Linear Regression Calculator

The linear regression calculator find the linear regression by using the least square method. Get instant calculations for a line of best fit along with graphical interpretation.

What Is Linear Regression?

“Linear regression is a predictive analysis method in which the value of one variable is predicted based on another variable.” Linear regression always indicates a linear relationship between the variables. For quick and accurate calculations, our linear regression calculator is a reliable tool you can use.

Linear Regression Formula:

You can evaluate the line that best fits the data points using the following linear regression formula:

ŷ = bX + a

Where:

ŷ = dependent variable (to be predicted)

b = slope of the line

X = independent variable

a = intercept (the value of y when X = 0)

The regression equation calculator uses the same formula to predict results. You can calculate the values of a and b using the following equations:

a = My − (b × Mx)

Where:

Mx = mean of X

My = mean of Y

b = SP / SSx

Where:

SP (Σxy) = Σ(X − Mx) * (Y − My)

SSx (Σx²) = Σ(X − Mx)²

How To Find Line of Best Fit?

Let’s solve a few examples to better understand linear regression analysis and determine the line of best fit for a given dataset:

Example:

Find the least squares regression line for the following dataset:

{(2, 9), (5, 7), (8, 8), (9, 2)}

Also, estimate the value of y for X = 2 and X = 3.

Solution:

Sum of X = 2 + 5 + 8 + 9 = 24

Sum of Y = 9 + 7 + 8 + 2 = 26

Mean values:

Mean of X = Mx = 24 / 4 = 6

Mean of Y = My = 26 / 4 = 6.5

Now, calculate the following quantities:

SSx (Σ(X − Mx)²) = 16 + 1 + 4 + 9 = 30

SP (Σ(X − Mx)*(Y − My)) = -10 - 0.5 + 3 - 13.5 = -21

Now, determine the linear regression equation:

ŷ = bX + a

Calculate the values of a and b:

b = SP / SSx = -21 / 30 = -0.7

a = My − (b × Mx) = 6.5 − (-0.7 × 6) = 6.5 + 4.2 = 10.7

Now, plug the values into the regression formula:

ŷ = -0.7X + 10.7

For given values of X, the estimated values of Y are as follows:

The graphical plot of line of best fit is as follows: