENT variable given that info I’d go SSR/n-1 (this is basic linear regression, just 1 ind variable now) to get variance where as the book example asks for the dependent variable and uses SST/n-1 there. Thanks ahead of time for any replies and good morning.

Bannisja, In this case, they have provided all information with regards to Y, which is the Dependent variable. In case you had a table where in the (Xi - XBar) and (Xi - XBar)^2 had been provided, what you are doing above would be correct. Not in this case. Yi - YBar and Yi - YHat and their squares information is provided, not Xi related information, hence what you have done above would not be correct. But in a table like in the book like Table 2, on page 225 – the above approach would be correct. If you looked at that example, Xi-Xbar is different from Yi - Ybar. CP

ok, then so I can just get my formulas straight: SST, total variation = sum thingie (Yi - Ybar)^2 SSE, unexplained variation = sum thingie (Yi - b-hat0 - b1Xi)^2 explained variation then? it doesn’t = sum thingie (Xi - XBar)^2 or SSR? if not, then given # observations, SST, SSE, and SSR I can only get the sample std deviation of the dependent but not the independent variable with that info provided? sorry if this is basic stuff… my quant skills are lacking.

Yes. Unless the X stuff (independent variable) is laid out as a table, given the various Y thingies, it would be difficult to get to the X thingies. X and Y are two different things. In the example in the book, (Problem 9 which you had picked out) Y was energy consumption. X was Temperature. By looking at the variance and difference of Energy consumption (which is what Yi-YBar means) you would not be able to say anything about Temperature change, or its variance. SSR = (Yi - YBar)^2 --> This tells you the Sum of square of the difference of Observation of Energy Consumption (Yi) from Mean Energy Consumption (YBar) Hope this helps CP

I think I’m almost there except you said SSR… you mean SST, yes? (Yi - Ybar)^2… it does tell you the sum of sq of the difference of the observation of energy consumption from the mean… but within that you have both the SSR (explained) and SSE (unexplained). The Yi - Ybar sq should be total, no, not just SSR? Gotcha on not being able to do much with the independent temperature variable given what that problem gave you. Thanks a lot!

yeah, got confused. SST = (Yi-YBar)^2 SSR = (Yi - YHat)^2 YHat = bhat0 + bhat1 * Xi CP