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Least Squares Best Fit Line

TopThe line of best fit represents the over heading points in the coordinate Geometry. That means a line passes through the center of a group of data, and making the greedy choice of representation. It is used to represent the results of gathering data of two variables which is said to be the least squares best fit line. It is also calculated by using an eyeball method by drawing a line on a scatter plot so that the Point which lies above and below the lines is equal.

Now we will see Line of Best Fit or least Square method:

This is the most applicable method for finding the line of best fit.

It is used to show the relationship between two variables:

We have to follow some steps for finding the line of best fit or the least square method:

Step 1: First we calculate the Mean of ‘x’ values and mean of ‘y’ values.

Step 2: After that we put the sum of squares of x – values in expression.

Step 3: Then we multiply it by its corresponding y – values.

Step 4: After then we find the Slope of the line.

And the formula for finding the Slope of the line is given as:

Suppose we have two variable ‘R’ and ‘S’, then the formula is:

$\varepsilon$RS - $\frac{(\varepsilon R)(\varepsilon S)}{n}$/ $\varepsilon R^{2}$ - $\frac{(\varepsilon R)^{2}}{N}$

Where, ‘n’ represents the total number of data points and ‘m’ is the slope of the line.

Step 5: Then we put the y – intercept of the line with the help of the formula:

b = ‘p’ – mq’;
Where, ‘p’ and ‘q’ both are the Median of the x – and y – coordinates of the data points respectively.

Step 6: At last we use the slope and y – intercept and we get the equation of the line.