Why Use the Least Squares Method for Finding Slope?

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Homework Help Overview

The discussion revolves around the use of the least squares method for determining the slope of a line in the context of data fitting, particularly when dealing with experimental data that may not align perfectly due to errors.

Discussion Character

  • Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • The original poster questions the necessity of the least squares method over the standard slope formula, expressing confusion about its application. Other participants discuss the advantages of least squares in accommodating multiple data points and providing a better overall fit to the data.

Discussion Status

Participants are exploring the rationale behind using the least squares method, with some providing insights into its benefits for fitting lines to data sets with more than two points. There is an indication of understanding developing among participants, but no explicit consensus has been reached.

Contextual Notes

Participants are considering the implications of measurement errors and the need for a fitting method that utilizes all available data points rather than just two.

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Homework Statement



why did you use the least squares method for finding m, rather than the standard slope formula?

Homework Equations





The Attempt at a Solution



I am totally confused about why you have to use the least squares method
 
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In the real world the measured values don't line on a perfect stright line - due to experimental and measurement errors.
The least squares fit gives the best 'average' fit to the data.
 
In addition to mgb's post, you may well have more then 2 points to fit your line to. Since you are attempting to find the line which best approximates ALL of your data you need method which uses information from all of your data points. The normal methods for determining the parameters of a line use information from only 2 points.
 
ok thanks a lot! i think i understand it now
 

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