# Least Squares

## Homework Statement

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?

## 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.

Related Calculus and Beyond Homework Help News on Phys.org
SteamKing
Staff Emeritus
Homework Helper

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.

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.

Ray Vickson