Calculating the regression equations I have four data points $(1,2), (2,4), (3,5), (5,7)$ and Im looking for the least squares regression line that best fits them.
I use the normal equation
$A^tAx=A^tb$
in this form -
$\begin{bmatrix} 1 & 1 & 1 & 1 \\ 1 & 2 & 3 & 4 \end{bmatrix}\begin{bmatrix} 1 & 1 \\ 1 & 2 \\ 1 & 3 \\ 1 & 4 \\ \end{bmatrix}\begin{bmatrix} c \\ m \end{bmatrix} = \begin{bmatrix} 1 & 1 & 1 & 1 \\ 1 & 2 & 3 & 4 \end{bmatrix}\begin{bmatrix} 2 \\ 4 \\ 5 \\ 7 \\ \end{bmatrix}$
this gives -
$\begin{bmatrix} 4 & 10 \\ 10 & 30 \end{bmatrix}\begin{bmatrix} c \\ m \end{bmatrix} = \begin{bmatrix} 18 \\ 53 \end{bmatrix}$
I solved this system and got 
$m = 1.3, c = 1.25$
so
$y = 1.3x + 1.25$
But if I put "linear fit {1,2},{2,4},{3,5},{4,7}" into wolfram alpha it gives
$1.6x + 0.5$
So have I got it wrong?

Everything looks good until
$\begin{bmatrix} 4 & 10 \\ 10 & 30 \end{bmatrix}\begin{bmatrix} c \\ m \end{bmatrix} = \begin{bmatrix} 18 \\ 53 \end{bmatrix}$, but then you have got bad solutions and wolframalpha is right. Also you should check last data point, is it $(4,7)$ or $(5,7)$?
