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I know the one for the one variable version... β =∑ xiyi / ∑ x2

but nobody seems to have the one for the multiple variable version is there a way to do it by hand for something like

y = β1x1 + β2x2 (no intercept)

EDIT: this is about the MULTIPLE variable model equation (MUST go through the origin)..the answer provided is the one I tried that doesn't go through the origin

enter image description here

Ken Latwork
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  • no, that's only one variable..i'm asking about TWO variables – Ken Latwork Nov 14 '19 at 18:22
  • the link provided shows a solution for b1 & b2 with intercept...unfortunately, it's not zero intercept...it's the same one i've been using with intercept..unless there's something i didn't see...I used that same equation at the bottom of the chosen answer and it's the same equation as the one with intercept..the answer he provided is wrong – Ken Latwork Nov 14 '19 at 18:56
  • The formula in the end of @Gunes' answer is 100% correct, I assure you. What seems off in his formula to you? Afterthought: the formula for the regression with the intercept will look similar with an important distinction, that $a_i,b_i,y_i$ are replaced with their DEMEANED versions $\hat a_i = a_i - \bar a_i, \hat b_i = b_i - \bar b_i, \hat y_i = y_i - \bar y_i$ – Konstantin Nov 14 '19 at 19:12
  • i'm lost about that last part...i've done the excel calculation for a with intercept model, which uses the exact same formula...so where in the process do i need to change to get the demeaned version? https://drive.google.com/open?id=1vTHtuvI3aEFsnfhqIcqUN9nR79DV_Uo_ or you can see a screen cap showing how i calculated the y = b1x + b2x2 formula – Ken Latwork Nov 14 '19 at 19:36
  • i mean, when i did the sum of squares, i already subtracted the mean from the a & b...i didn't do it for the y...but i'm trying to subtract the mean from y and it doesn't seem to give me a zero intercept..and it's giving me a negative bi , which shouldn't be – Ken Latwork Nov 14 '19 at 19:43
  • Let us [continue this discussion in chat](https://chat.stackexchange.com/rooms/101038/discussion-between-konstantin-and-ken-latwork). – Konstantin Nov 14 '19 at 19:51
  • hi, you're right..i removed the subtraction of mean and it works....so it's just the multiple variate (with intercept) formula, except instead of subtracting the mean from the x & y, i just use the x & y values in the equal..thanks alot, teacher – Ken Latwork Nov 14 '19 at 20:52

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