Correlation vs Regression — The Battle of Statistics Terms
By: Vijay Choubey
Tags: Mathematics, Statistics, Machine Learning, Data Science

Statistics is complex. For newbies, starting to learn statistics can be painful if they don’t have right resources to learn from. Well, this is my 3rdblog on statistics, I’m super excited to start with the concept of Correlation vs regression. So lets first understand it.

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.

— the correlation coefficient of the variables x and y. xi — the values of the x-variable is a representation.

— the values of the x-variable is a representation. x̅ — the mean of the values of the x-variable.

— the mean of the values of the x-variable. yi — the values of the y-variable in a representation.

— the values of the y-variable in a representation. ȳ — the mean of the values of the y-variable.

There are a few common types of tests to measure correlation, these are: Pearson, Spearman rank, and Kendall Tau. Each have their own assumptions about the data that needs to be meet in order for the test to be able to accurately measure the level of correlation. These are discussed further in the post. Each type of correlation test is testing the following hypothesis.

H0 hypothesis: There is not a relationship between variable 1 and variable 2

HA hypothesis: There is a relationship between variable 1 and variable 2

If the obtained p-value is less than what it is being tested at, then one can state that there is a significant relationship between the variables. Most fields use an alpha level of 0.05 which I will also use.

There are a few types of correlation:

Positive correlation: as one variable increases so does the other

Negative (inverse) correlation: as one variable increases the other variable decreases

No correlation: there is no association between the changes in the two variables

The strength of the correlation matters. The closer the absolute value is to -1 or 1, the stronger the correlation.

r valueStrength0.0–0.2Weak correlation0.3–0.6Moderate correlation0.7–1.0Strong correlation

Pearson correlation assumptions

Pearson correlation test is a parametric test that makes assumption about the data. In order for the results of a Pearson correlation test to be valid, the data must meet these assumptions:

The sample is independently and randomly drawn

A linear relationship between the two variables is present

When plotted, the lines form a line and is not curved

There is homogeneity of variance

The variables being used in the correlation test should be continuous and measured either on a ratio or interval sale, each variable must have equal number of non-missing observations, and there should be no outliers present.

Spearman Rank correlation assumptions

The Spearman rank correlation is a non-parametric test that does not make any assumptions about the distribution of the data. The assumption for the Spearman rank correlation test is:

There is a monotonic relationship between the variables being tested

A monotonic relationship exists when one variable increases so does the other

For the Spearman rank correlation, the data can be used on ranked data, if the data is not normally distributed, and even if the there is not homogeneity of variance.

Kendall’s Tau correlation assumptions

The Kendall’s Tau correlation is a non-parametric test that does not make any assumptions about the distribution of the data. The only assumption is:

There should be a monotonic relationship between the variables being tested

The data should be measured on either an ordinal, ratio, or interval scale.

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.

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.

— Dependent variable. X — Independent variable.

— Independent variable. a — Intercept.

— Intercept. b — Slope.

— 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:

Parameter for Correlation and Regression:

Definition: Correlation is used to measure statistics that determine the connection between two variables. Regression is used to represent the connection between the independent and dependent variables.

Usages :Correlation is used to show the linear connection between two variables. Regression is used to get the best data and to estimate a single variable on the basis of other variables.

Independent and dependent variables: In Correlation, there is no difference between both variables. In Regression, both of the variables are different from each other.

Indicate: The coefficient of Correlation signifies the extent to which the two variables values that move together.Regression signifies the effect of changes in the units that are known as a variable (X) on the estimated variable (Y).

Aim: Correlation helps to get the numeric values expressions’ relation between variables.Regression helps to determine the values of selected variables on the basis of the fixed variables.

Data representation: Correlation represents a single point. Regression can represent the data with a line.

Use mathematical equations: No, Correlation has no direct connection between mathematical equations.Yes, there is a direct connection between mathematical equations in Regression.

Conclusion

The above discussion on correlation vs regression shows that there are similarities and dissimilarities between the two mathematical concepts, even though both are studied together. The correlation is used by the researchers when they want to know the variable under the study are correlated or not if this is so. Then what is the strength of the association. Whereas, the regression analysis is used to get function relationship between the two variables to make the further projections of the events.

Thanks for the read. I am going to be writing more beginner-friendly posts in the future too. Follow me up to be informed about them.

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