Explore BrainMass

# Least squares method

This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

Using the least squares method answer the following in a word doc.

· What are the main strengths of this method?
· What are its main shortcomings?
· When would least squares be useful in the real world?
· Does the use of linear algebra make this method easier to understand or use?

https://brainmass.com/math/linear-algebra/least-squares-method-60848

#### Solution Preview

Using the least squares method answer the following in a word doc.
·What are the main strengths of this method?

The main strengths of this method are
(1) It can be used to make predictions.
(2) Since it is a linear model, it is easy to compute the dependent variable value.
(3) It has good effect when the dependent and independent variables show a good linear relation.

·What are its main shortcomings?

Since it is a linear model, if the dependent and independent variables don't show a good linear relation, instead, a quadratic relationship, then it doesn't fit data well.

·When would least squares be useful in the real world?

In the real world, when you need to make predictions for one variable Y based on one or more variables X, and if Y and X have a linear relation, then the least squares method would be useful.

·Does the use of linear algebra make this method easier to understand or use?

Since when we use least squares method, we need to find a linear equation
Y=a+bx,
So, we need to determine the coefficients a and b so we have to solve for an equations system for a and b. Hence, the use of linear algebra make this method easier to understand or use. Read the details below. Or use a link http://mathworld.wolfram.com/LeastSquaresFitting.html

Least Squares Fitting

A mathematical procedure for finding the best-fitting curve to a given set of points by minimizing the sum of the squares of the offsets ("the residuals") of the points from the curve. The sum of the squares of the offsets is used instead of the ...

#### Solution Summary

This describes strengths and weaknesses of the least squares method.

\$2.19