# help with using the “simple regression (least squares) method” of forecasting

This problem is from an engineering management textbook (Morse & Babcock, 5th ed) :

2005     $48k 2006$64k
2007     $67k 2008$83k


"What is the sales forecast for 2009, using the simple regression (least squares) method?"

The book works through an example (shown below and not to be confused with the above), but does not give enough information for me to understand what's going on. Hopefully it won't confuse my question, but I'll give the problem they worked through here also, so that I can get help understanding how they got their numbers. They have:

Table 3-2 data was:

2005  $1100 2006$1300
2007  $1200 2008$1600


in b of the given problem, I can't figure where they got the parenthesized numbers--any of them! It couldn't have been by multiplying the sum of X's by the sum of Y's, or by the sum of y's. So I can't possibly do the homework problem until I understand how they are doing the give example.

Any help is appreciated.

Update: here is my work on the homework question. Can anybody give me a bit of confirmation that I've done right?

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## migrated from meta.math.stackexchange.comSep 21 '11 at 23:28

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The quoted problem seems like a pedagogical nightmare on a number of levels, not the least of which is to suggest that fitting a simple linear regression to four data points is a reasonable idea in the first place. :) – cardinal Sep 21 '11 at 23:33
The formula for b you need here would look to be formula 14 here, while the formula for a would correspond to formula 28 in that link. But I agree with @cardinal, this seems to me a poor problem, pedagogically speaking. There is not even an indication to evaluate the goodness of fit... – J. M. Sep 21 '11 at 23:52
Does that mean the question in my book was unanswerable as given? The only difference between my book's formula and the one in the link (in my question) are the x & y designations are d and i, and that those variables in "a" have a horizontal bar over them with a note saying "where D and I are the mean values of D and I, repsectively, and indicate a summation from i=1 to n." The first D and I in the quote had horizontal bars over them too. – Captain Claptrap Sep 21 '11 at 23:55
Is it legal to take a picture of the page and post it? – Captain Claptrap Sep 22 '11 at 0:01
It's answerable, sure. @cardinal and me were just bemoaning the habit of mindlessly using linear fitting being implicitly pushed. BTW: it's just one page, so I think fair use covers it. Do post it. – J. M. Sep 22 '11 at 0:26

\begin{align} a&=\frac{n\sum(D_iI_i)-\sum I_i\sum D_i}{n\sum I_i^2-(\sum I_i)^2}\\ &=\frac{4(0\cdot1100+1\cdot1300+2\cdot1200+3\cdot1600)-(0+1+2+3)(1100+1300+1200+1600)}{4(0^2+1^2+2^2+3^2)-(0+1+2+3)^2}\\ &=\frac{4(8500)-(6)(5200)}{4(14)-(6)^2} \end{align}