Least Squares

The method of least squares is a standard approach to the approximate solution of over determined systems, i.e., sets of equations in which there are more equations than unknowns.

Least Squares is also a statistical method for finding a line or curve — the line of best fit — that best represents a correspondence between two measured quantities (e.g., height and weight of a group of college students). When the measurements are plotted as points on a graph and seem to fall near the same line, the least squares method may be used to determine the best-fitting line.

A line of best fit is drawn through a scatter plot to find the direction of an association between two variables. It can show various co-relations between two variables.

·         The line of best that rises quickly from left to right is called a positive correlation.

·         The line of best that falls down quickly from left to the right is called a negative correlation

·         Strong positive and negative correlations have data points very close to the line of best fit.

·         Weak positive and negative correlations have data points that are not clustered near or on the line of best fit.

·         Data points that are not close to the line of best fit are called outliers.

Conclusion

The least square method is used to compute estimations of parameters and fit data. It is one of the most popular statistical methods to draw the line of best fit. A line of best fit is drawn through a scatter plot to find the direction of an association between two variables. This line of best fit can then be used to make predictions. It can show various co-relations between two variables. It can be used to set the trend line regarding various business scenarios such as advertisement and sales, price and demand, etc.

The project taught us the Excel application in Mathematics to draw the line of best fit. It uses various tools like Chart Wizard, Chart Layout and Goal Seek to compute and graph the scatter plot diagram.