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How to calculate root mean square error for linear model in R?
To find the root mean square error, we first need to find the residuals (which are also called error and we need to root mean square for these values) then root mean of these residuals needs to be calculated. Therefore, if we have a linear regression model object say M then the root mean square error can be found as sqrt(mean(M$residuals^2)).
Example
x1<-rnorm(500,50,5) y1<-rnorm(500,50,2) M1<-lm(y1~x1) summary(M1)
Output
Call: lm(formula = y1 ~ x1) Residuals: Min 1Q Median 3Q Max -5.6621 -1.2257 -0.0272 1.4151 6.6421 Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) 50.178943 0.915473 54.812 <2e-16 *** x1 -0.002153 0.018241 -0.118 0.906 --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 Residual standard error: 1.966 on 498 degrees of freedom Multiple R-squared: 2.798e-05, Adjusted R-squared: -0.00198 F-statistic: 0.01393 on 1 and 498 DF, p-value: 0.9061
Finding the root mean square error from model M1 −
Example
sqrt(mean(M1$residuals^2))
Output
[1] 1.961622
Example
x2<-rnorm(5000,125,21) y2<-rnorm(5000,137,10) M2<-lm(y2~x2) summary(M2)
Output
Call: lm(formula = y2 ~ x2) Residuals: Min 1Q Median 3Q Max -37.425 -7.005 -0.231 6.836 36.627 Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) 138.683501 0.851247 162.918 <2e-16 *** x2 -0.014386 0.006735 -2.136 0.0327 * --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 Residual standard error: 10.06 on 4998 degrees of freedom Multiple R-squared: 0.0009121, Adjusted R-squared: 0.0007122 F-statistic: 4.563 on 1 and 4998 DF, p-value: 0.03272
Finding the root mean square error from model M2:
Example
sqrt(mean(M2$residuals^2))
Output
[1] 10.05584
Example
x37<-rpois(500,5) y3<-rpois(500,10) M3<-lm(y3~x3) summary(M3)
Output
Call: lm(formula = y3 ~ x3) Residuals: Min 1Q Median 3Q Max -7.9004 -1.9928 -0.2155 2.1921 9.3770 Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) 10.17770 0.32330 31.481 <2e-16 *** x3 -0.09244 0.06145 -1.504 0.133 --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 Residual standard error: 3.027 on 498 degrees of freedom Multiple R-squared: 0.004524, Adjusted R-squared: 0.002525 F-statistic: 2.263 on 1 and 498 DF, p-value: 0.1331
Finding the root mean square error from model M3 −
Example
sqrt(mean(M3$residuals^2))
Output
[1] 3.020734
Example
x4<-runif(50000,5,10) y4<-runif(50000,2,10) M4<-lm(y4~x4) summary(M4)
Output
Call: lm(formula = y4 ~ x4) Residuals: Min 1Q Median 3Q Max -4.0007 -1.9934 -0.0063 1.9956 3.9995 Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) 5.9994268 0.0546751 109.729 <2e-16 *** x4 0.0001572 0.0071579 0.022 0.982 --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 Residual standard error: 2.309 on 49998 degrees of freedom Multiple R-squared: 9.646e-09, Adjusted R-squared: -1.999e-05 F-statistic: 0.0004823 on 1 and 49998 DF, p-value: 0.9825
Finding the root mean square error from model M4 −
Example
sqrt(mean(M4$residuals^2))
Output
[1] 2.308586
Example
x5<-sample(5001:9999,100000,replace=TRUE) y5<-sample(1000:9999,100000,replace=TRUE) M5<-lm(y5~x5) summary(M5)
Output
Call: lm(formula = y5 ~ x5) Residuals: Min 1Q Median 3Q Max -4495 -2242 -4 2230 4512 Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) 5.504e+03 4.342e+01 126.765 <2e-16 *** x5 -1.891e-03 5.688e-03 -0.333 0.74 --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 Residual standard error: 2594 on 99998 degrees of freedom Multiple R-squared: 1.106e-06, Adjusted R-squared: -8.895e-06 F-statistic: 0.1106 on 1 and 99998 DF, p-value: 0.7395
Finding the root mean square error from model M5 <
Example
sqrt(mean(M5$residuals^2))
Output
[1] 2593.709
Updated on: 17-Oct-2020
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