Main Idea of Least Squares Method and Linear Regression

Tue, 07 Jul 2026 10:15:30 +0000

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Linear Regression is a method that finds the best fitting line for a set of data points.

It is used to predict the value of a dependent variable based on the value of one or more independent variables.

let's assume we have a set of data points $(x_1, y_1), (x_2, y_2), ..., (x_n, y_n)$.

The data points can be represented as a scatter plot.

The data points are scattered in a way that it may represent a line.

where each point $(x_i, y_i)$ represents a data point.

A line can be represented as $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept.

Usually, we have some random value of $m$ and $b$ and we want to find the best value of $m$ and $b$ such that the line passes through the data points.

For example in this graph there are mulitple data points, and we want to find the best fitting line for these data points.

This can be done using the least squares method.

Least Squares Method

The least squares method is a method that finds the best fitting line for a set of data points.

we calculate the sum of the squares of the differences between the actual values and the predicted values.

$(y_i - (mx_i + b))^2$

We want to minimize this value.

So, we check each state of line and calculate the sum of the squares of the differences between the actual values and the predicted values.

We choose the line that minimizes this value.

How this is done mathematically

This whole caculation can be done mathematically. I will discuss in depth in my next article.

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Main Idea of Least Squares Method and Linear Regression

Least Squares Method

How this is done mathematically