# Homework Help: Method of least squares

1. Feb 26, 2012

### Helpeme

1. The problem statement, all variables and given/known data

number of years(x): [1,2,3,4,5,6,]
number of accidents(y): [12,6,5,4,2,2]

or

(1,12),(2,6),(3,5),(4,4),(5,2),(6,2)

2. Relevant equations

the relation between x and y is on the form: y = a + b(1/x)
by changing (1/x) to z, the model become linear instead of inverse.
use this to 'find' a and b

3. The attempt at a solution

y = a+b(1/x)
z = 1/x
y = a+bz

matrix A = [(1,1),(1,2),(1,3),(1,4),(1,5),(1,6)]
vector y = [12,6,5,4,2,2]
vector x = [a,b]

finds a solution to ATAx = ATy

6a + 21b = 31
21a + 91b = 77

a = 11.4557
b = -1.8

y = 11.4667 - 1.8/x

but this is wrong the right answer is:
y = 0.3914 + 11.6945/x

i think my problem is how to deal with z and 1/x.

2. Feb 26, 2012

### Ray Vickson

Go back and look at what you wrote: you use the matrix A = [(1,1),(1,2),(1,3),(1,4),(1,5),(1,6)], so you are fitting the equation y = a + bx.

RGV

3. Feb 26, 2012

### Helpeme

do u mean the matrix should be [(1,1),(1,(1/2)),(1,(1/3)),(1,(1/4)),(1,(1/5)),(1,(1/6))]

4. Feb 26, 2012

### Ray Vickson

What do YOU think?

RGV

5. Feb 26, 2012

### Helpeme

i think thats not right at all and its not funny to trial and error matrix calculations.. they are pretty intense and tiresome

can you please give me some more hints.. if you know how to do this. because i have no clue anymore.

EDIT:

alright it worked..a little miss calculation. thanks for the replies :)

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