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# Help with method of least squares?

Topic: Problem solving in system analysis
July 16, 2019 / By Holly
Question: I don't understand this concept. Everything I've read on the subject is too advanced for me. My highest math class so far is calc 2. I have a data table and an equation to find an equation using the method of least squares but I can't seem to find the right answers. The problem in question goes like this: First here's the data points: (1, 2.3) (2, 6.2) (3, 18.9) (4, 35.6) (5, 56.5) But then it also says: Using the method of least squares, develop an equation for the best fit line through these data points of the form: y=A0*(x^A1) My answer is consistently wrong; I think this is because I don't understand how the form affects what I need to do. Other problems ask me to solve for different forms. I really need help understanding how this works, particularly in terms of the form alright I understand the conceptual side of what your saying... up until the end. I'm still too uneducated on the subject to follow the math. I calculated the slope as 3.14 and the y intercept at 14.54. What I need to know is what to do, mathematically, from there. Do I need to take the ln of one of those? Or does the first equation change? What I really need is more of a step by step. If Its any help, this is the equation I am using: http://www.fda.gov/ucm/groups/fdagov-public/documents/image/ucm174702.jpg That was a mistake. I actually got the slope is 13.78 and I don't know how to find the intercept. My textbook doesnt mention that

## Best Answers: Help with method of least squares?

Edana | 3 days ago
The textbook should walk you by the hand through the "best fit line" problem, where y= ax+b is the form you are trying to fit with N data points. In that case, you're basically using the form y=ax+b to generate N equations in 2 unknowns: you are given N (x,y) pairs, and your unknowns are (a,b). The method of least squares is the classical method of find a "best fit solution" to this overdetermined system. In a nutshell, the way it works is to consider e = y_{data} - y_{fit line}, then minimize the sum of the squares of the N values of e. Analytically, e(j) = y(j) - a x(j) - b. so you square it, sum over j, across the N data points, then take the partial derivative of the sum with respect a and set that to zero, then take the partial derivative of the sum with respect to b and set that to zero, and now you have 2 equation in the 2 unknowns (a,b). The trick to handling the form y = a x^b is to use logarithms to convert it into the form Y = A X + B, then use the previous analytical result. ln y = ln a + b ln x Y = B + A X Y = ln y B = ln a A = b X = ln x so take the logarithm of (x,y) to form (ln x, ln y) = (Y,X), plug (X,Y) into the least squares analysis to get (A,B), then transform (A,B) back to get (a,b)
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