When increase in one variable results increase in another variable is called?

Correlation and Regression are the two multivariate distribution-based analyses. A multivariate distribution is called multiple variables distribution. Correlation is described as the analysis that allows us to know the relationship between two variables 'x' and 'y' or the absence of it.

On the other hand, the Regression analysis predicts the value of the dependent variable based on the known value of the independent variable, assuming that there is an average mathematical relation between two or more variables.

Given Below are the Measures of Correlation 

• The correlation coefficient of Karl Pearson’s Product-moment

• Scatter diagram

• Coefficient of concurrent deviations

• Coefficient of Spearman’s rank correlation

Distinguish Between Correlation and Regression

Definition of Correlation

The term correlation is a combination of two words 'Co' (together) and the relation between two quantities. Correlation is when it is observed that a change in a unit in one variable is retaliated by an equivalent change in another variable, i.e., direct or indirect, at the time of study of two variables. Or else the variables are said to be uncorrelated when the motion in one variable does not amount to any movement in a specific direction in another variable. It is a statistical technique that represents the strength of the linkage between variable pairs.

Correlation can be either negative or positive. If the two variables move in the same direction, i.e. an increase in one variable results in the corresponding increase in another variable, and vice versa, then the variables are considered to be positively correlated. For example, Investment and profit.

On the contrary, if the two variables move in different directions so that an increase in one variable leads to a decline in another variable and vice versa, this situation is known as a negative correlation. For example, Product price and demand.

Definition of Regression

A statistical technique based on the average mathematical relationship between two or more variables is known as regression, to estimate the change in the metric dependent variable due to the change in one or more independent variables. It plays an important role in many human activities since it is a powerful and flexible tool that is used to forecast past, present, or future events based on past or present events. For example, The future profit of a business can be estimated on the basis of past records.

There are two variables x and y in a simple linear regression, wherein y depends on x or say that is influenced by x. Here y is called as a variable dependent, or criterion, and x is a variable independent or predictor. The line of regression y on x is expressed as below: 

Y = a + bx

where, a = constant,

b = regression coefficient,

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

Difference between Correlation and Regression

Basis For Comparison

Correlation

Regression

Meaning

Correlation is a statistical measure that determines the association or co-relationship between two variables.

Regression describes how to numerically relate an independent variable to the dependent variable.

Usage

To represent a linear relationship between two variables.

To fit the best line and to estimate one variable based on another.

Dependent and Independent variables

No difference

Both variables are different.

Indicates

Correlation coefficient indicates the extent to which two variables move together.

Regression indicates the impact of a change of unit on the estimated variable ( y) in the known variable (x).

  Objective

To find a numerical value expressing the relationship between variables.

To estimate values of random variables on the basis of the values of fixed variables.

Correlation and Regression Difference - They are Not the Same Thing 

Here’s the difference between correlation and regression analysis. To sum up, there are four key aspects that differ from those terms.

There is a relationship between the variables when it comes to correlation. In contrast, regression places emphasis on how one variable affects the other.

Correlation does not capture causality whilst it is based on regression. 

The correlation between x and y is identical to that between y and x. Contrary to this, a regression of x and y, and y and x, results completely differently. 

Finally, one single point is a graphical representation of a correlation. Whereas one line visualizes a linear regression.

Bottom Line on Difference Between Correlation and Regression Analysis 

Correlation and regression are two analyzes, based on multiple variables distribution. They can be used to describe the nature of the relationship and strength between two continuous quantitative variables.

It is evident with the above discussion that there is a big difference between correlation and regression, the two mathematical concepts although these two are being studied together. Correlation is used when the researcher wishes to know whether or not the variables being studied are correlated, if yes then what the strength of their association is. Pearson's correlation coefficient is considered as the best correlation measure. A functional relationship between two variables is established in regression analysis, in order to make future projections on events.

When we talk about statistical measures and their research there are two important concepts that come into play and they are correlation and regression. This is a measure of multiple variables and hence is also called the multivariate distribution. Correlation can be described as the analysis which lets us know regarding the association or the absence of the relationship between two variables such as ‘a’ and ‘b’.

Whereas on the other hand, regression analysis helps us to predict the value of the dependent variable based on the value that is known of the independent variable present after assuming about the average mathematical relation between the two or more than two variables that are present. Correlation and regression being an important chapter in Class 12 it is important that students note the Difference Between Correlation and Regression and learn about the same.

Advantage of Correlation Analysis:

Correlation analysis helps students to get a more clear and concise summary regarding the relation between the two variables.

Advantage of Regression Analysis:

By using regression analysis one of the greatest advantages is that it allows you to take a detailed look at the data and includes an equation that can be used to predict and optimize the data set in the future.

When one variable increases and the other increases?

What is it called when one variable affects another?

What is it called when two variables both increase?

When one variable increases and the other decreases result to a?