- #1

fog37

- 1,568

- 108

- TL;DR Summary
- understanding regression in general

Hello,

Regression analysis is about finding/estimating the coefficients for a particular function ##f## that would best fit the data. The function ##f## could be a straight line, an exponential, a power law, etc. The goal remains the same: finding the coefficients.

If the data does not show a linear trend, we cannot straight use linear regression. For example, in the case of data following an exponential trend, we can take the log of the ##Y## data (leaving the ##X## data alone) and get a straight line relation between ##log(Y)## and ##X##. At this point, we can apply least squares and get the required coefficients. That is nice hack: turn the problem into a linear regression problem to find the coefficient using logs...The same goes for a power law relation between ##Y## and ##X##...

A polynomial is simply an extension of the power law. I think we can apply least-squares to minimize the ##MSE## without any log transformation...Is that correct?

What about other more general relationships? I am looking into

thank for any clarification!

Regression analysis is about finding/estimating the coefficients for a particular function ##f## that would best fit the data. The function ##f## could be a straight line, an exponential, a power law, etc. The goal remains the same: finding the coefficients.

If the data does not show a linear trend, we cannot straight use linear regression. For example, in the case of data following an exponential trend, we can take the log of the ##Y## data (leaving the ##X## data alone) and get a straight line relation between ##log(Y)## and ##X##. At this point, we can apply least squares and get the required coefficients. That is nice hack: turn the problem into a linear regression problem to find the coefficient using logs...The same goes for a power law relation between ##Y## and ##X##...

A polynomial is simply an extension of the power law. I think we can apply least-squares to minimize the ##MSE## without any log transformation...Is that correct?

What about other more general relationships? I am looking into

**"nonlinear" least squares.**At high level, is it a technique to find the coefficients using a variation of least-squares (I guess the ordinary least-squares which minimizes the MSE is called linear least-squares) without having to transform our data so it follows a linear trend?thank for any clarification!