Differences Between Correlation and Regression in Statistics

# Differences Between Correlation and Regression in Statistics

Published
15th Sep, 2023
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14 Mins

Correlation and Regression are popular tools and have been widely used in businesses and research since a long time. The size and application of Big Data in Data Analytics are proving crucial for decision-making. Since the data size and its complex nature is impossible to handle manually, the importance of statistical tools like Correlation and Regression in applying them to business problems has become more valuable. Machine learning and Deep learning algorithms utilize them to provide accurate predictions in fields like computer vision, anomaly detection, etc.

Hence understanding these two concepts (Correlation and Regression), their terminology, governing equations, and possible use cases is immensely important for those interested in applying them in practice. Are the two terms the same? Is there any relation between them, and how can they be estimated? These are a few common questions in the minds of many of us. This article provides simple and adequate answers to these questions as well as highlights g the difference between correlation and regression. Additionally, you can explore the basics of Correlation and Regression in Data Science Bootcamp online course.

## Correlation vs Regression [Comparison Table]

Basis of DifferenceCorrelationRegression
DefinitionCorrelation is a statistical metric that determines the relationship or association between two variables.Regression indicates how an independent variable may be mathematically connected to any dependent variable.
CoefficientThe coefficient Correlation ranges from -1 to +1 and thus, a relative measure.The Regression coefficient is generally an absolute value.
Dependent / Independent variables
Both variables are mutually dependent.The first variable is independent, whereas the second is dependent.
IndicatesIt denotes the extent and manner in which two variables move together.Regression displays the effect of any unit change in the value of the known variable (x) on the value of the estimated variable (y).
Nature of Coefficient
Mutual and symmetrical correlation coefficients exist.Regression describes one variable as a linear function of another one in case of a linear relationship.
ObjectiveTo determine the numerical value that specifies the strength and direction of dependence between two variables.To explain the variability in a dependent variable by means of one or more of independent variables in simple or multiple regression respectively.
Responding Nature
The Correlation coefficient is designed to be independent of any changes in Scale or Origin.The Regression coefficient is affected by changes in Scale but is unaffected by changes in Origin.

## Key Differences Between Correlation and Regression

The points given below explain the key differences between Correlation and Regression in detail:

### 1. Definition

A) What is Correlation?

Correlation is a statistical measure used when we want to find out whether there exists a relationship that can link two variables with each other. This linking is beneficial when it is essential to know what is going to be the impact of some chosen parameter on a target to be achieved as to whether it will be positive or negative. The impact of linkage may then be estimated once the strength and direction are known.

Correlation can be a positive or negative value.

• Positive Correlation

Two variables are considered to be positively correlated when the value of one variable increases or decreases following an increase or decrease in the value of the other variable respectively.

• Negative Correlation

Two variables are considered to be negatively correlated when the value of one variable increases following a decrease in the value of the other variable.

• Zero Correlation

This indicates that there is no relationship between two variables. It is also known as a zero correlation. This is when a change in one variable doesn't affect the other variable in any way.

B) What is Regression?

Regression is another vital statistical tool usually supporting the conclusion of Correlation. Once a link of the impact of one variable (input or independent) over the other, usually the target or output, is established, either positive or negative, then Regression plays its role in estimating this impact in the quantitative term. Once developed, this relation can then be used to estimate output when the input variable changes.

There are different types of regression and some of them have been listed below:

• Linear Regression
• Logistic Regression
• Ridge Regression
• Laso Regression

### 2. Nature of Relationship

Correlation is a statistical measure that indicates the possibility of the existence of an association or relation between two variables. It only gives the strength and direction of the relationship. On the other hand, Regression gives the actual measure of the relationship in quantitative terms between the input and output variables.

### 3. Purpose of Application

The correlation only tells us whether one variable will impact the output variable positively or negatively. Hence the purpose is only to determine whether such a possibility of interdependence exists. Regression goes further in line with Correlation and is applied to find the exact impact on the output.

### 4. Interdependence

The correlation only tells us whether one variable will impact the output variable positively or negatively. Hence the purpose is only to determine whether such a possibility of interdependence exists. Regression goes further in line with Correlation and is applied to find the exact impact on the output.

### 5. Cause and Effect Consideration

In the application of Correlation, although a relation exists between two variables, it is not a case of cause-and-effect relationship. However, in case of Regression, it is definitely a case of a cause-and-effect relationship as a change in x values (cause) results in a change of y (effect).

### 6. Simplicity of Calculation

Relatively Correlation is subjective and easy to calculate, whereas Regression is difficult in estimate due to the number of possible input variables and their different effects on output.

## Correlation Vs Regression: Analysis

In this section, let us understand correlation and regression analysis

### Correlation Analysis

Many times, an analysis of data about two or more quantitative variables is needed to identify the presence of a statistical relationship between them. The outcome of such analysis regarding relationships becomes important in the decision-making process in given situations. For example, look at the following cases:

1. Quantity of fertilizer and the crop yield
2. Height and weight of individuals
3. Excessive rainfall and flood situation
4. Eye power and distance of vision

It can be seen that there exists a definite relationship between the two entities listed. Hence, now Correlation analysis can be defined as a technique that utilizes the strength and direction of the association or relationship between two quantitative variables. The coefficient of Correlation is a numerical value that points to the strength or magnitude and the direction of statistical association or relation between two variables.

Suppose a straight line is used on a graph to represent the association between these two variables, then the closeness or nearness of the points to the line represents the strength, and the slope, either increasing or decreasing, gives the dependence of increment or decrement of one variable with the other.

The correlation coefficient ‘r’ is used to decide the strength of the relationship between two variables, and its value ranges between -1 and 1, where:

• 1 indicates a strong positive relationship.
• -1 indicates a strong negative relationship.
• A result of zero indicates no relationship at all.

### Regression Analysis

Regression analysis is a statistical process explaining the relationship between two or more variables. This can be shown as a graph with the two variables on the x and y-axis. The independent variable or variables, when changed, they affect the dependent variables, and the regression analysis tries to provide an indication of which particular input variables affect the output most. Furthermore, the governing equation can also quantify this change.

## Correlation Vs Regression: Formula

### Correlation Formula

The Correlation coefficient, which is used to estimate the strength of the relationship between two variables, dependent and independent, is given by the following formula:

Where:

• rxy – the coefficient of Correlation of the linear association between the variables x and y
• x– the different values of the x-variable in a sample
• the mean or average of the values of the x-variable
• yi – the different values of the y-variable in a sample
• ȳ – the mean of the values of the y-variable

### Regression Formula

In simple Regression, for one input variable and one output variable, the formula is y= b1x + b0, where y is output, x is the input variable, b1 is the slope or Regression coefficient, and bis intercepted on the y axis.

As is well known, this is a simple equation of a straight line. The alphabets b1, b0, and c can be any chosen alphabets.

In practice, this equation is for the best fit line to be as close as possible to all data points. However, the actual data points have some distance from this line, called the error. Hence the error= y- yˆy^

where y is actual output and yˆy^ is predicted output. The least square equation is used to get the minimum value of this error. When input variables are more in number, then the governing equation becomes -

y = b0+b1x1 + b2 x2 + b3x3…bnxn and all the values of Regression coefficients b1, b2 etc. are to be found on similar lines like simple Regression. Know what is Data Science course and clear your doubts.

## Correlation Vs Regression: Examples

### Correlation Example

Two simple examples, one each for a strong positive and strong negative Correlation, can be given as under:

1. Speed of car and the distance it covers in a fixed time. So, if speed is 4km/min and 6 km/min, the distance covered will be 20 km in 5 min or 30 km, respectively; hence there is a strong positive correlation that if speed increases, the distance covered will also definitely increase.
2. If refrigerators' prices go up, demand or purchased quantity will decrease. Here price rise has a strong negative influence on demand.
3. When a strong positive or strong negative influence is not seen, it's a case of weak Correlation, e.g., regular exercise will not necessarily mean weight gain or weight loss, as this can vary due to various other factors.

### Regression Example

Simple Regression: If the height in cm is associated with age and the Regression line is given by y=mx+c where m is the slope and c is the intercept, then we can estimate the height of unknown age if we have the best fit line constructed on the given data.

Serial No.Age
(x) years
Height
(y)cm
1015
2120
3335
4670
59105
612140

With the best fit line (y=10.654x + 9.1203), the estimated value by the equation - the height for x= 8 years (randomly chosen point) = 10.654×8 +9.1203 = 94.23 cm. Also, looking at the graph, the seen value matches with the calculated value.

## Correlation vs Regression: When to Use?

### When to Use Correlation?

You have a Correlation issue when one has to make an urgent decision based on finding the influence of involved variables and if they are two are more in number.

### When to Use Regression?

Regression comes in only when the Correlation possibility is clear. Once a Correlation is obvious, then only you go to quantify their relationship. Hence, if the x variable has a Correlation with y, then if x changes, how much will the change in y?

## Similarities Between Correlation and Regression

### 1. What do These Give?

While Correlation gives the strength and direction of Association between two variables, Regression fortifies the indications of Correlation by estimations of changes in numerical terms.

### 2. Estimation of Parameters

Both Correlation and Regression parameters like strength, the direction of change or its value can be estimated by statistical measures like Correlation coefficient and Regression coefficient.

### 3. Assumptions

Both Correlation and Regression concepts are based on certain assumptions which need to be followed while using them.

### 4. Visual Representation

Both follow the same pattern i.e. when the Correlation showing a line in the graph has a positive or negative slope, the same pattern is seen in the Regression line.

## Advantages of Correlation and Regression

Correlation in statistics refers to the existence of a relation between various events. Correlation analysis is one way to determine whether such a relation exists. One of the main advantages is definitely its practicality in the application.

To undertake a valid Correlation study, we must consider the observed values of two variables, which provides us an advantage in obtaining results. Some of the most well-known advantages of Correlation analysis are:

• Identifying the Behavior Between Two Variables: A Correlation assists in determining the lack or existence of a link between two variables. It is more relevant to issues of everyday life.
• Appropriate Points to Undertake Research: This concept is useful as a starting point to undertake research in finding out the impact of one variable on the other related to the project under consideration. All further decision will prove valid if initial research of results is correct.
• Metrics Simplicity: As the findings are based on proper metrics and mathematical applications, they are simple to understand and classify.

Similarly, Regression offers the following advantages:

1. Regression analysis is beneficial for predicting and forecasting business metrics.
2. It allows estimating values of variables to support business decisions based on Regression analysis predictions.
3. It can be used to identify new opportunities in the market e.g., future demand of a different products or product features, investments based on stock prices, healthcare premiums, etc.

## Conclusion

Through the extensive coverage regarding the concept, advantages, disadvantages, and the mathematical equations, it is quite evident how useful the two terms Correlation and Regression are in present business and research scenarios. In fact, both of them are complementary to each other because if there is no Correlation, there is no point in going for Regression.

However, if there is either a positive or negative Correlation between the dependent variables and independent variables, applying the Regression equation and resulting analysis can prove crucial in decision-making in all domains. Hence, all organizations in manufacturing, sales and marketing, healthcare, agriculture, tourism or aviation, everywhere they are applied in sequence as research tools for better and beneficial decision making.

Hence, it is quite obvious that understanding these two is crucial for anybody working in Data Science domain. If you aspire to build a career in Data Science and would like to know more about the course, go for KnowledgeHut’s Data Science Bootcamp online.

### 1. Should I use Regression or Correlation?

If you are interested in only finding out the association or relation between two variables, you can go for Correlation. However, if you want to find out how exactly the output variables change quantitatively, you have to go for Regression. It must be mentioned that regression usually follows Correlation.

### 2. How are Regression and Correlation related?

As is well known, Correlation gives the measure and direction of two variables and their dependence on each other. However, Regression is the next step which gives a numerical value change on the output with a change in the input variable. We can say that whereas Regression gives cause and effect relationship, Correlation does not do so.

### 3. When should I use Regression analysis?

If your aim is to know how exactly the output will change corresponding to some change in the input variable, you have to go for Regression analysis. This situation is applicable in single or multiple Regression analysis depending on the number of input variables.

### 4. Should you do Correlation before Regression?

Definitely, Correlation should be considered before Regression because Correlation gives you an indication of the relationship between input and output variables. Then you go for Regression by analyzing and finding out the exact quantitative effect between the two variables on changing the input values.

### 5. What is the example of Regression?

Many examples can be given like:

• Monthly salary and expensive purchases
• Age and Height of individuals
• Electrical connections and monthly bill

Author

Devashree holds an M.Eng degree in Information Technology from Germany and a background in Data Science. She likes working with statistics and discovering hidden insights in varied datasets to create stunning dashboards. She enjoys sharing her knowledge in AI by writing technical articles on various technological platforms.
She loves traveling, reading fiction, solving Sudoku puzzles, and participating in coding competitions in her leisure time.