Correlation and regression are known the two important concepts in statistical research established on the distribution of variables. A variable distribution is clarified as a classification/distribution of various variables.

Correlation and regression are important chapters for grade 12 students.

They are used to explain the nature of the association and strength between the two constant quantitative variables. The extent of these associations and the effects of these predictions are used to observe these analytical structures in our everyday lives.

In this article, we’ll thoroughly go through the Correlation and Regression analysis, uses and differences.

Table of Contents

**What is Correlation?**

The term correlation is a combination of two ‘Co’ words (together) and the relationship between the two quantities. Correlation is when it is noticed that a change in one unit of one variable is offset by an equal change in another variable, i.e. directly or indirectly, at the time of the analysis of two variables.

In other words, the variables do not correlate when the movement in one given variable does not correspond to any activity in a certain direction in another variable. It is a statistical method that shows the resistance of the relationship between pairs of variables.

The correlation can be negative, or it can be positive too. If two variables are moving in the same direction and an increase in one variable leads to a subsequent increase in the other variable and vice versa, then these variables are known to be positively correlated—for example, investments and profits.

On the other hand, if the two variables tend to move in different directions so that an increase in one variable causes a decrease in another variable or vice versa, this is referred to as a negative correlation—for instance, price and demand for the product.

The positive change implies that the x and y variables are moving in the same direction, while the negative change implies that the x and y variables are moving in opposite directions.

**There are three types of correlation:**

- Positive Correlation- When two variables are moving in the same direction, increasing the value of one variable increases the other, and vice versa
- Negative correlation- When two variables move in different directions in such a way that every increase in one variable leads to a decrease in the value of the other and vice versa
- Zero Correlation- If a change in one variable does not depend on the other, then the zero correlation has the variables.

**What is Regression?**

A statistical technique that relies on the average mathematical relationship between two or more variables is called regression to assess the difference in the dependent variable on the scale due to the change in one or more independent variables.

It plays a vital role in several human activities because it is a useful and flexible tool for predicting past, current, or future events, depending on the past or present events. The records can be used, for example, to evaluate the future earnings of a company.

There are two given variables, x and y, in a simple linear regression, where y depends on x, or let’s say it is influenced by x. Here y is referred to as a dependent or criterion variable, and x is an independent or predictor variable. y over x is expressed as follows:

Y = a+bx

where,

a = constant,

b = regression coefficient,

and a, b are the two regression parameters in this equation.

The primary purpose of regression is a thorough analysis, which is more complex than correlation and builds an equation that can be used to optimise data structures for prospective outlines.

**There are two types of regression:**

- Simple linear regression- This is a statistical technique used to summarise and examine the associations of two constant variables: an independent variable and a dependent variable.
- Multiple linear regression- This examines the linear relationship of a dependent variable and more than one existing independent variable.

**When to Use It?**

Correlation: The association of two or more variables, i.e., correlation, comes into play when a direction needs to be understood immediately.

Regression: When the numerical response from y to x needs to be optimised and recognised, the regression is used to understand and approximate how y affects x.

**Differences between Correlation and Regression**

The major point of difference in correlation and regression is the degree of association between two variables; let them be x and y. Here, correlation is used to measure degree, while regression is the basis to deduce how one variable influences another.

**Key differences are as follows:**

- Correlation clearly emphasises a relationship between the two variables, whereas in contrast, emphasis on how one variable influences the other is crucial in regression.

- Correlation doesn’t capture causality while it is based on regression.

- In correlation, the link between x and y is identical to that between y and x. But contrary to this, in regression of x and y, and y and x, the outcome fully varies.

- One point in the difference is also the graphical representation of a correlation, whereas one line depicts a linear regression.

- The main goal of the correlation is to find a quantitative/numerical value that can correctly express the relationship between the values. When it comes to regression, your main goal is to compute the values of a random variable based on the values of the fixed variable.

- In correlation, the independent and dependent values have no difference; however, both the dependent and independent variables are different in regression.

- The correlation indicates the extent to which both variables can move together. Still, the regression indicates how the change in the known variable (p) unit affects the evaluated variable (q).

- In correlation, x and y can be interchanged, but the same is not applicable in regression.
- Prediction and optimisation only operate with the regression technique and would not be reasonable in the correlation analysis.

**Conclusion:**

To conclude, regression would be considered the best option when searching for an easy way to build a robust model, an equation, or for predicting response. Still, if you’re searching for an immediate answer in the form of a summary to recognise the strength of a relationship, then correlation would be the best possible approach.