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# Linear Correlation Coefficient Calculation

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## What is a Linear Correlation Coefficient?

A linear correlation coefficient is a value that denotes the strength of the linear relationship between two variables; x and y. Two variables have a linear relationship when their equation can be graphed to form a line.Â

The correlation coefficient, expressed as r, can indicate the strength and direction of the relationship between x and y. The value of r can range from -1 to +1. The sign of the linear correlation coefficient indicates the direction of the relationship between the two variables; a positive value indicates a positive relationship while a negative value indicates a negative relationship. The closer the value of r is to -1 or +1, the stronger the relationship is between the two variables. The closer the value of r is to 0, the weaker the relationship is between the two variables. A value of 0 indicates that there is no relationship between the two variables.Â

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## Requirements to use Pearsonâ€™s Correlation Coefficient

Although there are many different types of correlation coefficients, Pearsonâ€™s correlation coefficient is the most widely used. For this reason, when people refer to correlation coefficients, theyâ€™re often referring to Pearsonâ€™s correlation coefficient or Pearsonâ€™s R.Â

Before we can delve into the correlation coefficient formula and its application, we must first consider the different requirements for Pearsonâ€™s correlation coefficient:Â

• The variables must be on an interval or ratio scale.Â Â
• There should be no outliers in the data.Â
• The variables should be (approximately) normally distributed.
• The association must be linear.

## How to Calculate the Linear Correlation Coefficient of a Dataset?

If your data meets the aforementioned requirements, you can use Pearsonâ€™s correlation coefficient formula to calculate your correlation coefficient (r).Â Â

pxy =Cov(x,y)xy

Where,Â

• pxy : Pearson product-moment correlation coefficient
• Cov(x,y): Covariance of variables x and y
• x : Standard deviation of x
• y : Standard deviation of y

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## Strengths and Weaknesses of the Linear Correlation Coefficient Calculator

### Â Strengths

These are a few strengths of Pearsonâ€™s method of studying correlation:Â

• It indicates the presence or absence of correlation between data sets and also indicates the extent of the correlation.Â
• It indicates the direction of correlation (positive or negative).
• It facilitates the estimation of the value of a dependent variable using a particular value of an independent variable as a reference (through regression equations).Â

### Weaknesses

These are a few weaknesses of Pearsonâ€™s method of studying correlation:Â

• Can be difficult to compute owing to the intricate algebraic methods used to calculate r.Â
• The value of r can be easily skewed in the presence of extreme items.Â
• It cannot distinguish between dependent and independent variables.Â
• It requires the computation of probable error for a fair interpretation of results as it is subject to error.

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## FAQs on Linear Correlation Coefficient Calculator

A linear relationship, or linear association, describes the straight-line relationship between two variables. Any equation that forms a straight line when graphed depicts a linear relationship.

A linear correlation coefficient is a value that reflects the strength of the linear relationship between two variables, x and y.

The linear correlation coefficient between two variables can be calculated using Pearsonâ€™s correlation coefficient formula, which is;Â

pxy =Cov(x,y)xy

The value of the correlation coefficient, r, indicates the strength and direction of the relationship between x and y. A value above 0 indicates a positive relationship while a value below 0 indicates a negative relationship. The closer the value is to -1 or +1, the stronger the relationship between the variables. The closer the value is to 0, the weaker the relationship between the variables.

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### Types of Survey Research Techniques

Types of Survey Research Techniques SHARE THE ARTICLE ON Table of Contents In a modern world, where companies run totally on what and how their