Calculating Line of Best Fit: Least Squares Method

[EngNoob]

I need to calculate a line of best fit, using...

The least square fit method.

I am upto the stage where i have created my matrix 2 x 2, and then i have invesed the matrix 2 x 2 and then got a fraction and a [2x2] matrix.

Now i am stuck.

The textbook has the inverse matrix, and the matrix of co-ordinates used to create the original matrix, and i don't get how the anser is established

Any help most appreciated

 

[HallsofIvy]

I need to calculate a line of best fit, using...

The least square fit method.

I am upto the stage where i have created my matrix 2 x 2, and then i have invesed the matrix 2 x 2 and then got a fraction and a [2x2] matrix.

Now i am stuck.

The textbook has the inverse matrix, and the matrix of co-ordinates used to create the original matrix, and i don't get how the anser is established

Any help most appreciated

This tells us nothing about what you have actually done. What points is the line supposed to fit? What matrices did you construct? What formula are you using?

 

[EngNoob]

Ok, this was a very stupidly produced post, so sorry.

Here is the data i have.

I have a matrix, which is m x t,

[1][0]
[1][1]
[1][3]
[1][4]

and have another matrix b

[0]
[1]
[2]
[5]

Using the least square fit process, i need to establish an ATA Matrix or

[ sum m ] [ sum t ]
[ sum t ] [ sum t ^2 ]

I have been given the answer to this as

[4][8]
[8][26]

What i don't understand, is how does the 26 get their?

The forumula says sum t^2, or 8 x 8, which is 64. 8 doesn't go into 26 either, so i am at a loss what i am doing wrong?

Maybe i am using the wrong formula?

The det(ATA) is 40, which would indicate the 26 should be there, however, can't figure out from the data where 26 comes from?

Any help appreciated, and sorry for the weak post...

 

[TheoMcCloskey]

That last element is sum(t^2), ie, the sum of squares.

Perform the design matrix product (A^{T}A) yourself, and I think you'll see.

 

[EngNoob]

Spot on, i have the answer now, i was been a little thick, (t) t meaning transpose right, thanks...