Correlation and Regression Calculators

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

Pearson Correlation

Pearson Correlation Coefficient

Case 1 (First Formula)
Given: Datasets X and Y, Level of Significance
(If the significance level is not given, use 5% or 0.05)

To Calculate: Pearson's correlation coefficient, Least-squares regression line, Residuals, other details
Show all steps

Dataset X	Dataset Y

Significance Level is:
in

Data X
Sum of data values =

Sample size =

Mean =

Deviation from the Mean

Square of the Deviation

Sum of the squares =

Standard Deviation =

Quotient of the:
Deviation from the Mean and the Standard Deviation

Data Y
Sum of data values =

Sample size =

Mean =

Deviation from the Mean

Square of the Deviation

Sum of the squares =

Standard Deviation =

Quotient of the: Deviation from the Mean and the Standard Deviation

Product of each of the two Quotients

Sum of the products =

Sample size (Less 1) =

Pearson linear correlation coefficient =

Predicted Y-values

Residuals

Square of the Residuals

Sum of the squares =

Other details

Pearson Correlation Coefficient

Case 1 (Second Formula)
Given: Datasets X and Y, Level of Significance
(If the significance level is not given, use 5% or 0.05)

To Calculate: Pearson's correlation coefficient, Least-squares regression line, Residuals, other details
Show all steps

Dataset X	Dataset Y

Significance Level is:
in

Data X
Sample size =

Sum of data values =

Mean =

Standard Deviation =

Square of the data values for dataset X

Sum of the squares =

Data Y
Sample size =

Sum of data values =

Mean =

Standard Deviation =

Square of the data values for dataset Y

Sum of the squares =

Product of each data value of X and Y

Sum of the products =

Sample Size multiplied by the Sum of the products =

Sum of data values of X multiplied by the Sum of data values of Y =

Numerator (Difference of previous two) =

Sample Size multiplied by the Sum of the squares of data values of X =

Square of the sum of data values of X =

Square root of the difference of previous two for X =

Sample Size multiplied by the Sum of the squares of data values of Y =

Square of the sum of data values of Y =

Square root of the difference of previous two for Y =

Denominator (product of the square roots) =

Pearson linear correlation coefficient =

Predicted Y-values

Residuals

Square of the Residuals

Sum of the squares =

Other details

Least-Squares Regression Line

Case 2: Least-Squares Regression Line
Given: Pearson's correlation coefficient, Mean of data X, Standard Deviation of data X, Mean of data Y, Standard Deviation of data Y
To Calculate: Least-squares regression line, other details

Pearson's correlation coefficient is:

Mean of data X is:

Standard Deviation of data X is:

Mean of data Y is:

Standard Deviation of data Y is:

Least-Squares Regression Model

Residuals

Multiple Linear Regression for Two Independent Variables

Case 5: Multiple Linear Regression for Two Independent Variables
Given: Datasets X₁, X₂, Y

To Calculate: Multiple Regression Equation, other details
Show all steps

Dataset X₁	Dataset X₂	Dataset Y

Sample size of of X₁ = Sample size of of X₂ = Sample size of of Y =

Square of the data values for dataset X₁

Sum of the squares of X₁ =

Sum of the data values of X₁ =

Square of the sum of the data values of of X₁ =

Regression Sum for X₁ =

Square of the data values for dataset X₂

Sum of the squares of X₂ =

Sum of the data values of X₂ =

Square of the sum of the data values of of X₂ =

Regression Sum for X₂ =

Product of each value of X₁ and the corresponding value of X₂

Sum of the products of X₁ and X₂ =

Product of the sum of X₁ and the sum of X₂ =

Regression Sum for X₁ and X₂ =

Product of each value of X₁ and the corresponding value of Y

Sum of the products of X₁ and Y =

Product of the sum of X₁ and sum of Y =

Regression Sum for X₁ and Y =

Product of each value of X₂ and the corresponding value of Y

Sum of the products of X₂ and Y =

Product of the sum of X₂ and sum of Y =

Regression Sum for X₂ and Y =

Slope (coefficient of X₁) =

Slope (coefficient of X₂) =

Y-intercept =

Multiple linear regression equation is: ŷ =

Predicted Y-values

Residuals

Spearman Correlation

Spearman Correlation Coefficient

Case 1
Given: Datasets X and Y

To Calculate: Spearman correlation coefficient, Interpret Spearman's correlation coefficient
Show all steps

Dataset X	Dataset Y

Sorted Dataset X	Rank X

Sorted Dataset Y	Rank Y

Dataset X	Rank X

Dataset Y	Rank Y

Rank X	Rank Y

Rank X - Rank Y	(Rank X - Rank Y)²
Difference	Square of the difference

Sum of the square of the differences =

Spearman's correlation coefficient =