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# R-Squared

Go to solution Solved by Dipankar Acharya,

Correlation - is a statistical measure to quantify the strength of the relationship between two quantitative and continuous variables. The relationship can be one of the following

Positive - increasing one variable would increase the other
Negative - increasing one variable would decrease the other
No Correlation - increasing one variable has no impact on the other

R-Squared is also known as the Coefficient of Determination and is an output from regression analysis. It represents the percentage of response variable variation that is explained by its relationship with one or more predictor variables. In general, the higher the R-squared value, the better the model fits your data. It is always between 0 and 100%.

An application-oriented question on the topic along with responses can be seen below. The best answer was provided by Dipankar Acharya on 4th May 2021.

Applause for all the respondents - Ilavarasi P, Rajender Prasad, Dipankar Acharya

## Question

Q 361. Correlation coefficient is denoted by 'r' and R Squared (coefficient of determination) is the square of 'r'.

Why do we need to run a full regression analysis if the simpler correlation coefficient itself tells us about the extent of relationship between two variables?

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• Solution

The correlation coefficient merely shows the relationship (positive or negative) between two variables - and the extent of the same - via the value of the coefficient (-1 to +1).

It does not express the relationships between the 2 variables or can't predict the value of the dependent value based on the changing value of the independent one.

The Regression analysis expresses the same via an equation, analysis of R square (how much of the variation of the output is explained by the equation) and also can predict the "Y" based on changing values of the "X's".

Further MLR or Logistic Regression can predict relationships between Multiple factors as well as multiple types of (Discreet and Continuous) variables.

Thus Correlation coefficient does not give the complete picture and we need to do Regression as well.

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Regression analysis is used to find the relationship between the set of independent variable and the dependent variable or you can say how your independent variables that can influence the dependent variables. we are going for full regression because how the changes in each independent variable are related to changes in the dependent variable. It allows you to determine which factors brings most impact, the factor we no need to consider for analysis and how these factors influencing each other.

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 Correlation:- used when a researcher wants to know  if the variables under study are correlated or not, if yes then how strong are  their relation. For regression analysis, to make future projections,  a functional relationship between 2 variables is established.

 Comparison Summary Table Comparison Basis Correlation Regression Definition Correlation:  statistical measure to determine co-relationship of 2 known variables. Regression:  illustrates how  numerically associated dependent variable is related to an independent variable. Where used A representation of linear relationship between 2 variables. Best line is fitted and an estimation of one variable on the basis of another variable. Objective To obtain a numerical value that can  express relationship between variables. An estimation of values of random variable on the basis of the values of a fixed variable. Coefficient Nature Symmetrical and mutual Asymmetrical Represents An indication of correlation coefficient to  the extent to of 2 variables that moves together. Regression is an  indication of the impact of a unit change for the known variable (x) on the estimated variable (y). Independent & Dependent   variables No difference between the two. Both variables are different.

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While all published answers have highlighted that correlation will not be able to help us predict or optimize the relationship between the two variables, the other reason is that square of correlation coefficient gives R-Squared only for linear relationships with one factor. If there are multiple factors or it is a non-linear relationship then we again need to do the full regression.

Both these points were right highlighted by Dipankar and hence his answer has been chosen as the winner.

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