Coefficient of Determination & its Formula | Explained Variation | Unexplained Variation | Total Variation 2021

 COEFFICIENT OF DETERMINATION:

DEFINITION:

The Ratio of  Explained Variation to the Total Variation is called as Coefficient of Determination.

It is denoted as above "r square".

                   Coefficient of Determination = Explained Variation/Total Variation

Where

What is Explained Variation?

Explained Variation is...

&

What is Total Variation?

Total variation is...

So, we can write Coefficient of Determination Formula also as...

NOTE: Coefficient of Determination may also be written as...

             Coefficient of Determination = 1 - Unexplained Variation/Total Variation

What is Unexplained variation?

Unexplained Variation is...

So, Coefficient of Determination Formula will become...

It may also be written as...

Most Important Information:

Total Variation = Explained Variation + Unexplained Variation

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How to Make Easy Theory of Simple Linear Regression (PDF) 2021

 I have discussed here theory of REGRESSION STEP-BY-STEP with #secrets #shortcuts #concepts which nobody tells you about that.!

SEQUENCE: REGRESSION; REGRESSION EQUATION; REGRESSOR; REGRESSAND; EXACT RELATIONSHIP; INEXACT RELATIONSHIP; STANDARD ERROR OF ESTIMATE OF REGRESSION(STANDARD DEVIATION OF REGRESSION).

QUESTIONS WITH ANSWERS:

WHAT IS REGRESSION?

Dependence of One Variable on other Independent Variable is called as REGRESSION.

WHAT IS REGRESSION EQUATION?

An Equation which estimates the value of Dependent Variable with the help of Independent Variable by knowing the values of unknown parameters is called as REGRESSION EQUATION.

                                                          REGRESSION EQUATION

Y on X                                                          X on Y                                                                             

Y = a + b X                                        X = a + b Y                                                                                     

Y is Dependent Variable,                      X is Dependent Variable                                                             

X is Independent Variable,                   Y is Independent Variable                                                              

WHAT IS THE DIFFERENCE BETWEEN REGRESSOR AND REGRESSAND?

WHAT IS THE DIFFERENCE BETWEEN PREDICTOR AND PREDICTAND?

WHAT IS THE DIFFERENCE BETWEEN EXPLANATORY VARIABLE AND EXPLAINED VARIABLE?

The Independent Variable is called as REGRESSOR or PREDICTOR or EXPLANATORY VARIABLE.

The Dependent Variable is called as REGRESSAND or PREDICTAND or EXPLAINED VARIABLE.

WHAT IS THE DIFFERENCE BETWEEN EXACT RELATIONSHIP AND INEXACT RELATIONSHIP?

WHAT IS THE DIFFERENCE BETWEEN MATHEMATICAL RELATIONSHIP AND PROBABILISTIC RELATIONSHIP & ESTIMATED RELATIONSHIP?

Exact Relationship or Mathematical Relationship:

A Relationship which calculates the value of one Variable Exactly with the help of other Variable is called as Estimated Relationship or Mathematical Relationship.

For Example,

Inexact Relationship or Probabilistic Relationship or Estimated Relationship:

A Relationship which estimates the value of one Variable (Dependent Variable) with the help of other Variable (Independent Variable) is called as Inexact Relationship or Probabilistic Relationship or Estimated Relationship.

For Example, The Relationship between Age and Weight.

DEFINE STANDARD DEVIATION OF REGRESSION or STANDARD ERROR OF ESTIMATE OF REGRESSION?

Positive Square Root of Mean of Squared Deviation from Estimated Trend Values from Regression Equation is called as Standard Deviation of Regression or Standard Estimate for Regression.

For Y on X                                   Y = a + b X

& 

For X on Y                                   X = a + b Y

&

Most Important Point;

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