Herman Said:

Linear regression analysis 3?

We Answered:

You must give sufficient data to receive an answer. In this case, a table relating historical monthly profits vs. time, or at least something from which such a table can be constructed, is required.

Add 1: I have found the links to the other two parts of the question.

What you need to do is make a table of the units produced and the costs in the first two columns, x being the units produced and and y being the overhead cost, plus three more columns: one for x², in which you take the square of each of the entries in the first column; y², where you square the entries in the for the second column; and a third column in which you multiply x and y together. Each of these columns you then sum to get the numbers ?x, ?y, ?x², ?y², and ?xy.

Next step is to compute the sums of squares of your data. The formulas for SS(x) and SS(y) are the same as those for computing variance of x and y but without the N?1 in the denominator: The one for SS(xy) is the cross term and looks a little different but not that much.

SS(x) = ?x² ? (?x)²/N
SS(y) = ?y² ? (?y)²/N
SS(xy) = ?xy ? (?x)(?y)/N

Once you have these numbers, the slope of your line of best fit will be SS(xy) / SS(x) and the line will pass through the point corresponding to the mean values of x and y, or
through the point (?x / N, ?y / N). You now have the equation of your line in point-slope form, or
Y ? ?y/N = SS(xy)/SS(x) * (X ? ?x/N)
which you may then convert to slope-intercept form, which will be
Y = mX + b
= SS(xy)/SS(x) * X + (?y ? SS(xy)/SS(x)*?x) / N

The Pearson Correlation coefficient r will be given by
SS(xy) / ?[SS(x)*SS(y)]

I don't quite know what the coefficient of determination is, but I assume that it is r².