How to implement normal equation (least square solution) in Matlab

Consider the following problem. Problem Video link.

House Size	Price
1700	53000
2100	65000
1900	59000
1300	41000
1600	50000
2200	68000

From these data we want to predict the future house price from their size. Assuming the relationship between house price and size is linear, the question is

Price = (multi)*size + constant

We have to find two parameters here. First the multi and then constant.  Let us solve this problem using normal equation (it is also called least square solution). In this example house size is our only attribute. Therefore, we have to construct the following matrix.

 X=[1 1700;1 2100;1 1900;1 1300;1 1600;1 2200]

X =

           1        1700

           1        2100

           1        1900

           1        1300

           1        1600

           1        2200

Note that, here we augment the first column with 1.

Our price vector will be the following

p=[53000;65000;59000;41000;50000;68000]

p =

       53000

       65000

       59000

       41000

       50000

       68000

Now, using normal equation we can find those two parameters

THETA= inverse(X’X)X’p

Theta = (inv(X'*X)*X')*p

ans =

   1.0e+03 *

    2.0000

    0.0300

Therefore, multi=30 and constant=30