# Least Squares

1. Apr 2, 2013

### twoski

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

Given this data:

hours / value
-----------
2 | 1.6
4 | 1.5
6 | 1.45
8 | 1.42
10 | 1.38
12 | 1.36

fit a curve of the form Y ≈ $ae^{-bx}$

What value can you predict after 15 hours?

3. The attempt at a solution

So i can rewrite the equation as Y ≈ log(a)-bx by taking the logarithm of the original equation.

How do i go about doing a least squares approximation of this? Our lecture notes have no examples that actually show how we are supposed to compute these coefficients.

2. Apr 2, 2013

### SteamKing

Staff Emeritus

If y = a e^(-bx) then you must take logarithms of BOTH sides to obtain:

LN(y) = LN(a) - b*x

You can use least squares for linear equations to fit the data.

3. Apr 2, 2013

### twoski

Are there any suggested readings for actually figuring out how to compute a least squares approximation? I've read a handful of different notes and i'm still stumped. It would be nice if there was just a nice step by step methodology to this.

4. Apr 2, 2013

### Ray Vickson

Google is your friend. There are hundreds of explanatory articles, ranging from very elementary to very advanced.