Community
Search Options
Search Options
Log in
Skip to main content (Press Enter).
Sign in
Skip auxiliary navigation (Press Enter).
AI and Data Science
Topic areas
AI and DS Skills
Decision Optimization
Embeddable AI
Global AI and Data Science
IBM Advanced Studies
SPSS Statistics
watsonx Assistant
Watson Discovery
User groups
Events
Upcoming AI Events
IBM TechXchange Webinars
All IBM TechXchange Community Events
Participate
Gamification Program
Community Manager's Welcome
Post to Forum
Share a Resource
Share Your Expertise
Blogging on the Community
Connect with Data Science Users
All IBM TechXchange Community Users
Resources
IBM TechXchange Group
AI Learning
IBM Champions
IBM Cloud Support
IBM Documentation
IBM Support
IBM Technology Zone
IBM Training
TechXchange Conference
IBM TechXchange Conference 2024
Marketplace
Marketplace
AI and Data Science
Master the art of data science.
Join now
Skip main navigation (Press Enter).
Toggle navigation
Search Options
Global AI and Data Science
Group Navigator
View Only
Community Home
Discussion
2.2K
Library
267
Blogs
724
Events
9
Members
27.7K
Share
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
#GlobalAIandDataScience
#GlobalDataScience
0 comments
7 views
Permalink
IBM Community Home
Browse
Discussions
Resources
Groups
Events
IBM TechXchange Conference 2023
IBM Community Webinars
All IBM Community Events
Participate
Gamification Program
Community Manager's Welcome
Post to Forum
Share a Resource
Blogging on the Community
All IBM Community Users
Resources
Community Front Porch
IBM Champions
IBM Cloud Support
IBM Documentation
IBM Support
IBM Technology Zone
IBM Training
Marketplace
Marketplace
AI and Data Science
Topic areas
AI and DS Skills
Decision Optimization
Embeddable AI
Global AI and Data Science
IBM Advanced Studies
SPSS Statistics
watsonx Assistant
Watson Discovery
User groups
Events
Upcoming AI Events
IBM TechXchange Webinars
All IBM TechXchange Community Events
Participate
Gamification Program
Community Manager's Welcome
Post to Forum
Share a Resource
Share Your Expertise
Blogging on the Community
Connect with Data Science Users
All IBM TechXchange Community Users
Resources
IBM TechXchange Group
AI Learning
IBM Champions
IBM Cloud Support
IBM Documentation
IBM Support
IBM Technology Zone
IBM Training
TechXchange Conference
IBM TechXchange Conference 2024
Marketplace
Marketplace
Copyright © 2019 IBM Data Science Community. All rights reserved.
Powered by Higher Logic