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#### The method of least squares

Linear regression and its most popular method - least squares

The method of least squares is very useful in statistics as it allows us to fit a linear model to data. If we are conducting a scientific experiment and the results form a straight line, we can express it with the formula y = ax + b. To establish the value of the coefficients a and b, we need to write and solve a system of equations with two unknowns.

When is the method of least squares useful?
The method of least squares is used in correlation and regression analysis. If it appears to us that our data forms a straight line on the graph, it is worth making sure that other possibilities do not fit better. It might well be that our arrangement of points fits better with a logarithmic or exponential function. However, if we are sure that we are dealing with a linear function, we can use the method of least squares. It allows the value of any point on the straight line that is the graph of the function for our data to be calculated.

Where is the method of least squares used?
Methods related to a linear function such as least squares work well in many sciences where statistics are important. Biology, sociology, economics – these are just a few examples of fields where the data obtained in a study can form a straight line. The method of least squares does a great job of accentuating points that have values that differ from the line (outliers) – they are problematic as they least fit the line that we have taken as a function. Also, the method of least squares is very simple and easy to understand, which often cannot be said of other, more complicated function formulas.

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