Welcome to the IBM Community, a place to collaborate, share knowledge, & support one another in everyday challenges. Connect with your fellow members through forums, blogs, files, & face-to-face networking.
Log in
Search Options
Search Options
Skip to main content (Press Enter).
Sign in
Skip auxiliary navigation (Press Enter).
Data Science
Topic groups
Global Data Science
Decision Optimization
SPSS Modeler
SPSS Statistics
Watson Studio
Data and AI Learning
User groups
Events
Upcoming Events
On Demand Webinars
IBM Expert TV
Virtual Community Events
All IBM Community Events
Participate
Gamification Program
Post to Forum
Share a Resource
Share Your Expertise
Blogging on the Community
Connect with Data Science Users
All IBM Community Users
Resources
Community Front Porch
IBM Champions
IBM Cloud Support
IBM Documentation
IBM Support
IBM Technology Zone
IBM Training
Data Science Elite
Marketplace
Marketplace
IBM Data Science Community
Master the art of data science.
Join now
Skip main navigation (Press Enter).
Toggle navigation
Search Options
Global Data Science Forum
View Only
Group Home
Discussion
1.8K
Library
227
Blogs
562
Events
2
Members
21.4K
Back to Blog List
R Squared the Coefficient of Determination
By
Moloy De
posted
Thu February 18, 2021 08:19 PM
0
Like
In statistics, the coefficient of determination, denoted R
2
or r
2
is the proportion of the variance in the dependent variable that is predictable from the independent variables.
It is a statistic used in the context of statistical models whose main purpose is either the prediction of future outcomes or the testing of hypotheses, on the basis of other related information. It provides a measure of how well observed outcomes are replicated by the model, based on the proportion of total variation of outcomes explained by the model.
There are several definitions of R
2
that are only sometimes equivalent. One class of such cases includes that of simple linear regression where r
2
is used instead of R
2
. When an intercept is included, then r
2
is simply the square of the sample correlation coefficient between the observed outcomes and the observed predictor values. If additional regressors are included, R
2
is the square of the coefficient of multiple correlation. In both such cases, the coefficient of determination ranges from 0 to 1.
In all instances where R
2
is used, the predictors are calculated by ordinary least-squares regression: that is, by minimizing sum of squares. In this case, R
2
increases as the number of variables in the model is increased. R
2
is monotone increasing with the number of variables included—it will never decrease. This illustrates a drawback to one possible use of R
2
, where one might keep adding variables to increase the R
2
value. For example, if one is trying to predict the sales of a model of car from the car's gas mileage, price, and engine power, one can include such irrelevant factors as the first letter of the model's name or the height of the lead engineer designing the car because the R
2
will never decrease as variables are added and will probably experience an increase due to chance alone.
This leads to the alternative approach of looking at the adjusted R
2
.
The explanation of this statistic is almost the same as R
2
but it penalizes the statistic as extra variables are included in the model. For cases other than fitting by ordinary least squares, the R
2
statistic can be calculated as above and may still be a useful measure. If fitting is by weighted least squares or generalized least squares, alternative versions of R2 can be calculated appropriate to those statistical frameworks, while the "raw" R
2
may still be useful if it is more easily interpreted. Values for R
2
can be calculated for any type of predictive model, which need not have a statistical basis.
QUESTION I : Could R Squared be negative?
QUESTION II : When analyzing a Time Series data is it justified to calculate R Squared as the square of the correlation Coefficient be Actuals and Predicted?
REFERENCE :
Wikipedia
#Featured-area-3
#Featured-area-3-home
0 comments
6 views
Permalink
Data Science
Topic groups
Global Data Science
Decision Optimization
SPSS Modeler
SPSS Statistics
Watson Studio
Data and AI Learning
User groups
Events
Upcoming Events
On Demand Webinars
IBM Expert TV
Virtual Community Events
All IBM Community Events
Participate
Gamification Program
Post to Forum
Share a Resource
Share Your Expertise
Blogging on the Community
Connect with Data Science Users
All IBM Community Users
Resources
Community Front Porch
IBM Champions
IBM Cloud Support
IBM Documentation
IBM Support
IBM Technology Zone
IBM Training
Data Science Elite
Marketplace
Marketplace
Copyright © 2019 IBM Data Science Community. All rights reserved.
Powered by Higher Logic