Correlation and Regression

So then, it is not of him that willeth, nor of him that runneth, but of God that showeth mercy. - Romans 9:16

The Joy of a Teacher is the Success of his Students. - Samuel Dominic Chukwuemeka

1st Formula for Calculating Correlation Coefficient

Given: datasets X and Y (required), α (Use 5% if not given)

To calculate: Pearson correlation coefficient (Show all Steps); Least-squares regression line (Line of Best Fit); Residuals; other details

in













2nd Formula for Calculating Correlation Coefficient

Given: datasets X and Y, α (use 5% if not given)

To calculate: Pearson correlation coefficient (Show all Steps); Least-squares regression line (Line of Best Fit); Residuals; other details

in













Least - Squares Regression Line

Given: r, x̄, ȳ, sx, sy

To calculate: Least-squares regression line and other details



Predicted Y and Residual

Given: x, least-squares regression line (required), y (optional)

To calculate: predicted Y, residual

x +



Least Squares Regression Model

In the least-squares regression model, yi = β1xi + β0 + εi,
εi is a random error term with mean = 0, and
standard deviation σεi = σ

Given: x, least-squares regression line

To calculate: mean value of response variable

x +



Multiple Linear Regression for Two Independent Variables

Given: datasets X1, X2, Y

To calculate: Multiple regression equation and other details













Samdom For Peace

I greet you this day,

You may use these calculators to check your answers. You are encouraged to solve the questions first, and check your answers. These topics are covered in my Notes and Videos on Correlation and Regression.

I wrote the codes for these calculators using Javascript, a client-side scripting language. Please use the latest Internet browsers. The calculators should work.

Comments, ideas, areas of improvement, questions, and constructive criticisms are welcome. You may contact me. Please note that I may not respond to every message. If you are my student, please do not contact me here. Contact me via the school's system. Thank you for visiting.

Samuel Chukwuemeka (Samdom For Peace) B.Eng., A.A.T, M.Ed., M.S



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