Correlation vs Regression – The Battle of Statistics Terms

Correlation vs regression both of these terms of statistics that are used to measure and analyze the connections between two different variables and used to make the predictions. This method is commonly used in various industries; besides this, it is used in everyday lives.

For example, you might see that someone is wearing expensive attire; you automatically think that he/she might be financially successful. Another example of it is that you think to lose weight by working out in the morning, and then you start running from the next morning.

The above-mentioned examples are the real-life examples of correlation vs regression, as one variable, i.e., expensive attires, is directly related to other variables, i.e., being wealthy. Therefore, we have provided you the list of similarities and differences of correlation vs regression.

What is the correlation?

As correlation itself give you the meaning of the word that is ‘co’ means together, and ‘relation’ means a connection or the link between two quantities. Or we can say that if a variable change, then another variable will automatically change whether it could be directly or indirectly.

For instance, assume that we have two different variables x and y. The changes in these two variables are taken as positive or negative.  Whenever the two variables are changed in the same direction. Or we can say that if a single variable is increasing, then the second variable will also increase then the change is considered to be positive.

The formula of correlation

The correlation coefficient is used to indicate the data of the relationship between two variables by using the following formula:

Where

• rxy – the correlation coefficient of the variables x and y.
• xi – the values of the x-variable is a representation.
• – the mean of the values of the x-variable.
• yi – the values of the y-variable in a representation.
• ȳ – the mean of the values of the y-variable.

What is the regression?

Regression represents how the single variable affects the other variable, or a single variable can be responsible for the changes in another variable. It implies that the results are dependent on a single or more variable.

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For example, correlation is used to define the relationship between the two variables, Whereas regression is used to represent the effect of each other. The example of it is, because of heavy rainfall, several crops can be damaged. And it could lead to floods also.

The formula of regression

The regression is used to represent the relationship between a variable and an independent variable. So it can be represented as:

Where:

• Y – Dependent variable.
• X – Independent variable.
• a – Intercept.
• b – Slope.
• ϵ – error (Residual).

Now before proceeding to the differences of both correlation vs regression, let’s find out the similarities of both.

Similarities of both correlation vs regression

• Both terminologies are used to quantify the strength and direction of the relationship between two variables.
• There is a certain point when correlation and regression slope both are negative individually.
• Again both correlation and regression slope can be positive.

Differences between correlation vs regression

Besides the similarities, there are some differences that are listed below: