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Linear Correlation Coefficient Calculator + Online Solver With Free Steps

The online Linear Correlation Coefficient Calculator is a calculator that allows you to find the correlation coefficient between two variables.

The Linear Correlation Coefficient Calculator is a powerful tool that helps mathematicians and scientists easily calculate the correlation coefficient between two data values.

What Is a Linear Correlation Coefficient Calculator?

The Linear Correlation Coefficient Calculator is an online tool that lets you determine the correlation coefficient between two datasets. 

The Linear Correlation Coefficient Calculator takes in two inputs: data points of variable x and data points of value y. After inputting these data points, you make sure to click the “Submit” button. The calculator then displays the results at once.

How To Use a Linear Correlation Coefficient Calculator?

To use the Linear Correlation Coefficient Calculator, we need to enter the inputs and click the “Submit” button. The detailed instructions on using the Linear Correlation Coefficient Calculator are given below:

Step 1

First, we add the data point values for x into the Linear Correlation Coefficient Calculator. Make sure that commas separate the values.

Step 2

After adding the data point values for x, we add the data point values for y into the Linear Correlation Coefficient Calculator. We make sure that the values are separated using commas.

Step 3

Finally, after adding all the data point values in the Linear Correlation Coefficient Calculator, we click the “Submit” button. The calculator instantly produced the results and gives us the correlation coefficient between the two data points.

How Does a Linear Correlation Coefficient Calculator Work?

The Linear Correlation Coefficient Calculator works by taking in the inputs and calculating the correlation coefficient between the two variables. The Linear Correlation Coefficient Calculator uses the following equation to find the correlation coefficient:

\[ r = \frac{n(\sum x y) – (\sum x)(\sum y)}{\sqrt{\left [ n \sum x^{2}-(\sum x)^{2} \right ]\left [ n \sum y^{2} – (\sum y)^{2} \right ]}} \]

What Is Correlation Coefficient?

The correlation coefficient is a statistical measure of the strength of the association between two variables’ relative movements. The values range from -1.0 to 1.0. 

Correlation

A calculated number more than or less than 1.0 indicates that the correlation measurement was incorrect. A correlation of -1.0 suggests that there is no association, but a correlation of 1.0 means that there is no correlation. A correlation of 0.0 indicates no linear link between the two variables’ movement.

In investment and finance, correlation statistics are helpful. If you wanted to know how closely the price of crude oil and the stock price of an oil-producing firm are correlated, you could construct a correlation coefficient, for instance. The correlation between the two variables is extraordinarily positive since rising oil prices increase oil firms’ income.

In other words, investors can hedge their portfolios with negatively correlated assets or securities to lessen market risk due to volatility or extreme price changes. Because they want the dividend income or yield from the stock or security, many investors hedge the price risk of a portfolio, thus reducing any capital gains or losses.

What Is Pearson Coefficient?

The Pearson coefficient is a sort of correlation coefficient that illustrates the association between two variables measured on the same interval or ratio scale. The Pearson coefficient quantifies the strength of the link between two continuous variables.

Linear Relationship

The Pearson coefficient measures a linear relationship between two variables, indicating its intensity and direction. Both nonlinear interactions between two variables and the distinction between dependent and independent variables are not captured. 

The Pearson coefficient uses the following formula to calculate the correlation between two variables:

\[ r = \frac{n(\sum x y) – (\sum x)(\sum y)}{\sqrt{\left [ n \sum x^{2}-(\sum x)^{2} \right ]\left [ n \sum y^{2} – (\sum y)^{2} \right ]}} \]

Solved Examples

The Linear Correlation Coefficient Calculator can quickly help you find the correlation between two data points.

The following examples are solved using the Linear Correlation Coefficient Calculator:

Example 1

While working on his assignment, a college student comes across the following two datasets:

X values = 3,4,2,4,7,7

Y values = 8,10,11,13,16,18

The student needs to find the linear correlation coefficient between the variables. Using the Linear Correlation Coefficient Calculator, find the correlation coefficient between the two variables.

Solution

With help from the Linear Correlation Coefficient Calculator, we can easily find the correlation coefficient between the two variables. First, we input the X values into the Linear Correlation Coefficient Calculator; the X values are 3,4,2,4,7,7. After adding the X values into the calculator, we add the Y values into the Linear Correlation Coefficient Calculator; the Y values are 8,10,11,13,16,18.

Finally, after adding the X and Y values into the Linear Correlation Coefficient Calculator, we click the “Submit” button. The calculator quickly displays the results below the calculator and gives us the correlation coefficient between the two variables.

The following results are extracted from the Linear Correlation Coefficient Calculator:

Results:

0.868187

Example 2

While experimenting, a mathematician comes across the following dataset:

X values = 12,11,10,9,8,7,6,5,4

Y values = 13,14,15,16,17,18,19,20

To complete his experiment, the mathematician needs to find the linear correlation coefficient of the given data points. Using the Linear Correlation Coefficient Calculator, find the correlation between the two variables.

Solution

We can quickly determine the correlation coefficient between the two variables using the Linear Correlation Coefficient Calculator. The X values are 12,11,10,9,8,7,6,5,4 and are entered into the Linear Correlation Coefficient Calculator first. The Y values are 13, 14, 15, 16, 17, 18, 19, and 20. After entering the X values into the calculator, we enter the Y values into the Linear Correlation Coefficient Calculator.

We finally click the “Submit” button after entering the X and Y values into the Linear Correlation Coefficient Calculator. The calculator provides us with the correlation coefficient between the two variables and displays the findings instantly below the calculator.

The following results are generated from the Linear Correlation Coefficient Calculator:

Results:

Pearson correlation:

X = (12,11,10,9,8,7,6,5,4)

Y = (13, 14, 15, 16, 17, 18, 19, 20)

Example 2

Consider the following two data points:

X values = 2,4,6,8,10,12,14,16,18,20

Y values = 1,3,5,7,9,11,13,15,17,19

Using the Linear Correlation Coefficient Calculator, find the correlation coefficient between the two data points.

Solution

Using the Linear Correlation Coefficient Calculator, we can instantly calculate the correlation coefficient between the two variables. The X variables are 2,4,6,8,10,12,14,16,18,20 and are first entered into the Linear Correlation Coefficient Calculator. The Y values are 1,3,5,7,9,11,13,15,17, and 19. After entering the X values into the calculator, we enter the Y values into the Linear Correlation Coefficient Calculator.

After entering the X and Y values into the Linear Correlation Coefficient Calculator, we finally click the “Submit” button. The calculator calculates the correlation coefficient between the two variables and displays the results just below the calculator.

The following results are taken from the Linear Correlation Calculator:

Results: 

0

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