# Working out RSS in matrix regression

A

#### .ACS.

##### Guest
Hey everyone

Okay, I'm having a few problems. I'm fine with single variable matrix regression, using the formula $$\displaystyle RSS = \mathbf{e'e}$$ where $$\displaystyle \mathbf{e} = \mathbf{y} - \mathbf{Xb}$$
The huge issue arises with two variable regression where my value worked out by hand is completely different to that given by eViews.

$$\displaystyle \mathbf{y} = \left[ \begin{array}{c} 48 \\ 54 \\ 60 \\ 66 \\ 73 \end{array} \right]$$, $$\displaystyle \mathbf{X} = \left[ \begin{array}{ccc} 1 & 1 & 51 \\ 1 & 2 & 58 \\ 1 & 3 & 65 \\ 1 & 4 & 73 \\ 1 & 5 & 83 \end{array} \right]$$, $$\displaystyle \mathbf{b} = \left[ \begin{array}{c} 28.58 \\ 3.77 \\ 0.31 \end{array} \right]$$

$$\displaystyle \mathbf{e} = \left[ \begin{array}{c} 48 \\ 54 \\ 60 \\ 66 \\ 73 \end{array} \right] - \left[ \begin{array}{ccc} 1 & 1 & 51 \\ 1 & 2 & 58 \\ 1 & 3 & 65 \\ 1 & 4 & 73 \\ 1 & 5 & 83 \end{array} \right] \left[ \begin{array}{c} 28.58 \\ 3.77 \\ 0.31 \end{array} \right] = \left[ \begin{array}{c} -0.16 \\ -0.1 \\ -0.04 \\ -0.29 \\ -0.16 \end{array} \right]$$

$$\displaystyle \mathbf{e'e} = \left[ \begin{array}{ccccc} -0.16 & -0.1 & -0.04 & -0.29 & -0.16 \end{array} \right] \left[ \begin{array}{c} -0.16 \\ -0.1 \\ -0.04 \\ -0.29 \\ -0.16 \end{array} \right] = 0.1469$$ but eViews says it's $$\displaystyle 0.030769$$

So am I making a mistake in calculating $$\displaystyle RSS$$ for a two variable matrix regression? The thing is we've not been taught any other method.

Thanks!