Correlation and Regression

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- Samuel Dominic Chukwuemeka

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Samuel Dominic Chukwuemeka

Correlation and Regression Calculators


I greet you this day,
These calculators are for horizontal entries of data only
To use the calculators for vertical data entries, please visit Correlation and Regression Calculators (Vertical data entries only)
I wrote the codes for the calculators using JavaScript, a client-side scripting language.
For some calculators (calculators with Other details), it is recommended you refresh your browser after each calculation.
Comments, questions, and constructive criticisms are welcome. You may contact me. Thank you for visiting.
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 $y$


in


Data $x$




$x - \bar{x}$
$(x - \bar{x})^2$



$\dfrac{x - \bar{x}}{s_{x}}$

Data $y$




$y - \bar{y}$
$(y - \bar{y})^2$



$\dfrac{y - \bar{y}}{s_{y}}$

$\left(\dfrac{x - \bar{x}}{s_x}\right)\left(\dfrac{y - \bar{y}}{s_y}\right)$






$\hat{y}$
$y - \hat{y}$
$(y - \hat{y})^2$


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 $y$


in


Data $x$






$x^2$


Data $y$






$y^2$


$x * y$

























$\hat{y}$
$y - \hat{y}$
$(y - \hat{y})^2$


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









Least-Squares Regression Model

Case 3: Least-Squares Regression Model
Given: data X, Least-squares regression line
To Calculate: Mean value of response variable

x +


Residuals

Case 4: Residuals
Given: Input, Least-squares regression line (required), Output (optional)
To Calculate: Predicted Output, Residual



x +






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



$X_1^2$







$X_2^2$







$X_1 * X_2$





$X_1 * Y$





$X_2 * Y$















$\hat{y}$
$y - \hat{y}$

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
$R_X$ $R_Y$
$d = R_X - R_Y$ $d^2 = (R_X - R_Y)^2$