Correlation and Regression Calculators

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 What option? Percent Decimal

Calculate

Data $x$
$\Sigma x$ =

$n_x$ =

$\bar{x}$ =

$x - \bar{x}$

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

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

$s_x$ =

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

Data $y$
$\Sigma y$ =

$n_y$ =

$\bar{y}$ =

$y - \bar{y}$

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

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

$s_y$ =

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

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

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

$n - 1$ =

$r$ =

$\hat{y}$

$y - \hat{y}$

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

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

Other details

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 What option? Percent Decimal

Calculate

Data $x$
$n_x$ =

$\Sigma x$ =

$\bar{x}$ =

$s_x$ =

$x^2$

$\Sigma x^2$ =

Data $y$
$n_y$ =

$\Sigma y$ =

$\bar{y}$ =

$s_y$ =

$y^2$

$\Sigma y^2$ =

$x * y$

$\Sigma xy$ =

$n(\Sigma xy)$ =

$(\Sigma x)(\Sigma y)$ =

$n(\Sigma xy) - (\Sigma x)(\Sigma y)$ =

$n(\Sigma x^2)$ =

$(\Sigma x)^2$ =

$\sqrt{n(\Sigma x^2) - (\Sigma x)^2}$ =

$n(\Sigma y^2)$ =

$(\Sigma y)^2$ =

$\sqrt{n(\Sigma y^2) - (\Sigma y)^2}$ =

$\sqrt{n(\Sigma x^2) - (\Sigma x)^2} * \sqrt{n(\Sigma y^2) - (\Sigma y)^2}$ =

$r$ =

$\hat{y}$

$y - \hat{y}$

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

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

Other details

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

Calculate

$n_{X_1}$ = $n_{X_2}$ = $n_Y$ =

$X_1^2$

$\Sigma X_1^2$ =

$\Sigma X_1$ =

$(\Sigma X_1)^2$ =

$\Sigma x_1^2$ =

$X_2^2$

$\Sigma X_2^2$ =

$\Sigma X_2$ =

$(\Sigma X_2)^2$ =

$\Sigma x_2^2$ =

$X_1 * X_2$

$\Sigma X_1 X_2$ =

$\Sigma X_1 * \Sigma X_2$ =

$\Sigma x_1 x_2$ =

$X_1 * Y$

$\Sigma X_1 Y$ =

$\Sigma X_1 * \Sigma Y$ =

$\Sigma x_1 y$ =

$X_2 * Y$

$\Sigma X_2 Y$ =

$\Sigma X_2 * \Sigma Y$ =

$\Sigma x_2 y$ =



$b_1$ =

$b_2$ =

$b_0$ =

Multiple linear regression equation is: ŷ =

$\hat{y}$

$y - \hat{y}$

Case 1
Given: Datasets X and Y

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

Dataset X
Dataset Y

Calculate

Sorted Dataset X	Rank X

Sorted Dataset Y	Rank Y

Dataset X	Rank X

Dataset Y	Rank Y

$R_X$	$R_Y$

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

$\Sigma d^2$ =

$6\Sigma d^2$ =

$n(n^2 - 1)$ =

$\rho = 1 - \dfrac{6\Sigma d^2}{n(n^2 - 1)}$ =