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summary(USArrests)

#     Murder          Assault         UrbanPop          Rape      
#  Min.   : 0.800   Min.   : 45.0   Min.   :32.00   Min.   : 7.30  
#  1st Qu.: 4.075   1st Qu.:109.0   1st Qu.:54.50   1st Qu.:15.07  
#  Median : 7.250   Median :159.0   Median :66.00   Median :20.10  
#  Mean   : 7.788   Mean   :170.8   Mean   :65.54   Mean   :21.23  
#  3rd Qu.:11.250   3rd Qu.:249.0   3rd Qu.:77.75   3rd Qu.:26.18  
#  Max.   :17.400   Max.   :337.0   Max.   :91.00   Max.   :46.00  

fit <- lm(Murder ~ Assault, data = USArrests)

# Residuals
res <- residuals(fit)


# Root Mean Squared Error
rmse <- sqrt(mean(res^2))
rmse
# [1] 2.576236


# Residual Sum of Squares
rss <- sum(res^2)
rss
# [1] 331.8496


# Degrees of freedom of Residuals
df <- fit$df.residual
df
# [1] 48


# Residual Standard Error (or Standard Error of Regression or Standard Error of Estimate)
S <- sqrt(rss / df)
S
# [1] 2.62936