Q 616. R-squared (R-sq) or R-squared adjusted (R-sq(adj)) is the most sought after number after Regression or Multiple Linear Regression. While potentially R-sq can range from 0% to 100%, could there be a situation where it is 0%? Provide examples to support your answer.

 

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Regression analysis is used to describe relationship between a set of independent variables and the dependent variables.

 

R squared (R²) is generally defined as statistic that indicate % of Variance in dependent variable that the independent Variable could explain collectively. R Square evaluates the scatter of the data points around the fitted regression.  It is mostly referred as Coefficient of determination.

 

Example

Let us say there are 6 ingredients (X) used to finally make a tasty dish (Y). R square will help to determine which ingredient has more impact on the final taste of the dish(Y).

We need to see which ingredient has more impact on final taste of dish.

Salt R² 15%

Spices R² 35%

Pepper R² 10%

Tomato R² 20%

Onion R² 20%

Color Powder R² is 0%

 

Looking at R² of all the ingredients (X) it Indicating spices have a higher impact on the taste of the dish (Y) & Color Powder has no impact on the final taste of the dish.

 

Lets see one more example to see what it means when R square is 0. (Advertisement Vs Sales of Umbrellas)

 

 

Interesting thing to note here that when R square is zero the line becomes horizontally indicating you cannot in any way predict out put Y with respect to input X. As they have no correlation.

 

 

Lets see what it means when input (X) has some impact on the Output (Y)   (Rainfall Vs Sales of Umbrellas)

 

 

 

R-squared may seems like an easy to understand statistic that indicates how well a regression model fits a data set. However, it does not tell us the complete story. To get the full picture, you must consider R square values in combination with the residual plots refer above image.

R-Square-it determines how well the data fits in the regression model.

it determines the % of variation between the dependent variable with independent variable.

R-Square adjusted-It is same as Rsquare,but it is used when the predictors are more.

When new/more predictors are there then R-squared adjusted gives the data of relation between all the dependent variables with independent variable.

It depend upon dependent variable .

If the dependent variable is high then R-Squared adj  will be high.

R-squared predicted-It is a cross validation.

It is inversely proportional to dependent variable.

If the dependent variable will increase then R-squared predicted will decrease.

Yes, although it's rare but it is possible for the value to be zero- it means the independent variables don't explain any variability in the dependent variable. Some reasons are below:

1. Selection of incorrect controllable variables
2. Non linearity relationship between variables

Examples

1. Selection of incorrect independent variables

 

     Modelling company top line as dependent variable and employee birthday as independent variable. Since both the variables are completely unrelated, the results would be skewed.

2. Non linearity

 

     Creating a model using delivery time as output variable and inventory level as input variable (this is because of impact of other parameters like traffic, breakdown etc.). This can be solved by using polynomial or non linear regression model.

Keerthi Vasan has given the best answer to the question.