How do I use Least Square Fitting to Calculate the Best Line of Fit?

[EngNoob]

Hey

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

I have read loads, and can't 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)

I know the answer is

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

I however don't 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.