# Least Square Fitting Line

#### EngNoob

Hey

I need to use the Least Square Fitting approach to calculating the best line of fit.

I have read loads, and cant seem to figure out how to get passed the Inverse matrix part?

Anyone know any good links, or can guide me on how to do least square fitting?

Thanks

#### HallsofIvy

There are about a dozen different way of finding "least squares" lines, some of which use matrices. What matrix are finding an Inverse matrix for? What do you mean "get passed the inverse matrix".

#### EngNoob

Ok, here is what i have done

I have matrix "A" Matric "B".

Using Matrix "A" i can get "Matrix C"

I then inverse matrix "C", However, the numerical approach i am taking is giving me the wrong matrix where i compare it with a inverse from Maple

here is my matrix C

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

From this i get det (40)

1/20 [13][-4]
[-4][ 2]

I however dont get this...

So i am stuck on inversing the matrix.

i get det C at 1/40 and not 1/20

#### HallsofIvy

Since you refuse to show us what you did I can only suggest one thing: have you considered reducing fractions?

#### EngNoob

Sorry...

I have solved this now...

I never transposed matrix "A" to for ATA, once i have transposed then i got all the values for the determinent and inverse and ultimatly the solution.

Matrix A and B:

[■(1&1@1&3@1&7@1&4)] [■(C@D)]= [■(3@8@5@7)]

Transpose A to produce ATA

A^T A= [■(1&1&1&1@1&3&7&4)] [■(1&1@1&3@1&7@1&4)]= [■(4&15@15&75)]

This is how i solved it. thanks again for the help.

"Least Square Fitting Line"

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