What is the regress function doing?

I don't understand what the regress function is returning. My understanding that it should be the gradient of the line of best fit. For example:

x = [1:5]'
y = [2 4 6 8 10]'
b = regress(y, x)

returns b = 2 as expected, whereas:

x = [1:5]'
y = [5 4 3 2 1]'
b = regress(y, x)

returns b = 0.6364 as opposed to -1.

What is the regress function calculating in this case? Where does this value for b come from?

Answer 1

[Star Strider]

The reason the first data set returned the slope you expected is that the intercept was zero, and your design forced a zero intercept. The reason the second data set is not returning -1 for the slope is because you are forcing it to have an intercept at zero.

If you include an intercept term, you get the expected -1 slope with a y-intercept of +6:

x = [1:5]'
y = [5 4 3 2 1]'
b = regress(y, [x ones(size(x))])

b =
           -1
            6

Answer 2

[Matt J]

It is returning x\y

    >> x = [1:5]';  y = [5 4 3 2 1]';  b=x\y

    b =

        0.6364

In other words, the best fit to the equation y=b*x. It is just a coincidence that, in the first case, this happens to also be the slope of the line of best fit.