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? Note for website visitors - Two questions are asked every week on this platform. One on Tuesday and the other on Friday. All questions so far can be seen here - https://www.benchmarksixsigma.com/forum/lean-six-sigma-business-excellence-questions/ Please visit the forum home page at https://www.benchmarksixsigma.com/forum/ to respond to the latest question open till the next Tuesday/ Friday evening 5 PM as per Indian Standard Time. Questions launched on Tuesdays are open till Friday and questions launched on Friday are open till Tuesday. The best answer is always shown at the top among responses and the author finds honorable mention in our Business Excellence dictionary at https://www.benchmarksixsigma.com/forum/business-excellence-dictionary-glossary/ along with the related term

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.

Message added by Mayank Gupta, May 4, 20215 yr

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

R-Squared

Followers

April 30, 20215 yr

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?

Note for website visitors - Two questions are asked every week on this platform. One on Tuesday and the other on Friday.

All questions so far can be seen here - https://www.benchmarksixsigma.com/forum/lean-six-sigma-business-excellence-questions/
Please visit the forum home page at https://www.benchmarksixsigma.com/forum/ to respond to the latest question open till the next Tuesday/ Friday evening 5 PM as per Indian Standard Time. Questions launched on Tuesdays are open till Friday and questions launched on Friday are open till Tuesday.
The best answer is always shown at the top among responses and the author finds honorable mention in our Business Excellence dictionary at https://www.benchmarksixsigma.com/forum/business-excellence-dictionary-glossary/ along with the related term

Solved by Dipankar Acharya

May 4, 20215 yr

Go to solution

5 yr5 yr Mayank Gupta changed the title to R-Squared

May 3, 20215 yr

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.

May 3, 20215 yr

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.

May 4, 20215 yr

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.

5 yr5 yr Rohit Gandhi locked this topic

May 4, 20215 yr

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.