Basic Regression Diagnostics
Data Cars2004nh
data(Cars2004nh, package = "mffSM")
head(Cars2004nh)
## vname type drive price.retail price.dealer price cons.city cons.highway
## 1 Chevrolet.Aveo.4dr 1 1 11690 10965 11327.5 8.4 6.9
## 2 Chevrolet.Aveo.LS.4dr.hatch 1 1 12585 11802 12193.5 8.4 6.9
## 3 Chevrolet.Cavalier.2dr 1 1 14610 13697 14153.5 9.0 6.4
## 4 Chevrolet.Cavalier.4dr 1 1 14810 13884 14347.0 9.0 6.4
## 5 Chevrolet.Cavalier.LS.2dr 1 1 16385 15357 15871.0 9.0 6.4
## 6 Dodge.Neon.SE.4dr 1 1 13670 12849 13259.5 8.1 6.5
## consumption engine.size ncylinder horsepower weight iweight lweight wheel.base length width
## 1 7.65 1.6 4 103 1075 0.0009302326 6.980076 249 424 168
## 2 7.65 1.6 4 103 1065 0.0009389671 6.970730 249 389 168
## 3 7.70 2.2 4 140 1187 0.0008424600 7.079184 264 465 175
## 4 7.70 2.2 4 140 1214 0.0008237232 7.101676 264 465 173
## 5 7.70 2.2 4 140 1187 0.0008424600 7.079184 264 465 175
## 6 7.30 2.0 4 132 1171 0.0008539710 7.065613 267 442 170
## ftype fdrive
## 1 personal front
## 2 personal front
## 3 personal front
## 4 personal front
## 5 personal front
## 6 personal front
dim(Cars2004nh)
## [1] 425 20
summary(Cars2004nh)
## vname type drive price.retail price.dealer
## Length:425 Min. :1.000 Min. :1.000 Min. : 10280 Min. : 9875
## Class :character 1st Qu.:1.000 1st Qu.:1.000 1st Qu.: 20370 1st Qu.: 18973
## Mode :character Median :1.000 Median :1.000 Median : 27905 Median : 25672
## Mean :2.219 Mean :1.692 Mean : 32866 Mean : 30096
## 3rd Qu.:3.000 3rd Qu.:2.000 3rd Qu.: 39235 3rd Qu.: 35777
## Max. :6.000 Max. :3.000 Max. :192465 Max. :173560
##
## price cons.city cons.highway consumption engine.size ncylinder
## Min. : 10078 Min. : 6.20 Min. : 5.100 Min. : 5.65 Min. :1.300 Min. :-1.000
## 1st Qu.: 19600 1st Qu.:11.20 1st Qu.: 8.100 1st Qu.: 9.65 1st Qu.:2.400 1st Qu.: 4.000
## Median : 26656 Median :12.40 Median : 9.000 Median :10.70 Median :3.000 Median : 6.000
## Mean : 31481 Mean :12.36 Mean : 9.142 Mean :10.75 Mean :3.208 Mean : 5.791
## 3rd Qu.: 37514 3rd Qu.:13.80 3rd Qu.: 9.800 3rd Qu.:11.65 3rd Qu.:3.900 3rd Qu.: 6.000
## Max. :183012 Max. :23.50 Max. :19.600 Max. :21.55 Max. :8.300 Max. :12.000
## NA's :14 NA's :14 NA's :14
## horsepower weight iweight lweight wheel.base length
## Min. :100.0 Min. : 923 Min. :0.0003067 Min. :6.828 Min. :226.0 Min. :363.0
## 1st Qu.:165.0 1st Qu.:1412 1st Qu.:0.0005542 1st Qu.:7.253 1st Qu.:262.0 1st Qu.:450.0
## Median :210.0 Median :1577 Median :0.0006341 Median :7.363 Median :272.0 Median :472.0
## Mean :216.8 Mean :1626 Mean :0.0006412 Mean :7.373 Mean :274.9 Mean :470.6
## 3rd Qu.:255.0 3rd Qu.:1804 3rd Qu.:0.0007082 3rd Qu.:7.498 3rd Qu.:284.0 3rd Qu.:490.0
## Max. :500.0 Max. :3261 Max. :0.0010834 Max. :8.090 Max. :366.0 Max. :577.0
## NA's :2 NA's :2 NA's :2 NA's :2 NA's :26
## width ftype fdrive
## Min. :163.0 personal:242 front:223
## 1st Qu.:175.0 wagon : 30 rear :110
## Median :180.0 SUV : 60 4x4 : 92
## Mean :181.1 pickup : 24
## 3rd Qu.:185.0 sport : 49
## Max. :206.0 minivan : 20
## NA's :28
To be able to compare a model fitted here with other models where also other covariates will be included, we restrict ourselves to a subset of the dataset where all variables consumption, lweight and engine.size are known.
isComplete <- complete.cases(Cars2004nh[, c("consumption", "lweight", "engine.size")])
sum(!isComplete)
## [1] 16
CarsUsed <- subset(Cars2004nh, isComplete, select = c("consumption", "drive", "fdrive", "weight", "lweight", "engine.size"))
dim(CarsUsed)
## [1] 409 6
summary(CarsUsed)
## consumption drive fdrive weight lweight engine.size
## Min. : 5.65 Min. :1.000 front:212 Min. : 923 Min. :6.828 Min. :1.300
## 1st Qu.: 9.65 1st Qu.:1.000 rear :108 1st Qu.:1415 1st Qu.:7.255 1st Qu.:2.400
## Median :10.70 Median :1.000 4x4 : 89 Median :1577 Median :7.363 Median :3.000
## Mean :10.75 Mean :1.699 Mean :1622 Mean :7.371 Mean :3.178
## 3rd Qu.:11.65 3rd Qu.:2.000 3rd Qu.:1804 3rd Qu.:7.498 3rd Qu.:3.800
## Max. :21.55 Max. :3.000 Max. :2903 Max. :7.973 Max. :6.000
consumption on ldrivepar(mfrow = c(1, 1), bty = BTY, mar = c(4, 4, 1, 1) + 0.1)
plot(consumption ~ lweight, data = CarsUsed, pch = PCH, col = COL, bg = BGC,
xlab = "Log(weight) [log(kg)]", ylab = "Consumption [l/100 km]")
#lines(lowess(CarsUsed[, "lweight"], CarsUsed[, "consumption"]), col = "blue", lwd = 2)
m1 <- lm(consumption ~ lweight, data = CarsUsed)
summary(m1)
##
## Call:
## lm(formula = consumption ~ lweight, data = CarsUsed)
##
## Residuals:
## Min 1Q Median 3Q Max
## -3.6544 -0.7442 -0.1526 0.5160 5.1616
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -58.2480 1.8941 -30.75 <2e-16 ***
## lweight 9.3606 0.2569 36.44 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.035 on 407 degrees of freedom
## Multiple R-squared: 0.7654, Adjusted R-squared: 0.7648
## F-statistic: 1328 on 1 and 407 DF, p-value: < 2.2e-16
Ybar <- round(with(CarsUsed, mean(consumption)), 2)
be0 <- round(coef(m1)[1], 2)
be1 <- round(coef(m1)[2], 4)
par(mfrow = c(1, 1), bty = BTY, mar = c(4, 4, 1, 1) + 0.1)
plot(consumption ~ lweight, data = CarsUsed, pch = PCH, col = COL2, bg = BGC2,
xlab = "Log(weight) [log(kg)]", ylab = "Consumption [l/100 km]")
abline(m1, col = "red2", lwd = 2)
hatvalues(m1)
## 1 2 3 4 5 6 7 8
## 0.011878156 0.012334248 0.007704019 0.006925319 0.007704019 0.008204039 0.007583579 0.007764917
## 9 10 11 12 13 14 15 16
## 0.007857115 0.007857115 0.006736268 0.010678880 0.009477400 0.009259385 0.014420754 0.013592323
## 17 18 19 20
## 0.012520926 0.007464931 0.007464931 0.006656819
1 - hatvalues(m1)
## 1 2 3 4 5 6 7 8 9 10
## 0.9881218 0.9876658 0.9922960 0.9930747 0.9922960 0.9917960 0.9924164 0.9922351 0.9921429 0.9921429
## 11 12 13 14 15 16 17 18 19 20
## 0.9932637 0.9893211 0.9905226 0.9907406 0.9855792 0.9864077 0.9874791 0.9925351 0.9925351 0.9933432
summary(1 - hatvalues(m1))
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.9752 0.9941 0.9967 0.9951 0.9974 0.9976
residuals(m1)
## 1 2 3 4 5 6 7 8
## 0.56060511 0.64808761 -0.31710554 -0.52763929 -0.31710554 -0.59007308 -0.74859610 0.04867956
## 9 10 11 12 13 14 15 16
## -0.37759277 0.07240723 -0.23145786 -0.53008371 -1.68953471 -0.83893092 0.97471267 0.82944403
## 17 18 19 20
## 0.63331084 -0.12998107 -0.12998107 -0.35442857
rstandard(m1)
## 1 2 3 4 5 6 7 8
## 0.54508926 0.63029600 -0.30767983 -0.51175489 -0.30767983 -0.57267795 -0.72630061 0.04723405
## 9 10 11 12 13 14 15 16
## -0.36639740 0.07026040 -0.22446853 -0.51510011 -1.64078149 -0.81463308 0.94895728 0.80718799
## 17 18 19 20
## 0.61598309 -0.12610230 -0.12610230 -0.34371215
plot applied to objects of class lm (result of the fitting function lm) provides the basic residual plots. Its argument which determines which plot is produced.which = 1)par(mar = c(4, 4, 1, 1) + 0.1)
plot(m1, which = 1, pch = 21, col = "blue4", bg = "skyblue")
which = 2)par(mar = c(4, 4, 1, 1) + 0.1)
plot(m1, which = 2, pch = 21, col = "blue4", bg = "skyblue")
which = 3)par(mar = c(4, 4, 1, 1) + 0.1)
plot(m1, which = 3, pch = 21, col = "blue4", bg = "skyblue")
plotLM from package mffSM produces all three above residual plots at once.par(mar = c(4, 4, 3, 1) + 0.1)
plotLM(m1)
