I'm solving an exercise on multiple linear regression. Near the end I will be asked for the same data as the previous model, it is the maximum likelihood estimates.

The previous model:

I have the matrix \((X'X)^{-1}\) and the matrix \(X'y\) and the model is:

\(Y_i = B_0 + B_1x_i + B_2x^2_i + e_i\)

\(i= 1,...,10\)

Now I have:

\(Y_i = g_0 + g_1x^*_i + g_2(x^*_i)^2 + e_i\)

\( x^*_i = x_i -10\)

\(i=1,...,10\)

To transform the model can I decrease the Matrix data for 10?

The same thing can I make it also for the matrix \(X'y\)?

I have many doubts.

Publishing the text so it is more understandable.

Consider the regression model linear:

\(Y_i = B_0 + B_1x_i + B_2x^2_i + e_i\)

with \( e_1, ...., e_n \) independent and identically distributed random variables and x_i, i = 1, ..., 0 constant fix.

The only data I have are these:

https://s32.postimg.org/o20r1i5et/Immagine.png

I have to rewrite the whole thing ... I tried so:

\((X) =

\begin{bmatrix}

1 & x_1 & x^2_1\\

. & . & . \\

. & . & . \\

. & . & . \\

1 & x_{10} & x^2_{10}\\

\end{bmatrix}\)

\((X^*) =

\begin{bmatrix}

1 & x_1-10 & (x_{1}-10)^2\\

. & . & . \\

. & . & . \\

. & . & . \\

1 & x_{10}-10 & (x_{10}-10)^2\\

\end{bmatrix}\)

\(X^{*'}X^* =

\begin{bmatrix}

10 & \sum_{i=1}^{10} x_i-10 & \sum_{i=1}^{10}(x_{i}-10)^2\\

\sum_{i=1}^{10} x_i-10 & \sum_{i=1}^{10} (x_{i}-10)^2 & \sum_{i=1}^{10}(x_{i}-10)^3\\

\sum_{i=1}^{10} (x_{i}-10)^2 & \sum_{i=1}^{10}(x_{i}-10)^3 & \sum_{i=1}^{10}(x_{i}-10)^4\\

\end{bmatrix}\)

Now I have to calculate the inverse? I'm following proper solution?

Excuse me , but does not write well in English

Thanks.