Data Structure
Networking
RDBMS
Operating System
Java
MS Excel
iOS
HTML
CSS
Android
Python
C Programming
C++
C#
MongoDB
MySQL
Javascript
PHP
Physics
Chemistry
Biology
Mathematics
English
Economics
Psychology
Social Studies
Fashion Studies
Legal Studies
- Selected Reading
- UPSC IAS Exams Notes
- Developer's Best Practices
- Questions and Answers
- Effective Resume Writing
- HR Interview Questions
- Computer Glossary
- Who is Who
How to find residual variance of a linear regression model in R?
The residual variance is the variance of the values that are calculated by finding the distance between regression line and the actual points, this distance is actually called the residual. Suppose we have a linear regression model named as Model then finding the residual variance can be done as (summary(Model)$sigma)**2.
Example
x1<-rnorm(500,5,1) y1<-rnorm(500,5,2) Model1<-lm(y1~x1) summary(Model1)
Call
lm(formula = y1 ~ x1)
Residuals
Min 1Q Median 3Q Max -5.6621 -1.2257 -0.0272 1.4151 6.6421
Coefficients
Estimate Std. Error t value Pr(>|t|) (Intercept) 5.12511 0.46364 11.054 <2e-16 *** x1 -0.01077 0.09120 -0.118 0.906 --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error − 1.966 on 498 degrees of freedom
Multiple R-squared − 2.798e-05, Adjusted R-squared: -0.00198
F-statistic − 0.01393 on 1 and 498 DF, p-value: 0.9061
Finding the residual variance of the model −
(summary(Model1)$sigma)**2 [1] 3.863416
Example
x2<-rpois(5000,5) y2<-rpois(5000,2) Model2<-lm(y2~x2) summary(Model2)
Call
lm(formula = y2 ~ x2)
Residuals
Min 1Q Median 3Q Max -2.0474 -0.9898 0.0030 1.0102 6.0318
Coefficients
Estimate Std. Error t value Pr(>|t|) (Intercept) 1.953861 0.049840 39.203 <2e-16 *** x2 0.007192 0.009125 0.788 0.431 --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error − 1.423 on 4998 degrees of freedom
Multiple R-squared − 0.0001243, Adjusted R-squared: -7.578e-05
F-statistic − 0.6212 on 1 and 4998 DF, p-value: 0.4306
(summary(Model2)$sigma)**2 [1] 2.024254
Example
x3<-runif(5000,2,5) y3<-runif(5000,2,10) Model3<-lm(y3~x3) summary(Model3)
Call
lm(formula = y3 ~ x3)
Residuals
Min 1Q Median 3Q Max -3.9879 -2.0642 0.0001 2.0438 4.0109
Coefficients
Estimate Std. Error t value Pr(>|t|) (Intercept) 6.004373 0.136367 44.031 <2e-16 *** x3 -0.004376 0.037914 -0.115 0.908 --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error − 2.334 on 4998 degrees of freedom
Multiple R-squared − 2.666e-06, Adjusted R-squared: -0.0001974
F-statistic − 0.01332 on 1 and 4998 DF, p-value: 0.9081
(summary(Model3)$sigma)**2 [1] 5.445925
Example
x4<-rexp(100000,5.5) y4<-rexp(100000,7.5) Model4<-lm(y4~x4) summary(Model4)
Call
lm(formula = y4 ~ x4)
Residuals
Min 1Q Median 3Q Max -0.13359 -0.09515 -0.04089 0.05144 1.39856
Coefficients
Estimate Std. Error t value Pr(>|t|) (Intercept) 0.1335960 0.0005972 223.697 <2e-16 *** x4 -0.0010954 0.0023153 -0.473 0.636 --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error − 0.1335 on 99998 degrees of freedom
Multiple R-squared − 2.239e-06, Adjusted R-squared : -7.762e-06
F-statistic − 0.2239 on 1 and 99998 DF, p-value: 0.6361
(summary(Model4)$sigma)**2 [1] 0.01781908
Example
x5<-sample(0:9,25000,replace=TRUE) y5<-sample(91:99,25000,replace=TRUE) Model5<-lm(y5~x5) summary(Model5)
Call
lm(formula = y5 ~ x5)
Residuals
Min 1Q Median 3Q Max -3.9949 -1.9937 0.0075 2.0093 4.0105
Coefficients
Estimate Std. Error t value Pr(>|t|) (Intercept) 94.989520 0.030168 3148.693 <2e-16 *** x5 0.000595 0.005641 0.105 0.916 --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error − 2.57 on 24998 degrees of freedom
Multiple R-squared − 4.45e-07, Adjusted R-squared : -3.956e-05
F-statistic − 0.01112 on 1 and 24998 DF, p-value − 0.916
(summary(Model5)$sigma)**2
[1] 6.604745
4K+ Views
