How To Calculate The Least Squares Regression Line By Hand

Least squares regression line is a fundamental concept in statistics, used to find the best-fit straight line through a set of data points. Calculating it by hand is an essential skill for understanding the underlying mathematics and logic.

1. Enter comma-separated X and Y values in the respective input fields.
2. Click ‘Calculate’.
3. View the results below the calculator.

The formula for the least squares regression line is:

b = [(ΣXY) – (n * ΣX * ΣY) / (ΣX^2 – n * (ΣX)^2)]

a = (ΣY – b * ΣX) / n

Sample Data

X	Y
1	2

Calculated Values

ΣX	ΣY	ΣXY	ΣX^2
5	11	35	29

• Always check the assumptions of linear regression before using it.
• Consider using a logarithmic or exponential transformation if the data is not linear.

What are the assumptions of linear regression?

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