# From the book ISLR by Games,Witten,Hastie and Tibshirani
library(ISLR)
objects(grep("ISLR",search()))
## [1] "Auto" "Caravan" "Carseats" "College" "Default"
## [6] "Hitters" "Khan" "NCI60" "OJ" "Portfolio"
## [11] "Smarket" "Wage" "Weekly"
data("Carseats")
Carseats[1:5,]
## Sales CompPrice Income Advertising Population Price ShelveLoc Age
## 1 9.50 138 73 11 276 120 Bad 42
## 2 11.22 111 48 16 260 83 Good 65
## 3 10.06 113 35 10 269 80 Medium 59
## 4 7.40 117 100 4 466 97 Medium 55
## 5 4.15 141 64 3 340 128 Bad 38
## Education Urban US
## 1 17 Yes Yes
## 2 10 Yes Yes
## 3 12 Yes Yes
## 4 14 Yes Yes
## 5 13 Yes No
#?Carseats
str(Carseats)
## 'data.frame': 400 obs. of 11 variables:
## $ Sales : num 9.5 11.22 10.06 7.4 4.15 ...
## $ CompPrice : num 138 111 113 117 141 124 115 136 132 132 ...
## $ Income : num 73 48 35 100 64 113 105 81 110 113 ...
## $ Advertising: num 11 16 10 4 3 13 0 15 0 0 ...
## $ Population : num 276 260 269 466 340 501 45 425 108 131 ...
## $ Price : num 120 83 80 97 128 72 108 120 124 124 ...
## $ ShelveLoc : Factor w/ 3 levels "Bad","Good","Medium": 1 2 3 3 1 1 3 2 3 3 ...
## $ Age : num 42 65 59 55 38 78 71 67 76 76 ...
## $ Education : num 17 10 12 14 13 16 15 10 10 17 ...
## $ Urban : Factor w/ 2 levels "No","Yes": 2 2 2 2 2 1 2 2 1 1 ...
## $ US : Factor w/ 2 levels "No","Yes": 2 2 2 2 1 2 1 2 1 2 ...
table(Carseats$ShelveLoc)
##
## Bad Good Medium
## 96 85 219
table(Carseats$Urban)
##
## No Yes
## 118 282
table(Carseats$US)
##
## No Yes
## 142 258
summary(Carseats)
## Sales CompPrice Income Advertising
## Min. : 0.000 Min. : 77 Min. : 21.00 Min. : 0.000
## 1st Qu.: 5.390 1st Qu.:115 1st Qu.: 42.75 1st Qu.: 0.000
## Median : 7.490 Median :125 Median : 69.00 Median : 5.000
## Mean : 7.496 Mean :125 Mean : 68.66 Mean : 6.635
## 3rd Qu.: 9.320 3rd Qu.:135 3rd Qu.: 91.00 3rd Qu.:12.000
## Max. :16.270 Max. :175 Max. :120.00 Max. :29.000
## Population Price ShelveLoc Age
## Min. : 10.0 Min. : 24.0 Bad : 96 Min. :25.00
## 1st Qu.:139.0 1st Qu.:100.0 Good : 85 1st Qu.:39.75
## Median :272.0 Median :117.0 Medium:219 Median :54.50
## Mean :264.8 Mean :115.8 Mean :53.32
## 3rd Qu.:398.5 3rd Qu.:131.0 3rd Qu.:66.00
## Max. :509.0 Max. :191.0 Max. :80.00
## Education Urban US
## Min. :10.0 No :118 No :142
## 1st Qu.:12.0 Yes:282 Yes:258
## Median :14.0
## Mean :13.9
## 3rd Qu.:16.0
## Max. :18.0
Carseats$ShelveLoc <- as.factor(Carseats$ShelveLoc)
Carseats$ShelveLoc <- factor(Carseats$ShelveLoc,levels = c("Bad","Medium","Good"))
class(Carseats$ShelveLoc)
## [1] "factor"
summary(Carseats)
## Sales CompPrice Income Advertising
## Min. : 0.000 Min. : 77 Min. : 21.00 Min. : 0.000
## 1st Qu.: 5.390 1st Qu.:115 1st Qu.: 42.75 1st Qu.: 0.000
## Median : 7.490 Median :125 Median : 69.00 Median : 5.000
## Mean : 7.496 Mean :125 Mean : 68.66 Mean : 6.635
## 3rd Qu.: 9.320 3rd Qu.:135 3rd Qu.: 91.00 3rd Qu.:12.000
## Max. :16.270 Max. :175 Max. :120.00 Max. :29.000
## Population Price ShelveLoc Age
## Min. : 10.0 Min. : 24.0 Bad : 96 Min. :25.00
## 1st Qu.:139.0 1st Qu.:100.0 Medium:219 1st Qu.:39.75
## Median :272.0 Median :117.0 Good : 85 Median :54.50
## Mean :264.8 Mean :115.8 Mean :53.32
## 3rd Qu.:398.5 3rd Qu.:131.0 3rd Qu.:66.00
## Max. :509.0 Max. :191.0 Max. :80.00
## Education Urban US
## Min. :10.0 No :118 No :142
## 1st Qu.:12.0 Yes:282 Yes:258
## Median :14.0
## Mean :13.9
## 3rd Qu.:16.0
## Max. :18.0
aggregate(Carseats$Sales~Carseats$ShelveLoc+Carseats$Urban,Carseats,mean)
## Carseats$ShelveLoc Carseats$Urban Carseats$Sales
## 1 Bad No 5.547273
## 2 Medium No 7.240882
## 3 Good No 9.931429
## 4 Bad Yes 5.515676
## 5 Medium Yes 7.336159
## 6 Good Yes 10.352807
aggregate(Carseats$Sales~Carseats$ShelveLoc+Carseats$Advertising,Carseats,mean)
## Carseats$ShelveLoc Carseats$Advertising Carseats$Sales
## 1 Bad 0 5.109429
## 2 Medium 0 6.720000
## 3 Good 0 9.270714
## 4 Bad 1 3.150000
## 5 Medium 1 5.752000
## 6 Good 1 11.395000
## 7 Bad 2 5.150000
## 8 Medium 2 6.295000
## 9 Good 2 9.245000
## 10 Bad 3 5.475000
## 11 Medium 3 7.613333
## 12 Good 3 12.660000
## 13 Bad 4 4.514000
## 14 Medium 4 6.555000
## 15 Good 4 11.706667
## 16 Bad 5 6.590000
## 17 Medium 5 6.194167
## 18 Good 5 9.750000
## 19 Bad 6 4.635000
## 20 Medium 6 5.964000
## 21 Bad 7 3.593333
## 22 Medium 7 7.791667
## 23 Good 7 11.235000
## 24 Bad 8 7.690000
## 25 Medium 8 8.108571
## 26 Good 8 8.440000
## 27 Bad 9 8.320000
## 28 Medium 9 6.508000
## 29 Good 9 10.440000
## 30 Bad 10 5.853333
## 31 Medium 10 8.413636
## 32 Good 10 10.257500
## 33 Bad 11 6.128333
## 34 Medium 11 7.441667
## 35 Good 11 9.972500
## 36 Bad 12 6.150000
## 37 Medium 12 8.464545
## 38 Good 12 9.840000
## 39 Bad 13 6.711667
## 40 Medium 13 7.268889
## 41 Good 13 8.994000
## 42 Medium 14 8.591000
## 43 Good 14 13.440000
## 44 Bad 15 5.127500
## 45 Medium 15 8.310000
## 46 Good 15 11.410000
## 47 Bad 16 9.075000
## 48 Medium 16 8.875000
## 49 Good 16 11.180000
## 50 Medium 17 7.745000
## 51 Good 17 11.670000
## 52 Bad 18 1.420000
## 53 Medium 18 9.534000
## 54 Bad 19 6.835000
## 55 Medium 19 8.300000
## 56 Good 19 13.445000
## 57 Bad 20 6.900000
## 58 Medium 20 5.740000
## 59 Good 20 12.980000
## 60 Bad 21 3.900000
## 61 Bad 22 7.680000
## 62 Medium 22 10.260000
## 63 Bad 23 8.550000
## 64 Good 23 9.580000
## 65 Good 24 12.490000
## 66 Medium 25 8.750000
## 67 Medium 26 8.030000
## 68 Medium 29 9.530000
x <- seq(1,10)
y <- x
plot(x,y,col="green")
f <-outer(x,y,function(x,y)cos(y)/(1+x^2))
contour(x,y,f,nlevels = 45,add = T)
fa <- (f-t(f))/2
contour(x,y,fa,nlevels = 15)
image(x,y,fa)
persp(x,y,fa)
persp(x,y,fa,theta = 30)
persp(x,y,fa,theta = 30,phi = 20)
persp(x,y,fa,theta = 30,phi = 70)
persp(x,y,fa,theta = 30,phi = 40)
A <- matrix(1:16,4,4)
A
## [,1] [,2] [,3] [,4]
## [1,] 1 5 9 13
## [2,] 2 6 10 14
## [3,] 3 7 11 15
## [4,] 4 8 12 16
A[c(1,3)]
## [1] 1 3
A[,c(2,4)]
## [,1] [,2]
## [1,] 5 13
## [2,] 6 14
## [3,] 7 15
## [4,] 8 16
A[c(1,3),c(2,4)]
## [,1] [,2]
## [1,] 5 13
## [2,] 7 15
data("Auto")
#fix(Auto)
setwd("C:\\Users\\Luis\\Desktop\\ISLR")
auto <- read.csv("C:\\Users\\Luis\\Desktop\\ISLR\\Auto.csv",
header = TRUE,
sep = ",")
auto[1:5,]
## mpg cylinders displacement horsepower weight acceleration year origin
## 1 18 8 307 130 3504 12.0 70 1
## 2 15 8 350 165 3693 11.5 70 1
## 3 18 8 318 150 3436 11.0 70 1
## 4 16 8 304 150 3433 12.0 70 1
## 5 17 8 302 140 3449 10.5 70 1
## name
## 1 chevrolet chevelle malibu
## 2 buick skylark 320
## 3 plymouth satellite
## 4 amc rebel sst
## 5 ford torino
str(auto)
## 'data.frame': 397 obs. of 9 variables:
## $ mpg : num 18 15 18 16 17 15 14 14 14 15 ...
## $ cylinders : int 8 8 8 8 8 8 8 8 8 8 ...
## $ displacement: num 307 350 318 304 302 429 454 440 455 390 ...
## $ horsepower : Factor w/ 94 levels "?","100","102",..: 17 35 29 29 24 42 47 46 48 40 ...
## $ weight : int 3504 3693 3436 3433 3449 4341 4354 4312 4425 3850 ...
## $ acceleration: num 12 11.5 11 12 10.5 10 9 8.5 10 8.5 ...
## $ year : int 70 70 70 70 70 70 70 70 70 70 ...
## $ origin : int 1 1 1 1 1 1 1 1 1 1 ...
## $ name : Factor w/ 304 levels "amc ambassador brougham",..: 49 36 231 14 161 141 54 223 241 2 ...
dim(auto)
## [1] 397 9
auto$cylinders <- as.factor(auto$cylinders)
# auto$cylinders <-factor(auto$cylinders,levels = c("3","4","5","6","8"))
str(auto)
## 'data.frame': 397 obs. of 9 variables:
## $ mpg : num 18 15 18 16 17 15 14 14 14 15 ...
## $ cylinders : Factor w/ 5 levels "3","4","5","6",..: 5 5 5 5 5 5 5 5 5 5 ...
## $ displacement: num 307 350 318 304 302 429 454 440 455 390 ...
## $ horsepower : Factor w/ 94 levels "?","100","102",..: 17 35 29 29 24 42 47 46 48 40 ...
## $ weight : int 3504 3693 3436 3433 3449 4341 4354 4312 4425 3850 ...
## $ acceleration: num 12 11.5 11 12 10.5 10 9 8.5 10 8.5 ...
## $ year : int 70 70 70 70 70 70 70 70 70 70 ...
## $ origin : int 1 1 1 1 1 1 1 1 1 1 ...
## $ name : Factor w/ 304 levels "amc ambassador brougham",..: 49 36 231 14 161 141 54 223 241 2 ...
table(auto$cylinders)
##
## 3 4 5 6 8
## 4 203 3 84 103
aggregate(auto$mpg~auto$cylinders+auto$horsepower,mean,data = auto)
## auto$cylinders auto$horsepower auto$mpg
## 1 4 ? 31.00000
## 2 6 ? 21.00000
## 3 3 100 23.70000
## 4 4 100 32.90000
## 5 6 100 18.43333
## 6 4 102 20.00000
## 7 5 103 20.30000
## 8 4 105 25.55000
## 9 6 105 18.70000
## 10 8 105 26.60000
## 11 6 107 21.00000
## 12 6 108 19.00000
## 13 3 110 21.50000
## 14 4 110 22.75000
## 15 6 110 19.42500
## 16 8 110 18.96667
## 17 4 112 18.50000
## 18 6 112 22.00000
## 19 4 113 26.00000
## 20 4 115 23.30000
## 21 6 115 25.70000
## 22 6 116 25.40000
## 23 6 120 19.60000
## 24 8 120 15.50000
## 25 6 122 20.00000
## 26 6 125 17.00000
## 27 8 125 21.10000
## 28 8 129 15.30000
## 29 8 130 15.20000
## 30 6 132 32.70000
## 31 6 133 16.20000
## 32 8 135 18.20000
## 33 8 137 14.00000
## 34 8 138 16.50000
## 35 8 139 19.15000
## 36 8 140 16.34286
## 37 8 142 15.50000
## 38 8 145 15.45714
## 39 8 148 14.00000
## 40 8 149 16.00000
## 41 8 150 14.70455
## 42 8 152 14.50000
## 43 8 153 14.00000
## 44 8 155 14.95000
## 45 8 158 13.00000
## 46 8 160 13.00000
## 47 6 165 17.70000
## 48 8 165 14.00000
## 49 8 167 12.00000
## 50 8 170 14.50000
## 51 8 175 13.40000
## 52 8 180 13.50000
## 53 8 190 14.50000
## 54 8 193 9.00000
## 55 8 198 13.50000
## 56 8 200 10.00000
## 57 8 208 11.00000
## 58 8 210 11.00000
## 59 8 215 12.33333
## 60 8 220 14.00000
## 61 8 225 13.33333
## 62 8 230 16.00000
## 63 4 46 26.00000
## 64 4 48 43.60000
## 65 4 49 29.00000
## 66 4 52 34.20000
## 67 4 53 33.00000
## 68 4 54 23.00000
## 69 4 58 37.55000
## 70 4 60 32.16000
## 71 4 61 32.00000
## 72 4 62 33.75000
## 73 4 63 34.40000
## 74 4 64 39.00000
## 75 4 65 35.48000
## 76 4 66 36.10000
## 77 4 67 33.33636
## 78 5 67 36.40000
## 79 4 68 32.18333
## 80 4 69 32.76667
## 81 4 70 32.47500
## 82 4 71 29.02000
## 83 4 72 25.47500
## 84 6 72 15.00000
## 85 4 74 33.53333
## 86 4 75 29.03571
## 87 4 76 31.16667
## 88 6 76 30.70000
## 89 5 77 25.40000
## 90 4 78 28.56000
## 91 6 78 18.00000
## 92 4 79 27.00000
## 93 4 80 28.60000
## 94 4 81 25.00000
## 95 6 81 24.00000
## 96 4 82 31.00000
## 97 4 83 28.12500
## 98 4 84 30.13333
## 99 4 85 24.60000
## 100 6 85 22.90000
## 101 4 86 24.20000
## 102 4 87 23.00000
## 103 4 88 26.75333
## 104 6 88 18.80000
## 105 4 89 25.50000
## 106 3 90 18.00000
## 107 4 90 27.00000
## 108 6 90 20.20000
## 109 8 90 23.90000
## 110 4 91 20.00000
## 111 4 92 27.63333
## 112 4 93 26.00000
## 113 4 94 22.00000
## 114 4 95 24.22857
## 115 6 95 20.00000
## 116 4 96 27.16667
## 117 3 97 19.00000
## 118 4 97 24.42000
## 119 6 97 19.33333
## 120 4 98 22.00000
## 121 6 98 18.50000
summary(auto)
## mpg cylinders displacement horsepower weight
## Min. : 9.00 3: 4 Min. : 68.0 150 : 22 Min. :1613
## 1st Qu.:17.50 4:203 1st Qu.:104.0 90 : 20 1st Qu.:2223
## Median :23.00 5: 3 Median :146.0 88 : 19 Median :2800
## Mean :23.52 6: 84 Mean :193.5 110 : 18 Mean :2970
## 3rd Qu.:29.00 8:103 3rd Qu.:262.0 100 : 17 3rd Qu.:3609
## Max. :46.60 Max. :455.0 75 : 14 Max. :5140
## (Other):287
## acceleration year origin name
## Min. : 8.00 Min. :70.00 Min. :1.000 ford pinto : 6
## 1st Qu.:13.80 1st Qu.:73.00 1st Qu.:1.000 amc matador : 5
## Median :15.50 Median :76.00 Median :1.000 ford maverick : 5
## Mean :15.56 Mean :75.99 Mean :1.574 toyota corolla: 5
## 3rd Qu.:17.10 3rd Qu.:79.00 3rd Qu.:2.000 amc gremlin : 4
## Max. :24.80 Max. :82.00 Max. :3.000 amc hornet : 4
## (Other) :368
class(auto$cylinders)
## [1] "factor"
plot(auto$cylinders,auto$mpg)
plot(auto$cylinders,auto$mpg,col="red")
plot(auto$cylinders,auto$mpg,col="red",
varwidth=TRUE)
plot(auto$cylinders,auto$mpg,
col="red",varwidth=TRUE,
horizontal=TRUE)
plot(auto$cylinders,auto$mpg,
col="red",varwidth=TRUE,
horizontal=TRUE,xlab="MPG",ylab="Cylinders")
hist(auto$mpg)
hist(auto$mpg,col = 2)
hist(auto$mpg,col = 2,breaks=15)
pairs(auto)
pairs(~auto$mpg+auto$displacement+auto$horsepower+
auto$weight+auto$acceleration,auto)
plot(auto$horsepower,auto$mpg)
identify(auto$horsepower,auto$mpg,auto$name)
## integer(0)
setwd("C:\\Users\\Luis\\Desktop\\ISLR")
college <- read.csv("C:\\Users\\Luis\\Desktop\\ISLR\\college.csv")
#fix(college)
row.names(college)<-college[,1]
#fix(college)
college <- college[,-1]
#fix(college)
summary(college)
## Private Apps Accept Enroll Top10perc
## No :212 Min. : 81 Min. : 72 Min. : 35 Min. : 1.00
## Yes:565 1st Qu.: 776 1st Qu.: 604 1st Qu.: 242 1st Qu.:15.00
## Median : 1558 Median : 1110 Median : 434 Median :23.00
## Mean : 3002 Mean : 2019 Mean : 780 Mean :27.56
## 3rd Qu.: 3624 3rd Qu.: 2424 3rd Qu.: 902 3rd Qu.:35.00
## Max. :48094 Max. :26330 Max. :6392 Max. :96.00
## Top25perc F.Undergrad P.Undergrad Outstate
## Min. : 9.0 Min. : 139 Min. : 1.0 Min. : 2340
## 1st Qu.: 41.0 1st Qu.: 992 1st Qu.: 95.0 1st Qu.: 7320
## Median : 54.0 Median : 1707 Median : 353.0 Median : 9990
## Mean : 55.8 Mean : 3700 Mean : 855.3 Mean :10441
## 3rd Qu.: 69.0 3rd Qu.: 4005 3rd Qu.: 967.0 3rd Qu.:12925
## Max. :100.0 Max. :31643 Max. :21836.0 Max. :21700
## Room.Board Books Personal PhD
## Min. :1780 Min. : 96.0 Min. : 250 Min. : 8.00
## 1st Qu.:3597 1st Qu.: 470.0 1st Qu.: 850 1st Qu.: 62.00
## Median :4200 Median : 500.0 Median :1200 Median : 75.00
## Mean :4358 Mean : 549.4 Mean :1341 Mean : 72.66
## 3rd Qu.:5050 3rd Qu.: 600.0 3rd Qu.:1700 3rd Qu.: 85.00
## Max. :8124 Max. :2340.0 Max. :6800 Max. :103.00
## Terminal S.F.Ratio perc.alumni Expend
## Min. : 24.0 Min. : 2.50 Min. : 0.00 Min. : 3186
## 1st Qu.: 71.0 1st Qu.:11.50 1st Qu.:13.00 1st Qu.: 6751
## Median : 82.0 Median :13.60 Median :21.00 Median : 8377
## Mean : 79.7 Mean :14.09 Mean :22.74 Mean : 9660
## 3rd Qu.: 92.0 3rd Qu.:16.50 3rd Qu.:31.00 3rd Qu.:10830
## Max. :100.0 Max. :39.80 Max. :64.00 Max. :56233
## Grad.Rate
## Min. : 10.00
## 1st Qu.: 53.00
## Median : 65.00
## Mean : 65.46
## 3rd Qu.: 78.00
## Max. :118.00
pairs(college[,1:10])
names(college)
## [1] "Private" "Apps" "Accept" "Enroll" "Top10perc"
## [6] "Top25perc" "F.Undergrad" "P.Undergrad" "Outstate" "Room.Board"
## [11] "Books" "Personal" "PhD" "Terminal" "S.F.Ratio"
## [16] "perc.alumni" "Expend" "Grad.Rate"
plot(college$Outstate~college$Private)
college$elite <- rep("No",nrow(college))
#fix(college)
college$elite[college$Top10perc>50]="Yes"
#fix(college)
college$elite <-as.factor(college$elite)
college<-data.frame(college,college$elite)
summary(college)
## Private Apps Accept Enroll Top10perc
## No :212 Min. : 81 Min. : 72 Min. : 35 Min. : 1.00
## Yes:565 1st Qu.: 776 1st Qu.: 604 1st Qu.: 242 1st Qu.:15.00
## Median : 1558 Median : 1110 Median : 434 Median :23.00
## Mean : 3002 Mean : 2019 Mean : 780 Mean :27.56
## 3rd Qu.: 3624 3rd Qu.: 2424 3rd Qu.: 902 3rd Qu.:35.00
## Max. :48094 Max. :26330 Max. :6392 Max. :96.00
## Top25perc F.Undergrad P.Undergrad Outstate
## Min. : 9.0 Min. : 139 Min. : 1.0 Min. : 2340
## 1st Qu.: 41.0 1st Qu.: 992 1st Qu.: 95.0 1st Qu.: 7320
## Median : 54.0 Median : 1707 Median : 353.0 Median : 9990
## Mean : 55.8 Mean : 3700 Mean : 855.3 Mean :10441
## 3rd Qu.: 69.0 3rd Qu.: 4005 3rd Qu.: 967.0 3rd Qu.:12925
## Max. :100.0 Max. :31643 Max. :21836.0 Max. :21700
## Room.Board Books Personal PhD
## Min. :1780 Min. : 96.0 Min. : 250 Min. : 8.00
## 1st Qu.:3597 1st Qu.: 470.0 1st Qu.: 850 1st Qu.: 62.00
## Median :4200 Median : 500.0 Median :1200 Median : 75.00
## Mean :4358 Mean : 549.4 Mean :1341 Mean : 72.66
## 3rd Qu.:5050 3rd Qu.: 600.0 3rd Qu.:1700 3rd Qu.: 85.00
## Max. :8124 Max. :2340.0 Max. :6800 Max. :103.00
## Terminal S.F.Ratio perc.alumni Expend
## Min. : 24.0 Min. : 2.50 Min. : 0.00 Min. : 3186
## 1st Qu.: 71.0 1st Qu.:11.50 1st Qu.:13.00 1st Qu.: 6751
## Median : 82.0 Median :13.60 Median :21.00 Median : 8377
## Mean : 79.7 Mean :14.09 Mean :22.74 Mean : 9660
## 3rd Qu.: 92.0 3rd Qu.:16.50 3rd Qu.:31.00 3rd Qu.:10830
## Max. :100.0 Max. :39.80 Max. :64.00 Max. :56233
## Grad.Rate elite college.elite
## Min. : 10.00 No :699 No :699
## 1st Qu.: 53.00 Yes: 78 Yes: 78
## Median : 65.00
## Mean : 65.46
## 3rd Qu.: 78.00
## Max. :118.00
plot(college$Outstate~college$elite)
setwd("C:\\Users\\Luis\\Desktop\\ISLR")
advertising <- read.csv("C:\\Users\\Luis\\Desktop\\ISLR\\Advertising.csv",
header = TRUE,sep = ",")
#fix(advertising)
names(advertising)
## [1] "X" "TV" "Radio" "Newspaper" "Sales"
advertising <- advertising[,-1]
#fix(advertising)
attach(advertising)
model_1 <- lm(Sales~TV,data = advertising)
summary(model_1)
##
## Call:
## lm(formula = Sales ~ TV, data = advertising)
##
## Residuals:
## Min 1Q Median 3Q Max
## -8.3860 -1.9545 -0.1913 2.0671 7.2124
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 7.032594 0.457843 15.36 <2e-16 ***
## TV 0.047537 0.002691 17.67 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 3.259 on 198 degrees of freedom
## Multiple R-squared: 0.6119, Adjusted R-squared: 0.6099
## F-statistic: 312.1 on 1 and 198 DF, p-value: < 2.2e-16
plot(model_1)
# 3.6.2 Simple Linear Regression
library(MASS)
objects(grep("MASS",search()))
## [1] "abbey" "accdeaths" "addterm"
## [4] "Aids2" "Animals" "anorexia"
## [7] "area" "as.fractions" "bacteria"
## [10] "bandwidth.nrd" "bcv" "beav1"
## [13] "beav2" "biopsy" "birthwt"
## [16] "Boston" "boxcox" "cabbages"
## [19] "caith" "Cars93" "cats"
## [22] "cement" "chem" "con2tr"
## [25] "contr.sdif" "coop" "corresp"
## [28] "cov.mcd" "cov.mve" "cov.rob"
## [31] "cov.trob" "cpus" "crabs"
## [34] "Cushings" "DDT" "deaths"
## [37] "denumerate" "dose.p" "drivers"
## [40] "dropterm" "eagles" "enlist"
## [43] "epil" "eqscplot" "farms"
## [46] "fbeta" "fgl" "fitdistr"
## [49] "forbes" "fractions" "frequency.polygon"
## [52] "GAGurine" "galaxies" "gamma.dispersion"
## [55] "gamma.shape" "gehan" "genotype"
## [58] "geyser" "gilgais" "ginv"
## [61] "glm.convert" "glm.nb" "glmmPQL"
## [64] "hills" "hist.FD" "hist.scott"
## [67] "housing" "huber" "hubers"
## [70] "immer" "Insurance" "is.fractions"
## [73] "isoMDS" "kde2d" "lda"
## [76] "ldahist" "leuk" "lm.gls"
## [79] "lm.ridge" "lmsreg" "lmwork"
## [82] "loglm" "loglm1" "logtrans"
## [85] "lqs" "lqs.formula" "ltsreg"
## [88] "mammals" "mca" "mcycle"
## [91] "Melanoma" "menarche" "michelson"
## [94] "minn38" "motors" "muscle"
## [97] "mvrnorm" "nclass.freq" "neg.bin"
## [100] "negative.binomial" "negexp.SSival" "newcomb"
## [103] "nlschools" "npk" "npr1"
## [106] "Null" "oats" "OME"
## [109] "painters" "parcoord" "petrol"
## [112] "phones" "Pima.te" "Pima.tr"
## [115] "Pima.tr2" "polr" "psi.bisquare"
## [118] "psi.hampel" "psi.huber" "qda"
## [121] "quine" "Rabbit" "rational"
## [124] "renumerate" "rlm" "rms.curv"
## [127] "rnegbin" "road" "rotifer"
## [130] "Rubber" "sammon" "select"
## [133] "Shepard" "ships" "shoes"
## [136] "shrimp" "shuttle" "Sitka"
## [139] "Sitka89" "Skye" "snails"
## [142] "SP500" "stdres" "steam"
## [145] "stepAIC" "stormer" "studres"
## [148] "survey" "synth.te" "synth.tr"
## [151] "theta.md" "theta.ml" "theta.mm"
## [154] "topo" "Traffic" "truehist"
## [157] "ucv" "UScereal" "UScrime"
## [160] "VA" "waders" "whiteside"
## [163] "width.SJ" "write.matrix" "wtloss"
data("Boston")
Boston[1:5,]
## crim zn indus chas nox rm age dis rad tax ptratio black
## 1 0.00632 18 2.31 0 0.538 6.575 65.2 4.0900 1 296 15.3 396.90
## 2 0.02731 0 7.07 0 0.469 6.421 78.9 4.9671 2 242 17.8 396.90
## 3 0.02729 0 7.07 0 0.469 7.185 61.1 4.9671 2 242 17.8 392.83
## 4 0.03237 0 2.18 0 0.458 6.998 45.8 6.0622 3 222 18.7 394.63
## 5 0.06905 0 2.18 0 0.458 7.147 54.2 6.0622 3 222 18.7 396.90
## lstat medv
## 1 4.98 24.0
## 2 9.14 21.6
## 3 4.03 34.7
## 4 2.94 33.4
## 5 5.33 36.2
str(Boston)
## 'data.frame': 506 obs. of 14 variables:
## $ crim : num 0.00632 0.02731 0.02729 0.03237 0.06905 ...
## $ zn : num 18 0 0 0 0 0 12.5 12.5 12.5 12.5 ...
## $ indus : num 2.31 7.07 7.07 2.18 2.18 2.18 7.87 7.87 7.87 7.87 ...
## $ chas : int 0 0 0 0 0 0 0 0 0 0 ...
## $ nox : num 0.538 0.469 0.469 0.458 0.458 0.458 0.524 0.524 0.524 0.524 ...
## $ rm : num 6.58 6.42 7.18 7 7.15 ...
## $ age : num 65.2 78.9 61.1 45.8 54.2 58.7 66.6 96.1 100 85.9 ...
## $ dis : num 4.09 4.97 4.97 6.06 6.06 ...
## $ rad : int 1 2 2 3 3 3 5 5 5 5 ...
## $ tax : num 296 242 242 222 222 222 311 311 311 311 ...
## $ ptratio: num 15.3 17.8 17.8 18.7 18.7 18.7 15.2 15.2 15.2 15.2 ...
## $ black : num 397 397 393 395 397 ...
## $ lstat : num 4.98 9.14 4.03 2.94 5.33 ...
## $ medv : num 24 21.6 34.7 33.4 36.2 28.7 22.9 27.1 16.5 18.9 ...
lm.fit <- lm(Boston$medv~Boston$lstat,data = Boston)
lm.fit
##
## Call:
## lm(formula = Boston$medv ~ Boston$lstat, data = Boston)
##
## Coefficients:
## (Intercept) Boston$lstat
## 34.55 -0.95
summary(lm.fit)
##
## Call:
## lm(formula = Boston$medv ~ Boston$lstat, data = Boston)
##
## Residuals:
## Min 1Q Median 3Q Max
## -15.168 -3.990 -1.318 2.034 24.500
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 34.55384 0.56263 61.41 <2e-16 ***
## Boston$lstat -0.95005 0.03873 -24.53 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 6.216 on 504 degrees of freedom
## Multiple R-squared: 0.5441, Adjusted R-squared: 0.5432
## F-statistic: 601.6 on 1 and 504 DF, p-value: < 2.2e-16
names(lm.fit)
## [1] "coefficients" "residuals" "effects" "rank"
## [5] "fitted.values" "assign" "qr" "df.residual"
## [9] "xlevels" "call" "terms" "model"
coefficients(lm.fit)
## (Intercept) Boston$lstat
## 34.5538409 -0.9500494
confint(lm.fit)
## 2.5 % 97.5 %
## (Intercept) 33.448457 35.6592247
## Boston$lstat -1.026148 -0.8739505
predict(lm.fit,data.frame(lstat=(c(5,10,15))),
interval="confidence")
## Warning: 'newdata' had 3 rows but variables found have 506 rows
## fit lwr upr
## 1 29.8225951 29.0252990 30.6198912
## 2 25.8703898 25.2652456 26.4755340
## 3 30.7251420 29.8734766 31.5768074
## 4 31.7606958 30.8435939 32.6777976
## 5 29.4900778 28.7120765 30.2680791
## 6 29.6040837 28.8195155 30.3886520
## 7 22.7447274 22.2015728 23.2878820
## 8 16.3603958 15.6261142 17.0946773
## 9 6.1188637 4.6964329 7.5412945
## 10 18.3079969 17.6682721 18.9477218
## 11 15.1253316 14.3211061 15.9295571
## 12 21.9466860 21.4017704 22.4916015
## 13 19.6285655 19.0379343 20.2191967
## 14 26.7064332 26.0688676 27.3439989
## 15 24.8063345 24.2337154 25.3789536
## 16 26.5069229 25.8775896 27.1362562
## 17 28.3025161 27.5895545 29.0154778
## 18 20.6166169 20.0524476 21.1807861
## 19 23.4477639 22.8999502 23.9955777
## 20 23.8372842 23.2844310 24.3901373
## 21 14.5838035 13.7470635 15.4205434
## 22 21.4146583 20.8644307 21.9648859
## 23 16.7689170 16.0562575 17.4815765
## 24 15.6668597 14.8940813 16.4396381
## 25 19.0680364 18.4583230 19.6777498
## 26 18.8685260 18.2513745 19.4856776
## 27 20.4836100 19.9164496 21.0507703
## 28 18.1369880 17.4899128 18.7840633
## 29 22.3932092 21.8502047 22.9362136
## 30 23.1722496 22.6269495 23.7175497
## 31 13.0827255 12.1512199 14.0142311
## 32 22.1651973 21.6215101 22.7088845
## 33 8.2279733 6.9600530 9.4958936
## 34 17.1204352 16.4256854 17.8151851
## 35 15.2298370 14.4317674 16.0279067
## 36 25.3573631 24.7692166 25.9455097
## 37 23.7137778 23.1627087 24.2648468
## 38 26.2219080 25.6038085 26.8400076
## 39 24.9298409 24.3539993 25.5056826
## 40 30.4496277 29.6148475 31.2844078
## 41 32.6727432 31.6958039 33.6496824
## 42 29.9556020 29.1504707 30.7607333
## 43 29.0340541 28.2817852 29.7863231
## 44 27.4854737 26.8130853 28.1578620
## 45 25.4808696 24.8888470 26.0728921
## 46 24.8538370 24.2799965 25.4276775
## 47 21.1106425 20.5559305 21.6653546
## 48 16.6929130 15.9762946 17.4095315
## 49 5.2828203 3.7982718 6.7673688
## 50 19.1630413 18.5567540 19.7693287
## 51 21.7756771 21.2294109 22.3219432
## 52 25.5948755 24.9991517 26.1905993
## 53 29.5375803 28.7568490 30.3183116
## 54 26.5449248 25.9140464 27.1758033
## 55 20.4931104 19.9261699 21.0600510
## 56 29.9841035 29.1772848 30.7909222
## 57 29.0720561 28.3176769 29.8264354
## 58 30.8011459 29.9447810 31.6575109
## 59 28.0365023 27.3371644 28.7358402
## 60 25.7943858 25.1919064 26.3968653
## 61 22.0606919 21.5164871 22.6048967
## 62 20.8351282 20.2754673 21.3947892
## 63 28.1600087 27.4543928 28.8656246
## 64 25.5283720 24.9348216 26.1219225
## 65 26.9059436 26.2598551 27.5520321
## 66 30.1171104 29.3023789 30.9318418
## 67 24.8253355 24.2522306 25.3984404
## 68 26.8584411 26.2144076 27.5024746
## 69 22.1176948 21.5737883 22.6616014
## 70 26.2029071 25.5855337 26.8202804
## 71 28.1695092 27.4634070 28.8756115
## 72 25.1673533 24.5848920 25.7498145
## 73 29.3095684 28.5418575 30.0772794
## 74 27.3904688 26.7225420 28.0583955
## 75 28.1125063 27.4093148 28.8156977
## 76 26.0603997 25.4483794 26.6724199
## 77 23.1817501 22.6363780 23.7271222
## 78 24.7968340 24.2244565 25.3692115
## 79 22.8302319 22.2868201 23.3736436
## 80 25.9083918 25.3018967 26.5148869
## 81 29.5280798 28.7478952 30.3082644
## 82 27.6944845 27.0120847 28.3768844
## 83 28.1695092 27.4634070 28.8756115
## 84 27.4189702 26.7497109 28.0882295
## 85 25.4143661 24.8244481 26.0042841
## 86 28.3500186 27.6345847 29.0654525
## 87 22.3362062 21.7930886 22.8793238
## 88 26.5354243 25.9049332 27.1659155
## 89 29.3285694 28.5597816 30.0973572
## 90 29.1385596 28.3804719 29.8966472
## 91 26.1839061 25.5672560 26.8005562
## 92 26.7634362 26.1234646 27.4034078
## 93 26.8014382 26.1598495 27.4430268
## 94 28.6540344 27.9225070 29.3855618
## 95 24.4928182 23.9276839 25.0579525
## 96 28.2360127 27.5264925 28.9455329
## 97 23.7802812 23.2282728 24.3322896
## 98 30.5541331 29.7129765 31.3952897
## 99 31.1621647 30.2832444 32.0410850
## 100 28.6730354 27.9404870 29.4055838
## 101 25.6043760 25.0083385 26.2004135
## 102 27.2669623 26.6047498 27.9291749
## 103 24.4548162 23.8905200 25.0191125
## 104 21.7851776 21.2389954 22.3313598
## 105 22.8397323 22.2962867 23.3831780
## 106 18.9065280 18.2908184 19.5222377
## 107 16.8259199 16.1162099 17.5356300
## 108 21.1676455 20.6138531 21.7214379
## 109 22.8967353 22.3530640 23.4404067
## 110 19.7805734 19.1946310 20.3665159
## 111 22.2031993 21.6596684 22.7467302
## 112 24.9013394 24.3262550 25.4764239
## 113 19.1535409 18.5469143 19.7601674
## 114 18.3174974 17.6781748 18.9568201
## 115 24.6258251 24.0576390 25.1940113
## 116 19.5810631 18.9889229 20.1732032
## 117 23.1152467 22.5703565 23.6601369
## 118 24.7683325 24.1966742 25.3399908
## 119 19.9515823 19.3706548 20.5325098
## 120 21.6236692 21.0759176 22.1714208
## 121 20.9016317 20.3432411 21.4600222
## 122 20.9966366 20.4399775 21.5532957
## 123 17.5194560 16.8441884 18.1947235
## 124 10.4130868 9.3008106 11.5253630
## 125 17.8519732 17.1921972 18.5117493
## 126 20.4836100 19.9164496 21.0507703
## 127 8.6554955 7.4184349 9.8925561
## 128 18.2224925 17.5791184 18.8658666
## 129 19.9325813 19.3511104 20.5140522
## 130 17.1299357 16.4356605 17.8242109
## 131 22.5832190 22.0403147 23.1261233
## 132 22.9062358 22.3625231 23.4499485
## 133 23.9892921 23.4340089 24.5445752
## 134 20.2745991 19.7023691 20.8468291
## 135 18.1084866 17.4601662 18.7568069
## 136 18.4410038 17.8068503 19.0751574
## 137 18.4980068 17.8662010 19.1298126
## 138 20.6926208 20.1300773 21.2551643
## 139 14.2987887 13.4445481 15.1530292
## 140 17.0159298 16.3159259 17.7159337
## 141 11.6006485 10.5703489 12.6309481
## 142 1.8626426 0.1202312 3.6050541
## 143 9.0735172 7.8664540 10.2805804
## 144 9.4535370 8.2735814 10.6334925
## 145 6.7268953 5.3493556 8.1044350
## 146 8.1424688 6.8683558 9.4165819
## 147 18.7355191 18.1132302 19.3578080
## 148 6.4988835 5.1045396 7.8932273
## 149 7.6484432 6.3384222 8.9584642
## 150 14.1752822 13.3133807 15.0371838
## 151 21.1581450 20.6042018 21.7120882
## 152 21.9371855 21.3922039 22.4821671
## 153 23.0392427 22.4948400 23.5836454
## 154 19.5525616 18.9595062 20.1456170
## 155 20.1890947 19.6146630 20.7635263
## 156 20.2840996 19.7121097 20.8560895
## 157 19.2200443 18.6157758 19.8243128
## 158 30.1931143 29.3738334 31.0123953
## 159 28.4450235 27.7246102 29.1654369
## 160 27.5329762 26.8583359 28.2076164
## 161 29.3285694 28.5597816 30.0973572
## 162 32.9102555 31.9174432 33.9030678
## 163 32.7297461 31.7490076 33.7104847
## 164 31.3996770 30.5057178 32.2936362
## 165 23.4952664 22.9469306 24.0436022
## 166 25.2338567 24.6494444 25.8182690
## 167 31.0386583 30.1674966 31.9098200
## 168 23.0202417 22.4759503 23.5645332
## 169 24.0082931 23.4526882 24.5638979
## 170 23.7992822 23.2469962 24.3515682
## 171 20.8446287 20.2851522 21.4041052
## 172 23.1247472 22.5797913 23.6697030
## 173 20.5976159 20.0330307 21.1622011
## 174 25.9653947 25.3568503 26.5739391
## 175 25.3953651 24.8060409 25.9846893
## 176 29.4900778 28.7120765 30.2680791
## 177 24.9488419 24.3724910 25.5251928
## 178 28.5780304 27.8505694 29.3054914
## 179 27.9794994 27.2830307 28.6759680
## 180 29.7655921 28.9716338 30.5595504
## 181 27.3714678 26.7044264 28.0385091
## 182 25.5758745 24.9807757 26.1709733
## 183 29.9746030 29.1683471 30.7808589
## 184 29.1575606 28.3984099 29.9167112
## 185 21.2721509 20.7199504 21.8243514
## 186 22.0606919 21.5164871 22.6048967
## 187 30.3261213 29.4988312 31.1534114
## 188 28.2075112 27.4994587 28.9155637
## 189 30.2216158 29.4006237 31.0426079
## 190 29.4330749 28.6583375 30.2078122
## 191 29.7085892 28.9179564 30.4992219
## 192 30.0981094 29.2845122 30.9117066
## 193 31.8271992 30.9057987 32.7485998
## 194 29.7750926 28.9805789 30.5696064
## 195 30.3926247 29.5613078 31.2239417
## 196 31.7321943 30.8169314 32.6474571
## 197 30.6776395 29.8289023 31.5263767
## 198 26.3739159 25.7499038 26.9979281
## 199 28.2645142 27.5535219 28.9755064
## 200 30.2216158 29.4006237 31.0426079
## 201 30.3261213 29.4988312 31.1534114
## 202 27.4949742 26.8221366 28.1678118
## 203 31.5991874 30.6924798 32.5058950
## 204 30.9341528 30.0695221 31.7987836
## 205 31.8176987 30.8969129 32.7384845
## 206 24.2268044 23.6672150 24.7863938
## 207 24.1317995 23.5740064 24.6895925
## 208 17.3959496 16.7147525 18.0771466
## 209 20.6261174 20.0621547 21.1900800
## 210 12.6172013 11.6551493 13.5792533
## 211 18.1464885 17.4998271 18.7931500
## 212 11.7716574 10.7529741 12.7903406
## 213 19.3245497 18.7239101 19.9251894
## 214 25.6423779 25.0450775 26.2396784
## 215 6.4798825 5.0841366 7.8756284
## 216 25.5568735 24.9623965 26.1513505
## 217 21.7186741 21.1718822 22.2654660
## 218 25.3478626 24.7600084 25.9357169
## 219 17.5289565 16.8541412 18.2037718
## 220 24.5783227 24.0112476 25.1453978
## 221 25.3288617 24.7415895 25.9161338
## 222 14.1657817 13.3032890 15.0282745
## 223 25.1198508 24.5387572 25.7009444
## 224 27.3334658 26.6681885 27.9987431
## 225 30.6206366 29.7754040 31.4658691
## 226 30.1551124 29.3381087 30.9721161
## 227 31.5801864 30.6746974 32.4856754
## 228 28.5115270 27.7876008 29.2354531
## 229 30.8296474 29.9715157 31.6877792
## 230 30.9816553 30.1140599 31.8492507
## 231 23.4857659 22.9375366 24.0339952
## 232 29.5660818 28.7837082 30.3484554
## 233 32.2072190 31.2610537 33.1533843
## 234 30.8011459 29.9447810 31.6575109
## 235 26.9059436 26.2598551 27.5520321
## 236 24.2173039 23.6578985 24.7767093
## 237 25.4903700 24.8980436 26.0826965
## 238 30.0601074 29.2487749 30.8714400
## 239 28.5115270 27.7876008 29.2354531
## 240 27.5519771 26.8764322 28.2275221
## 241 23.7422792 23.1908137 24.2937448
## 242 22.7732289 22.2299981 23.3164596
## 243 23.8942871 23.3405528 24.4480214
## 244 29.6230847 28.8374170 30.4087525
## 245 22.6782240 22.1352097 23.2212382
## 246 17.0159298 16.3159259 17.7159337
## 247 25.8513888 25.2469154 26.4558622
## 248 24.9108399 24.3355040 25.4861759
## 249 25.5093710 24.9164342 26.1023078
## 250 28.3215171 27.6075680 29.0354662
## 251 28.9485497 28.2010055 29.6960939
## 252 31.1431637 30.2654398 32.0208876
## 253 31.2001667 30.3188505 32.0814828
## 254 31.1906662 30.3099493 32.0713830
## 255 28.3120166 27.5985615 29.0254718
## 256 25.7658844 25.1643914 26.3673773
## 257 31.5991874 30.6924798 32.5058950
## 258 29.6895882 28.9000612 30.4791152
## 259 27.1529564 26.4959304 27.8099824
## 260 27.9985003 27.3010773 28.6959234
## 261 25.4428676 24.8520526 26.0336825
## 262 27.6564826 26.9759227 28.3370425
## 263 28.9390492 28.1920279 29.6860705
## 264 23.8657856 23.3124965 24.4190748
## 265 26.8584411 26.2144076 27.5024746
## 266 24.6258251 24.0576390 25.1940113
## 267 20.5026109 19.9358892 21.0693327
## 268 27.4854737 26.8130853 28.1578620
## 269 31.5516849 30.6480220 32.4553478
## 270 21.5856672 21.0375026 22.1338318
## 271 22.2031993 21.6596684 22.7467302
## 272 28.2930156 27.5805471 29.0054842
## 273 27.2099594 26.5503508 27.8695680
## 274 28.3025161 27.5895545 29.0154778
## 275 31.2001667 30.3188505 32.0814828
## 276 31.7226938 30.8080435 32.6373441
## 277 28.8060423 28.0662988 29.5457858
## 278 30.6016356 29.7575690 31.4457021
## 279 27.7229860 27.0392006 28.4067715
## 280 29.9461015 29.1415320 30.7506710
## 281 30.9816553 30.1140599 31.8492507
## 282 30.1931143 29.3738334 31.0123953
## 283 31.6941923 30.7813783 32.6070063
## 284 31.5516849 30.6480220 32.4553478
## 285 27.0959535 26.4414884 27.7504186
## 286 26.7349347 26.0961690 27.3737004
## 287 22.2697027 21.7264045 22.8130009
## 288 27.7704885 27.0843830 28.4565940
## 289 27.3334658 26.6681885 27.9987431
## 290 25.5188715 24.9256283 26.1121147
## 291 31.3901765 30.4968218 32.2835312
## 292 31.1716652 30.2921463 32.0511841
## 293 30.0886089 29.2755783 30.9016395
## 294 26.4024174 25.7772765 27.0275583
## 295 24.6733276 24.1040072 25.2426480
## 296 28.5970314 27.8685565 29.3255064
## 297 27.5329762 26.8583359 28.2076164
## 298 19.5050591 18.9104619 20.0996563
## 299 29.8320956 29.0342420 30.6299492
## 300 30.0506069 29.2398397 30.8613742
## 301 28.7870413 28.0483308 29.5257518
## 302 25.5283720 24.9348216 26.1219225
## 303 26.3169130 25.6951394 26.9386865
## 304 29.9366010 29.1325930 30.7406091
## 305 27.9699989 27.2740067 28.6659911
## 306 26.0699002 25.4575282 26.6822721
## 307 28.4070216 27.6886055 29.1254376
## 308 27.3999692 26.7315989 28.0683396
## 309 30.2406168 29.4184824 31.0627513
## 310 25.0818488 24.5018338 25.6618639
## 311 22.5452170 22.0023268 23.0881072
## 312 28.8725457 28.1291735 29.6159179
## 313 23.4192625 22.8717494 23.9667755
## 314 27.0484510 26.3961032 27.7007987
## 315 25.7373829 25.1368693 26.3378965
## 316 23.6282733 23.0783385 24.1782081
## 317 17.1394362 16.4456351 17.8332373
## 318 19.4100542 18.8123127 20.0077956
## 319 24.7113296 24.1410850 25.2815741
## 320 22.4597126 21.9167917 23.0026335
## 321 27.7134855 27.0301625 28.3968086
## 322 28.0270018 27.3281434 28.7258602
## 323 27.2384609 26.5775529 27.8993688
## 324 23.4002615 22.8529438 23.9475792
## 325 28.7395388 28.0034034 29.4756743
## 326 29.7275902 28.9358503 30.5193301
## 327 28.7110374 27.9764418 29.4456329
## 328 22.4027096 21.8597204 22.9456989
## 329 25.0818488 24.5018338 25.6618639
## 330 27.5804786 26.9035726 28.2573847
## 331 25.9178923 25.3110575 26.5247270
## 332 22.7447274 22.2015728 23.2878820
## 333 27.1149544 26.4596381 27.7702708
## 334 29.1575606 28.3984099 29.9167112
## 335 28.1410077 27.4363631 28.8456524
## 336 26.9439456 26.2962017 27.5916894
## 337 25.2433572 24.6586627 25.8280517
## 338 24.5213197 23.9555470 25.0870925
## 339 26.4689209 25.8411218 27.0967200
## 340 25.3003602 24.7139549 25.8867654
## 341 25.7278824 25.1276937 26.3280711
## 342 29.3380699 28.5687431 30.1073967
## 343 26.3359140 25.7133971 26.9584309
## 344 27.7324865 27.0482381 28.4167349
## 345 30.1741134 29.3559717 30.9922550
## 346 24.5498212 23.9834015 25.1162409
## 347 22.5167156 21.9738247 23.0596064
## 348 28.5115270 27.7876008 29.2354531
## 349 28.8630453 28.1201927 29.6058978
## 350 28.9580502 28.2099826 29.7061177
## 351 28.8725457 28.1291735 29.6159179
## 352 29.3380699 28.5687431 30.1073967
## 353 27.1529564 26.4959304 27.8099824
## 354 30.2786188 29.4541960 31.1030416
## 355 26.9059436 26.2598551 27.5520321
## 356 29.2620660 28.4970407 30.0270913
## 357 17.8329723 17.1723301 18.4936144
## 358 21.9466860 21.4017704 22.4916015
## 359 23.6472743 23.0970946 24.1974540
## 360 22.5167156 21.9738247 23.0596064
## 361 27.1529564 26.4959304 27.8099824
## 362 21.0726405 20.5172954 21.6279857
## 363 24.8728380 24.2985026 25.4471734
## 364 20.6451183 20.0815659 21.2086707
## 365 29.5280798 28.7478952 30.3082644
## 366 27.7894895 27.1024523 28.4765267
## 367 21.2531499 20.7006691 21.8056308
## 368 21.8896830 21.3443551 22.4350109
## 369 31.4566800 30.5590890 32.3542710
## 370 31.0101568 30.1407794 31.8795342
## 371 31.7416948 30.8258192 32.6575704
## 372 25.4998705 24.9072393 26.0925018
## 373 26.1174026 25.5032610 26.7315443
## 374 1.5206248 -0.2478391 3.2890888
## 375 -1.5195331 -3.5211516 0.4820854
## 376 21.7851776 21.2389954 22.3313598
## 377 12.4746939 11.5031968 13.4461910
## 378 14.3747926 13.5252436 15.2243416
## 379 12.0471717 11.0470929 13.0472505
## 380 13.8617660 12.9802176 14.7433144
## 381 18.2034915 17.5592994 18.8476836
## 382 14.5268005 13.6865809 15.3670201
## 383 12.1326761 11.1383423 13.1270100
## 384 11.2206288 10.1643364 12.2769211
## 385 5.4538292 3.9820212 6.9256372
## 386 5.2828203 3.7982718 6.7673688
## 387 7.6864452 6.3791938 8.9936965
## 388 4.1617621 2.5932928 5.7302313
## 389 5.4633297 3.9922290 6.9344304
## 390 14.7453119 13.9183735 15.5722502
## 391 18.2984964 17.6583687 18.9386242
## 392 16.7309150 16.0162798 17.4455502
## 393 10.1565735 9.0263197 11.2868272
## 394 20.1415922 19.5659058 20.7172786
## 395 19.0205339 18.4090793 19.6319886
## 396 18.2889959 17.6484647 18.9295272
## 397 16.1513849 15.4057280 16.8970418
## 398 15.6288578 14.8539101 16.4038054
## 399 5.4918311 4.0228520 6.9608103
## 400 6.0808617 4.6556170 7.5061065
## 401 9.1210197 7.9173537 10.3246857
## 402 15.2488380 14.4518832 16.0457928
## 403 15.2583385 14.4619407 16.0547363
## 404 15.7713652 15.0045215 16.5382088
## 405 8.5414896 7.2962170 9.7867621
## 406 12.7217067 11.7665537 13.6768597
## 407 12.3796890 11.4018718 13.3575061
## 408 23.0297422 22.4853957 23.5740888
## 409 9.4725379 8.2939335 10.6511424
## 410 15.7618647 14.9944833 16.5292460
## 411 24.9488419 24.3724910 25.5251928
## 412 14.3937936 13.5454147 15.2421725
## 413 1.9006446 0.1611253 3.6401639
## 414 15.4768499 14.6931671 16.2605326
## 415 -0.5789842 -2.5081970 1.3502286
## 416 6.9549072 5.5941340 8.3156803
## 417 10.0520680 8.9144652 11.1896709
## 418 9.2445261 8.0496812 10.4393710
## 419 14.9638232 14.1500064 15.7776400
## 420 12.9497186 12.0095351 13.8899021
## 421 20.2840996 19.7121097 20.8560895
## 422 19.6380660 19.0477342 20.2283979
## 423 21.1581450 20.6042018 21.7120882
## 424 12.4271914 11.4525366 13.4018463
## 425 18.2509940 17.6088421 18.8931459
## 426 11.3821371 10.3369210 12.4273532
## 427 19.6475665 19.0575331 20.2375999
## 428 20.7591243 20.1979530 21.3202955
## 429 14.1087788 13.2427333 14.9748243
## 430 11.6766524 10.6515220 12.7017829
## 431 17.7949703 17.1325889 18.4573517
## 432 15.8473691 15.0848129 16.6099253
## 433 23.1247472 22.5797913 23.6697030
## 434 19.1440404 18.5370739 19.7510069
## 435 20.1415922 19.5659058 20.7172786
## 436 12.4461924 11.4728012 13.4195836
## 437 17.4054500 16.7247123 18.0861877
## 438 9.4250355 8.2430525 10.6070185
## 439 2.2331619 0.5189267 3.9473970
## 440 12.8167117 11.8678100 13.7656134
## 441 13.5482497 12.6467830 14.4497163
## 442 16.0088775 15.2553498 16.7624052
## 443 18.7925221 18.1724521 19.4125921
## 444 16.6454106 15.9263026 17.3645185
## 445 11.9521668 10.9456884 12.9586451
## 446 11.7716574 10.7529741 12.7903406
## 447 17.6524629 16.9834761 18.3214496
## 448 18.9350295 18.3203935 19.5496655
## 449 17.3294461 16.6450182 18.0138740
## 450 16.2083879 15.4658534 16.9509223
## 451 17.9849801 17.3311996 18.6387607
## 452 17.7094658 17.0431368 18.3757948
## 453 18.1464885 17.4998271 18.7931500
## 454 18.6500147 18.0243497 19.2756797
## 455 16.7784175 16.0662507 17.4905842
## 456 17.3294461 16.6450182 18.0138740
## 457 16.4934027 15.7662519 17.2205534
## 458 18.4600048 17.8266365 19.0933731
## 459 19.1345399 18.5272327 19.7418471
## 460 20.5881154 20.0233208 21.1529100
## 461 18.9540305 18.3401067 19.5679543
## 462 20.6356178 20.0718608 21.1993749
## 463 21.2626504 20.7103102 21.8149906
## 464 24.7778330 24.2059359 25.3497301
## 465 21.9941884 21.4495875 22.5387893
## 466 21.1296435 20.5752420 21.6840450
## 467 18.2604945 17.6187487 18.9022402
## 468 14.2987887 13.4445481 15.1530292
## 469 17.3294461 16.6450182 18.0138740
## 470 20.5311124 19.9650415 21.0971833
## 471 19.0775369 18.4681695 19.6869043
## 472 22.3267057 21.7835655 22.8698459
## 473 20.9111322 20.3529192 21.4693451
## 474 23.4762654 22.9281416 24.0243893
## 475 17.3199456 16.6350541 18.0048371
## 476 11.6576515 10.6312297 12.6840732
## 477 16.8069190 16.0962277 17.5176102
## 478 10.8881115 9.8088847 11.9673382
## 479 17.4244510 16.7446305 18.1042716
## 480 22.0986939 21.5546921 22.6426956
## 481 24.3503108 23.7882407 24.9123810
## 482 27.2004589 26.5412822 27.8596355
## 483 27.8939949 27.2017959 28.5861939
## 484 24.6543266 24.0854627 25.2231906
## 485 21.8801825 21.3347822 22.4255828
## 486 24.5023187 23.9369726 25.0676649
## 487 20.3221016 19.7510629 20.8931402
## 488 23.6757758 23.1252211 24.2263305
## 489 17.3959496 16.7147525 18.0771466
## 490 11.7811579 10.7631185 12.7991973
## 491 6.3563761 4.9515111 7.7612410
## 492 17.3864491 16.7047920 18.0681061
## 493 21.8706820 21.3252083 22.4161558
## 494 23.1437481 22.5986577 23.6888385
## 495 21.6426702 21.0951188 22.1902215
## 496 17.8329723 17.1723301 18.4936144
## 497 14.4697975 13.6260879 15.3135072
## 498 21.1581450 20.6042018 21.7120882
## 499 22.2792032 21.7359340 22.8224724
## 500 20.2080956 19.6341596 20.7820317
## 501 20.9396336 20.3819475 21.4973198
## 502 25.3668636 24.7784239 25.9553033
## 503 25.9273927 25.3202176 26.5345679
## 504 29.1955625 28.4342810 29.9568440
## 505 28.3975211 27.6796032 29.1154389
## 506 27.0674520 26.4142591 27.7206448
predict(lm.fit,data.frame(lstat=(c(5,10,15))),
interval="prediction")
## Warning: 'newdata' had 3 rows but variables found have 506 rows
## fit lwr upr
## 1 29.8225951 17.5846032 42.06059
## 2 25.8703898 13.6434129 38.09737
## 3 30.7251420 18.4834878 42.96680
## 4 31.7606958 19.5143151 44.00708
## 5 29.4900778 17.2533279 41.72683
## 6 29.6040837 17.3669145 41.84125
## 7 22.7447274 10.5206618 34.96879
## 8 16.3603958 4.1263477 28.59444
## 9 6.1188637 -6.1756909 18.41342
## 10 18.3079969 6.0792598 30.53673
## 11 15.1253316 2.8868863 27.36378
## 12 21.9466860 9.7225420 34.17083
## 13 19.6285655 7.4022984 31.85483
## 14 26.7064332 14.4778089 38.93506
## 15 24.8063345 12.5809243 37.03174
## 16 26.5069229 14.2787250 38.73512
## 17 28.3025161 16.0697291 40.53530
## 18 20.6166169 8.3915995 32.84163
## 19 23.4477639 11.2234904 35.67204
## 20 23.8372842 11.6127838 36.06178
## 21 14.5838035 2.3431786 26.82443
## 22 21.4146583 9.1902764 33.63904
## 23 16.7689170 4.5361476 29.00169
## 24 15.6668597 3.4304407 27.90328
## 25 19.0680364 6.8408326 31.29524
## 26 18.8685260 6.6409490 31.09610
## 27 20.4836100 8.2584542 32.70877
## 28 18.1369880 5.9078642 30.36611
## 29 22.3932092 10.1691502 34.61727
## 30 23.1722496 10.9480885 35.39641
## 31 13.0827255 0.8352577 25.33019
## 32 22.1651973 9.9411080 34.38929
## 33 8.2279733 -4.0496643 20.50561
## 34 17.1204352 4.8886962 29.35217
## 35 15.2298370 2.9917948 27.46788
## 36 25.3573631 13.1312158 37.58351
## 37 23.7137778 11.4893579 35.93820
## 38 26.2219080 13.9942832 38.44953
## 39 24.9298409 12.7042793 37.15540
## 40 30.4496277 18.2091366 42.69012
## 41 32.6727432 20.4217361 44.92375
## 42 29.9556020 17.7170972 42.19411
## 43 29.0340541 16.7989133 41.26919
## 44 27.4854737 15.2549843 39.71596
## 45 25.4808696 13.2545351 37.70720
## 46 24.8538370 12.6283694 37.07930
## 47 21.1106425 8.8860579 33.33523
## 48 16.6929130 4.4599124 28.92591
## 49 5.2828203 -7.0190758 17.58472
## 50 19.1630413 6.9360079 31.39007
## 51 21.7756771 9.5514728 33.99988
## 52 25.5948755 13.3683612 37.82139
## 53 29.5375803 17.3006565 41.77450
## 54 26.5449248 14.3166473 38.77320
## 55 20.4931104 8.2679648 32.71826
## 56 29.9841035 17.7454876 42.22272
## 57 29.0720561 16.8367853 41.30733
## 58 30.8011459 18.5591639 43.04313
## 59 28.0365023 15.8045018 40.26850
## 60 25.7943858 13.5675406 38.02123
## 61 22.0606919 9.8365795 34.28480
## 62 20.8351282 8.6103180 33.05994
## 63 28.1600087 15.9276477 40.39237
## 64 25.5283720 13.3019635 37.75478
## 65 26.9059436 14.6768719 39.13502
## 66 30.1171104 17.8779703 42.35625
## 67 24.8253355 12.5999025 37.05077
## 68 26.8584411 14.6294778 39.08740
## 69 22.1176948 9.8935958 34.34179
## 70 26.2029071 13.9753189 38.43050
## 71 28.1695092 15.9371201 40.40190
## 72 25.1673533 12.9414781 37.39323
## 73 29.3095684 17.0734684 41.54567
## 74 27.3904688 15.1602239 39.62071
## 75 28.1125063 15.8802848 40.34473
## 76 26.0603997 13.8330806 38.28772
## 77 23.1817501 10.9575858 35.40591
## 78 24.7968340 12.5714351 37.02223
## 79 22.8302319 10.6061548 35.05431
## 80 25.9083918 13.6813480 38.13544
## 81 29.5280798 17.2911908 41.76497
## 82 27.6944845 15.4634407 39.92553
## 83 28.1695092 15.9371201 40.40190
## 84 27.4189702 15.1886525 39.64929
## 85 25.4143661 13.1881334 37.64060
## 86 28.3500186 16.1170873 40.58295
## 87 22.3362062 10.1121422 34.56027
## 88 26.5354243 14.3071668 38.76368
## 89 29.3285694 17.0924018 41.56474
## 90 29.1385596 16.9030596 41.37406
## 91 26.1839061 13.9563544 38.41146
## 92 26.7634362 14.5346862 38.99219
## 93 26.8014382 14.5726034 39.03027
## 94 28.6540344 16.4201513 40.88792
## 95 24.4928182 12.2677563 36.71788
## 96 28.2360127 16.0034258 40.46860
## 97 23.7802812 11.5558190 36.00474
## 98 30.5541331 18.3132055 42.79506
## 99 31.1621647 18.9185842 43.40575
## 100 28.6730354 16.4390912 40.90698
## 101 25.6043760 13.3778464 37.83091
## 102 27.2669623 15.0370282 39.49690
## 103 24.4548162 12.2297930 36.67984
## 104 21.7851776 9.5609770 34.00938
## 105 22.8397323 10.6156538 35.06381
## 106 18.9065280 6.6790237 31.13403
## 107 16.8259199 4.5933220 29.05852
## 108 21.1676455 8.9431026 33.39219
## 109 22.8967353 10.6726467 35.12082
## 110 19.7805734 7.5545319 32.00661
## 111 22.2031993 9.9791169 34.42728
## 112 24.9013394 12.6758135 37.12687
## 113 19.1535409 6.9264905 31.38059
## 114 18.3174974 6.0887813 30.54621
## 115 24.6258251 12.4006217 36.85103
## 116 19.5810631 7.3547229 31.80740
## 117 23.1152467 10.8911038 35.33939
## 118 24.7683325 12.5429672 36.99370
## 119 19.9515823 7.7257801 32.17738
## 120 21.6236692 9.3993984 33.84794
## 121 20.9016317 8.6768796 33.12638
## 122 20.9966366 8.7719635 33.22131
## 123 17.5194560 5.2888080 29.75010
## 124 10.4130868 -1.8494546 22.67563
## 125 17.8519732 5.6221708 30.08178
## 126 20.4836100 8.2584542 32.70877
## 127 8.6554955 -3.6189936 20.92998
## 128 18.2224925 5.9935639 30.45142
## 129 19.9325813 7.7067533 32.15841
## 130 17.1299357 4.8982236 29.36165
## 131 22.5832190 10.3591645 34.80727
## 132 22.9062358 10.6821454 35.13033
## 133 23.9892921 11.7646815 36.21390
## 134 20.2745991 8.0492071 32.49999
## 135 18.1084866 5.8792968 30.33768
## 136 18.4410038 6.2125569 30.66945
## 137 18.4980068 6.2696814 30.72633
## 138 20.6926208 8.4676783 32.91756
## 139 14.2987887 2.0569550 26.54062
## 140 17.0159298 4.7838912 29.24797
## 141 11.6006485 -0.6547291 23.85603
## 142 1.8626426 -10.4730277 14.19831
## 143 9.0735172 -3.1979849 21.34502
## 144 9.4535370 -2.8153285 21.72240
## 145 6.7268953 -5.5625465 19.01634
## 146 8.1424688 -4.1358098 20.42075
## 147 18.7355191 6.5076818 30.96336
## 148 6.4988835 -5.7924533 18.79022
## 149 7.6484432 -4.6336136 19.93050
## 150 14.1752822 1.9329116 26.41765
## 151 21.1581450 8.9335952 33.38269
## 152 21.9371855 9.7130385 34.16133
## 153 23.0392427 10.8151216 35.26336
## 154 19.5525616 7.3261771 31.77895
## 155 20.1890947 7.9635994 32.41459
## 156 20.2840996 8.0587188 32.50948
## 157 19.2200443 6.9931108 31.44698
## 158 30.1931143 17.9536705 42.43256
## 159 28.4450235 16.2118000 40.67825
## 160 27.5329762 15.3023628 39.76359
## 161 29.3285694 17.0924018 41.56474
## 162 32.9102555 20.6579725 45.16254
## 163 32.7297461 20.4784355 44.98106
## 164 31.3996770 19.1550077 43.64435
## 165 23.4952664 11.2709695 35.71956
## 166 25.2338567 13.0078884 37.45983
## 167 31.0386583 18.7956323 43.28168
## 168 23.0202417 10.7961255 35.24436
## 169 24.0082931 11.7836679 36.23292
## 170 23.7992822 11.5748074 36.02376
## 171 20.8446287 8.6198270 33.06943
## 172 23.1247472 10.9006014 35.34889
## 173 20.5976159 8.3725793 32.82265
## 174 25.9653947 13.7382491 38.19254
## 175 25.3953651 13.1691610 37.62157
## 176 29.4900778 17.2533279 41.72683
## 177 24.9488419 12.7232563 37.17443
## 178 28.5780304 16.3443898 40.81167
## 179 27.9794994 15.7476625 40.21134
## 180 29.7655921 17.5278173 42.00337
## 181 27.3714678 15.1412712 39.60166
## 182 25.5758745 13.3493907 37.80236
## 183 29.9746030 17.7360242 42.21318
## 184 29.1575606 16.9219946 41.39313
## 185 21.2721509 9.0476800 33.49662
## 186 22.0606919 9.8365795 34.28480
## 187 30.3261213 18.0861387 42.56610
## 188 28.2075112 15.9750093 40.44001
## 189 30.2216158 17.9820574 42.46117
## 190 29.4330749 17.1965320 41.66962
## 191 29.7085892 17.4710296 41.94615
## 192 30.0981094 17.8590447 42.33717
## 193 31.8271992 19.5804959 44.07390
## 194 29.7750926 17.5372817 42.01290
## 195 30.3926247 18.1523693 42.63288
## 196 31.7321943 19.4859512 43.97844
## 197 30.6776395 18.4361887 42.91909
## 198 26.3739159 14.1459908 38.60184
## 199 28.2645142 16.0318418 40.49719
## 200 30.2216158 17.9820574 42.46117
## 201 30.3261213 18.0861387 42.56610
## 202 27.4949742 15.2644601 39.72549
## 203 31.5991874 19.3535807 43.84479
## 204 30.9341528 18.6915898 43.17672
## 205 31.8176987 19.5710417 44.06436
## 206 24.2268044 12.0019975 36.45161
## 207 24.1317995 11.9070747 36.35652
## 208 17.3959496 5.1649728 29.62693
## 209 20.6261174 8.4011095 32.85113
## 210 12.6172013 0.3673724 24.86703
## 211 18.1464885 5.9173866 30.37559
## 212 11.7716574 -0.4827491 24.02606
## 213 19.3245497 7.0977950 31.55130
## 214 25.6423779 13.4157868 37.86897
## 215 6.4798825 -5.8116134 18.77138
## 216 25.5568735 13.3304200 37.78333
## 217 21.7186741 9.4944463 33.94290
## 218 25.3478626 13.1217293 37.57400
## 219 17.5289565 5.2983335 29.75958
## 220 24.5783227 12.3531708 36.80347
## 221 25.3288617 13.1027563 37.55497
## 222 14.1657817 1.9233695 26.40819
## 223 25.1198508 12.8940407 37.34566
## 224 27.3334658 15.1033653 39.56357
## 225 30.6206366 18.3794282 42.86184
## 226 30.1551124 17.9158208 42.39440
## 227 31.5801864 19.3346699 43.82570
## 228 28.5115270 16.2780961 40.74496
## 229 30.8296474 18.5875417 43.07175
## 230 30.9816553 18.7388825 43.22443
## 231 23.4857659 11.2614738 35.71006
## 232 29.5660818 17.3290531 41.80311
## 233 32.2072190 19.9586275 44.45581
## 234 30.8011459 18.5591639 43.04313
## 235 26.9059436 14.6768719 39.13502
## 236 24.2173039 11.9925054 36.44210
## 237 25.4903700 13.2640209 37.71672
## 238 30.0601074 17.8211931 42.29902
## 239 28.5115270 16.2780961 40.74496
## 240 27.5519771 15.3213139 39.78264
## 241 23.7422792 11.5178415 35.96672
## 242 22.7732289 10.5491599 34.99730
## 243 23.8942871 11.6697469 36.11883
## 244 29.6230847 17.3858450 41.86032
## 245 22.6782240 10.4541646 34.90228
## 246 17.0159298 4.7838912 29.24797
## 247 25.8513888 13.6244451 38.07833
## 248 24.9108399 12.6853021 37.13638
## 249 25.5093710 13.2829923 37.73575
## 250 28.3215171 16.0886725 40.55436
## 251 28.9485497 16.7136984 41.18340
## 252 31.1431637 18.8996690 43.38666
## 253 31.2001667 18.9564139 43.44392
## 254 31.1906662 18.9469565 43.43438
## 255 28.3120166 16.0792009 40.54483
## 256 25.7658844 13.5390877 37.99268
## 257 31.5991874 19.3535807 43.84479
## 258 29.6895882 17.4521000 41.92708
## 259 27.1529564 14.9233020 39.38261
## 260 27.9985003 15.7666091 40.23039
## 261 25.4428676 13.2165915 37.66914
## 262 27.6564826 15.4255413 39.88742
## 263 28.9390492 16.7042299 41.17387
## 264 23.8657856 11.6412655 36.09031
## 265 26.8584411 14.6294778 39.08740
## 266 24.6258251 12.4006217 36.85103
## 267 20.5026109 8.2774755 32.72775
## 268 27.4854737 15.2549843 39.71596
## 269 31.5516849 19.3063033 43.79707
## 270 21.5856672 9.3613779 33.80996
## 271 22.2031993 9.9791169 34.42728
## 272 28.2930156 16.0602574 40.52577
## 273 27.2099594 14.9801660 39.43975
## 274 28.3025161 16.0697291 40.53530
## 275 31.2001667 18.9564139 43.44392
## 276 31.7226938 19.4764965 43.96889
## 277 28.8060423 16.5716652 41.04042
## 278 30.6016356 18.3605077 42.84276
## 279 27.7229860 15.4918648 39.95411
## 280 29.9461015 17.7076337 42.18457
## 281 30.9816553 18.7388825 43.22443
## 282 30.1931143 17.9536705 42.43256
## 283 31.6941923 19.4481320 43.94025
## 284 31.5516849 19.3063033 43.79707
## 285 27.0959535 14.8664364 39.32547
## 286 26.7349347 14.5062477 38.96362
## 287 22.2697027 10.0456307 34.49377
## 288 27.7704885 15.5392374 40.00174
## 289 27.3334658 15.1033653 39.56357
## 290 25.5188715 13.2924779 37.74527
## 291 31.3901765 19.1455513 43.63480
## 292 31.1716652 18.9280417 43.41529
## 293 30.0886089 17.8495819 42.32764
## 294 26.4024174 14.1744346 38.63040
## 295 24.6733276 12.4480714 36.89858
## 296 28.5970314 16.3633305 40.83073
## 297 27.5329762 15.3023628 39.76359
## 298 19.5050591 7.2785997 31.73152
## 299 29.8320956 17.5940674 42.07012
## 300 30.0506069 17.8117301 42.28948
## 301 28.7870413 16.5527266 41.02136
## 302 25.5283720 13.3019635 37.75478
## 303 26.3169130 14.0891018 38.54472
## 304 29.9366010 17.6981701 42.17503
## 305 27.9699989 15.7381892 40.20181
## 306 26.0699002 13.8425634 38.29724
## 307 28.4070216 16.1739155 40.64013
## 308 27.3999692 15.1697001 39.63024
## 309 30.2406168 18.0009817 42.48025
## 310 25.0818488 12.8560899 37.30761
## 311 22.5452170 10.3211632 34.76927
## 312 28.8725457 16.6379487 41.10714
## 313 23.4192625 11.1950024 35.64352
## 314 27.0484510 14.8190470 39.27785
## 315 25.7373829 13.5106343 37.96413
## 316 23.6282733 11.4039045 35.85264
## 317 17.1394362 4.9077510 29.37112
## 318 19.4100542 7.1834415 31.63667
## 319 24.7113296 12.4860303 36.93663
## 320 22.4597126 10.2356574 34.68377
## 321 27.7134855 15.4823902 39.94458
## 322 28.0270018 15.7950287 40.25897
## 323 27.2384609 15.0085973 39.46832
## 324 23.4002615 11.1760102 35.62451
## 325 28.7395388 16.5053793 40.97370
## 326 29.7275902 17.4899590 41.96522
## 327 28.7110374 16.4769704 40.94510
## 328 22.4027096 10.1786514 34.62677
## 329 25.0818488 12.8560899 37.30761
## 330 27.5804786 15.3497401 39.81122
## 331 25.9178923 13.6908316 38.14495
## 332 22.7447274 10.5206618 34.96879
## 333 27.1149544 14.8853918 39.34452
## 334 29.1575606 16.9219946 41.39313
## 335 28.1410077 15.9087027 40.37331
## 336 26.9439456 14.7147863 39.17310
## 337 25.2433572 13.0173754 37.46934
## 338 24.5213197 12.2962282 36.74641
## 339 26.4689209 14.2408018 38.69704
## 340 25.3003602 13.0742964 37.52642
## 341 25.7278824 13.5011498 37.95461
## 342 29.3380699 17.1018684 41.57427
## 343 26.3359140 14.1080650 38.56376
## 344 27.7324865 15.5013394 39.96363
## 345 30.1741134 17.9347458 42.41348
## 346 24.5498212 12.3246997 36.77494
## 347 22.5167156 10.2926617 34.74077
## 348 28.5115270 16.2780961 40.74496
## 349 28.8630453 16.6284797 41.09761
## 350 28.9580502 16.7231669 41.19293
## 351 28.8725457 16.6379487 41.10714
## 352 29.3380699 17.1018684 41.57427
## 353 27.1529564 14.9233020 39.38261
## 354 30.2786188 18.0388297 42.51841
## 355 26.9059436 14.6768719 39.13502
## 356 29.2620660 17.0261342 41.49800
## 357 17.8329723 5.6031231 30.06282
## 358 21.9466860 9.7225420 34.17083
## 359 23.6472743 11.4228945 35.87165
## 360 22.5167156 10.2926617 34.74077
## 361 27.1529564 14.9233020 39.38261
## 362 21.0726405 8.8480272 33.29725
## 363 24.8728380 12.6473472 37.09833
## 364 20.6451183 8.4201294 32.87011
## 365 29.5280798 17.2911908 41.76497
## 366 27.7894895 15.5581861 40.02079
## 367 21.2531499 9.0286664 33.47763
## 368 21.8896830 9.6655206 34.11385
## 369 31.4566800 19.2117450 43.70161
## 370 31.0101568 18.7672576 43.25306
## 371 31.7416948 19.4954059 43.98798
## 372 25.4998705 13.2735066 37.72623
## 373 26.1174026 13.8899772 38.34483
## 374 1.5206248 -10.8187523 13.86000
## 375 -1.5195331 -13.8944771 10.85541
## 376 21.7851776 9.5609770 34.00938
## 377 12.4746939 0.2241196 24.72527
## 378 14.3747926 2.1332855 26.61630
## 379 12.0471717 -0.2057023 24.30005
## 380 13.8617660 1.6179965 26.10554
## 381 18.2034915 5.9745199 30.43246
## 382 14.5268005 2.2859373 26.76766
## 383 12.1326761 -0.1197303 24.38508
## 384 11.2206288 -1.0369614 23.47822
## 385 5.4538292 -6.8465360 17.75419
## 386 5.2828203 -7.0190758 17.58472
## 387 7.6864452 -4.5953165 19.96821
## 388 4.1617621 -8.1505431 16.47407
## 389 5.4633297 -6.8369508 17.76361
## 390 14.7453119 2.5053531 26.98527
## 391 18.2984964 6.0697382 30.52725
## 392 16.7309150 4.4980303 28.96380
## 393 10.1565735 -2.1076117 22.42076
## 394 20.1415922 7.9160379 32.36715
## 395 19.0205339 6.7932431 31.24782
## 396 18.2889959 6.0602166 30.51778
## 397 16.1513849 3.9166488 28.38612
## 398 15.6288578 3.3923016 27.86541
## 399 5.4918311 -6.8081958 17.79186
## 400 6.0808617 -6.2140187 18.37574
## 401 9.1210197 -3.1501488 21.39219
## 402 15.2488380 3.0108684 27.48681
## 403 15.2583385 3.0204051 27.49627
## 404 15.7713652 3.5353195 28.00741
## 405 8.5414896 -3.7338299 20.81681
## 406 12.7217067 0.4724177 24.97100
## 407 12.3796890 0.1286119 24.63077
## 408 23.0297422 10.8056236 35.25386
## 409 9.4725379 -2.7961976 21.74127
## 410 15.7618647 3.5257853 27.99794
## 411 24.9488419 12.7232563 37.17443
## 412 14.3937936 2.1523676 26.63522
## 413 1.9006446 -10.4346175 14.23591
## 414 15.4768499 3.2397374 27.71396
## 415 -0.5789842 -12.9424233 11.78445
## 416 6.9549072 -5.3326665 19.24248
## 417 10.0520680 -2.2127966 22.31693
## 418 9.2445261 -3.0257802 21.51483
## 419 14.9638232 2.7247439 27.20290
## 420 12.9497186 0.7015878 25.19785
## 421 20.2840996 8.0587188 32.50948
## 422 19.6380660 7.4118133 31.86432
## 423 21.1581450 8.9335952 33.38269
## 424 12.4271914 0.1763663 24.67802
## 425 18.2509940 6.0221297 30.47986
## 426 11.3821371 -0.8745035 23.63878
## 427 19.6475665 7.4213282 31.87380
## 428 20.7591243 8.5342449 32.98400
## 429 14.1087788 1.8661158 26.35144
## 430 11.6766524 -0.5782917 23.93160
## 431 17.7949703 5.5650270 30.02491
## 432 15.8473691 3.6115914 28.08315
## 433 23.1247472 10.9006014 35.34889
## 434 19.1440404 6.9169732 31.37111
## 435 20.1415922 7.9160379 32.36715
## 436 12.4461924 0.1954678 24.69692
## 437 17.4054500 5.1744988 29.63640
## 438 9.4250355 -2.8440251 21.69410
## 439 2.2331619 -10.0985601 14.56488
## 440 12.8167117 0.5679085 25.06551
## 441 13.5482497 1.3030300 25.79347
## 442 16.0088775 3.7736592 28.24410
## 443 18.7925221 6.5647974 31.02025
## 444 16.6454106 4.4122638 28.87856
## 445 11.9521668 -0.3012312 24.20556
## 446 11.7716574 -0.4827491 24.02606
## 447 17.6524629 5.4221601 29.88277
## 448 18.9350295 6.7075792 31.16248
## 449 17.3294461 5.0982890 29.56060
## 450 16.2083879 3.9738417 28.44293
## 451 17.9849801 5.7554997 30.21446
## 452 17.7094658 5.4793081 29.93962
## 453 18.1464885 5.9173866 30.37559
## 454 18.6500147 6.4220050 30.87802
## 455 16.7784175 4.5456768 29.01116
## 456 17.3294461 5.0982890 29.56060
## 457 16.4934027 4.2597805 28.72702
## 458 18.4600048 6.2315986 30.68841
## 459 19.1345399 6.9074558 31.36162
## 460 20.5881154 8.3630691 32.81316
## 461 18.9540305 6.7266160 31.18145
## 462 20.6356178 8.4106195 32.86062
## 463 21.2626504 9.0381732 33.48713
## 464 24.7778330 12.5524566 37.00321
## 465 21.9941884 9.7700585 34.21832
## 466 21.1296435 8.9050730 33.35421
## 467 18.2604945 6.0316515 30.48934
## 468 14.2987887 2.0569550 26.54062
## 469 17.3294461 5.0982890 29.56060
## 470 20.5311124 8.3060071 32.75622
## 471 19.0775369 6.8503503 31.30472
## 472 22.3267057 10.1026407 34.55077
## 473 20.9111322 8.6863882 33.13588
## 474 23.4762654 11.2519780 35.70055
## 475 17.3199456 5.0887625 29.55113
## 476 11.6576515 -0.5974008 23.91270
## 477 16.8069190 4.5742641 29.03957
## 478 10.8881115 -1.3714764 23.14770
## 479 17.4244510 5.1935508 29.65535
## 480 22.0986939 9.8745906 34.32280
## 481 24.3503108 12.1253901 36.57523
## 482 27.2004589 14.9706888 39.43023
## 483 27.8939949 15.6624005 40.12559
## 484 24.6543266 12.4290917 36.87956
## 485 21.8801825 9.6560169 34.10435
## 486 24.5023187 12.2772470 36.72739
## 487 20.3221016 8.0967652 32.54744
## 488 23.6757758 11.4513791 35.90017
## 489 17.3959496 5.1649728 29.62693
## 490 11.7811579 -0.4731951 24.03551
## 491 6.3563761 -5.9361586 18.64891
## 492 17.3864491 5.1554467 29.61745
## 493 21.8706820 9.6465131 34.09485
## 494 23.1437481 10.9195964 35.36790
## 495 21.6426702 9.4184084 33.86693
## 496 17.8329723 5.6031231 30.06282
## 497 14.4697975 2.2286943 26.71090
## 498 21.1581450 8.9335952 33.38269
## 499 22.2792032 10.0551325 34.50327
## 500 20.2080956 7.9826236 32.43357
## 501 20.9396336 8.7149137 33.16435
## 502 25.3668636 13.1407021 37.59303
## 503 25.9273927 13.7003152 38.15447
## 504 29.1955625 16.9598642 41.43126
## 505 28.3975211 16.1644442 40.63060
## 506 27.0674520 14.8380029 39.29690
plot(Boston$lstat,Boston$medv)
abline(lm.fit,col="red",lwd=3)
par(mfrow=c(2,2))
plot(lm.fit)
plot(hatvalues(lm.fit))
which.max(hatvalues(lm.fit))
## 375
## 375
# 3.6.3 Multiple Linear Regression
lm.fit1 <- lm(Boston$medv~Boston$lstat+Boston$age,
data = Boston)
lm.fit1
##
## Call:
## lm(formula = Boston$medv ~ Boston$lstat + Boston$age, data = Boston)
##
## Coefficients:
## (Intercept) Boston$lstat Boston$age
## 33.22276 -1.03207 0.03454
summary(lm.fit1)
##
## Call:
## lm(formula = Boston$medv ~ Boston$lstat + Boston$age, data = Boston)
##
## Residuals:
## Min 1Q Median 3Q Max
## -15.981 -3.978 -1.283 1.968 23.158
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 33.22276 0.73085 45.458 < 2e-16 ***
## Boston$lstat -1.03207 0.04819 -21.416 < 2e-16 ***
## Boston$age 0.03454 0.01223 2.826 0.00491 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 6.173 on 503 degrees of freedom
## Multiple R-squared: 0.5513, Adjusted R-squared: 0.5495
## F-statistic: 309 on 2 and 503 DF, p-value: < 2.2e-16
lm.fit2 <- lm(Boston$medv~.,data = Boston)
lm.fit2
##
## Call:
## lm(formula = Boston$medv ~ ., data = Boston)
##
## Coefficients:
## (Intercept) crim zn indus chas
## 3.646e+01 -1.080e-01 4.642e-02 2.056e-02 2.687e+00
## nox rm age dis rad
## -1.777e+01 3.810e+00 6.922e-04 -1.476e+00 3.060e-01
## tax ptratio black lstat
## -1.233e-02 -9.527e-01 9.312e-03 -5.248e-01
summary(lm.fit2)
##
## Call:
## lm(formula = Boston$medv ~ ., data = Boston)
##
## Residuals:
## Min 1Q Median 3Q Max
## -15.595 -2.730 -0.518 1.777 26.199
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 3.646e+01 5.103e+00 7.144 3.28e-12 ***
## crim -1.080e-01 3.286e-02 -3.287 0.001087 **
## zn 4.642e-02 1.373e-02 3.382 0.000778 ***
## indus 2.056e-02 6.150e-02 0.334 0.738288
## chas 2.687e+00 8.616e-01 3.118 0.001925 **
## nox -1.777e+01 3.820e+00 -4.651 4.25e-06 ***
## rm 3.810e+00 4.179e-01 9.116 < 2e-16 ***
## age 6.922e-04 1.321e-02 0.052 0.958229
## dis -1.476e+00 1.995e-01 -7.398 6.01e-13 ***
## rad 3.060e-01 6.635e-02 4.613 5.07e-06 ***
## tax -1.233e-02 3.760e-03 -3.280 0.001112 **
## ptratio -9.527e-01 1.308e-01 -7.283 1.31e-12 ***
## black 9.312e-03 2.686e-03 3.467 0.000573 ***
## lstat -5.248e-01 5.072e-02 -10.347 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 4.745 on 492 degrees of freedom
## Multiple R-squared: 0.7406, Adjusted R-squared: 0.7338
## F-statistic: 108.1 on 13 and 492 DF, p-value: < 2.2e-16
lm.fit3 <-update(lm.fit2,~.-age)
summary(lm.fit3)
##
## Call:
## lm(formula = Boston$medv ~ crim + zn + indus + chas + nox + rm +
## dis + rad + tax + ptratio + black + lstat, data = Boston)
##
## Residuals:
## Min 1Q Median 3Q Max
## -15.6054 -2.7313 -0.5188 1.7601 26.2243
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 36.436927 5.080119 7.172 2.72e-12 ***
## crim -0.108006 0.032832 -3.290 0.001075 **
## zn 0.046334 0.013613 3.404 0.000719 ***
## indus 0.020562 0.061433 0.335 0.737989
## chas 2.689026 0.859598 3.128 0.001863 **
## nox -17.713540 3.679308 -4.814 1.97e-06 ***
## rm 3.814394 0.408480 9.338 < 2e-16 ***
## dis -1.478612 0.190611 -7.757 5.03e-14 ***
## rad 0.305786 0.066089 4.627 4.75e-06 ***
## tax -0.012329 0.003755 -3.283 0.001099 **
## ptratio -0.952211 0.130294 -7.308 1.10e-12 ***
## black 0.009321 0.002678 3.481 0.000544 ***
## lstat -0.523852 0.047625 -10.999 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 4.74 on 493 degrees of freedom
## Multiple R-squared: 0.7406, Adjusted R-squared: 0.7343
## F-statistic: 117.3 on 12 and 493 DF, p-value: < 2.2e-16
# 3.6.4 Interaction Terms
summary(lm(Boston$medv~Boston$lstat*Boston$age,
data = Boston))
##
## Call:
## lm(formula = Boston$medv ~ Boston$lstat * Boston$age, data = Boston)
##
## Residuals:
## Min 1Q Median 3Q Max
## -15.806 -4.045 -1.333 2.085 27.552
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 36.0885359 1.4698355 24.553 < 2e-16 ***
## Boston$lstat -1.3921168 0.1674555 -8.313 8.78e-16 ***
## Boston$age -0.0007209 0.0198792 -0.036 0.9711
## Boston$lstat:Boston$age 0.0041560 0.0018518 2.244 0.0252 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 6.149 on 502 degrees of freedom
## Multiple R-squared: 0.5557, Adjusted R-squared: 0.5531
## F-statistic: 209.3 on 3 and 502 DF, p-value: < 2.2e-16
# 3.6.5 Non-linear Transformations
# of the Predictors
lm.fit4 <- lm(Boston$medv~Boston$lstat+I(Boston$lstat^2))
summary(lm.fit4)
##
## Call:
## lm(formula = Boston$medv ~ Boston$lstat + I(Boston$lstat^2))
##
## Residuals:
## Min 1Q Median 3Q Max
## -15.2834 -3.8313 -0.5295 2.3095 25.4148
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 42.862007 0.872084 49.15 <2e-16 ***
## Boston$lstat -2.332821 0.123803 -18.84 <2e-16 ***
## I(Boston$lstat^2) 0.043547 0.003745 11.63 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 5.524 on 503 degrees of freedom
## Multiple R-squared: 0.6407, Adjusted R-squared: 0.6393
## F-statistic: 448.5 on 2 and 503 DF, p-value: < 2.2e-16
anova(lm.fit,lm.fit4)
## Analysis of Variance Table
##
## Model 1: Boston$medv ~ Boston$lstat
## Model 2: Boston$medv ~ Boston$lstat + I(Boston$lstat^2)
## Res.Df RSS Df Sum of Sq F Pr(>F)
## 1 504 19472
## 2 503 15347 1 4125.1 135.2 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
par(mfrow=c(2,2))
plot(lm.fit4)
# using the poly() function
# poly()
# to create the polynomial within lm()
lm.fit5 <- lm(Boston$medv~poly(Boston$lstat,5))
summary(lm.fit5)
##
## Call:
## lm(formula = Boston$medv ~ poly(Boston$lstat, 5))
##
## Residuals:
## Min 1Q Median 3Q Max
## -13.5433 -3.1039 -0.7052 2.0844 27.1153
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 22.5328 0.2318 97.197 < 2e-16 ***
## poly(Boston$lstat, 5)1 -152.4595 5.2148 -29.236 < 2e-16 ***
## poly(Boston$lstat, 5)2 64.2272 5.2148 12.316 < 2e-16 ***
## poly(Boston$lstat, 5)3 -27.0511 5.2148 -5.187 3.10e-07 ***
## poly(Boston$lstat, 5)4 25.4517 5.2148 4.881 1.42e-06 ***
## poly(Boston$lstat, 5)5 -19.2524 5.2148 -3.692 0.000247 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 5.215 on 500 degrees of freedom
## Multiple R-squared: 0.6817, Adjusted R-squared: 0.6785
## F-statistic: 214.2 on 5 and 500 DF, p-value: < 2.2e-16
# Of course, we are in no way
# restricted to using polynomial transformations
# of the predictors. Here we try a
# log transformation
summary(lm(Boston$medv~log(Boston$rm),data = Boston))
##
## Call:
## lm(formula = Boston$medv ~ log(Boston$rm), data = Boston)
##
## Residuals:
## Min 1Q Median 3Q Max
## -19.487 -2.875 -0.104 2.837 39.816
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -76.488 5.028 -15.21 <2e-16 ***
## log(Boston$rm) 54.055 2.739 19.73 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 6.915 on 504 degrees of freedom
## Multiple R-squared: 0.4358, Adjusted R-squared: 0.4347
## F-statistic: 389.3 on 1 and 504 DF, p-value: < 2.2e-16
# 3.6.6 Qualitative Predictors
library(ISLR)
data(Carseats)
# The Carseats data includes qualitative predictors
# such as Shelveloc, an indicator
# of the quality of the shelving location-that is,
# the space within
# a store in which the car seat is displayed-at
# each location. The predictor
# Shelveloc takes on three possible values, Bad,
# Medium, and Good.
# Given a qualitative variable such as
# Shelveloc, R generates dummy variables
# automatically
names(Carseats)
## [1] "Sales" "CompPrice" "Income" "Advertising" "Population"
## [6] "Price" "ShelveLoc" "Age" "Education" "Urban"
## [11] "US"
str(Carseats)
## 'data.frame': 400 obs. of 11 variables:
## $ Sales : num 9.5 11.22 10.06 7.4 4.15 ...
## $ CompPrice : num 138 111 113 117 141 124 115 136 132 132 ...
## $ Income : num 73 48 35 100 64 113 105 81 110 113 ...
## $ Advertising: num 11 16 10 4 3 13 0 15 0 0 ...
## $ Population : num 276 260 269 466 340 501 45 425 108 131 ...
## $ Price : num 120 83 80 97 128 72 108 120 124 124 ...
## $ ShelveLoc : Factor w/ 3 levels "Bad","Good","Medium": 1 2 3 3 1 1 3 2 3 3 ...
## $ Age : num 42 65 59 55 38 78 71 67 76 76 ...
## $ Education : num 17 10 12 14 13 16 15 10 10 17 ...
## $ Urban : Factor w/ 2 levels "No","Yes": 2 2 2 2 2 1 2 2 1 1 ...
## $ US : Factor w/ 2 levels "No","Yes": 2 2 2 2 1 2 1 2 1 2 ...
lm.fit_1 <- lm(Sales~.+Income:Advertising+Price:Age,
data = Carseats)
summary(lm.fit_1)
##
## Call:
## lm(formula = Sales ~ . + Income:Advertising + Price:Age, data = Carseats)
##
## Residuals:
## Min 1Q Median 3Q Max
## -2.9208 -0.7503 0.0177 0.6754 3.3413
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 6.5755654 1.0087470 6.519 2.22e-10 ***
## CompPrice 0.0929371 0.0041183 22.567 < 2e-16 ***
## Income 0.0108940 0.0026044 4.183 3.57e-05 ***
## Advertising 0.0702462 0.0226091 3.107 0.002030 **
## Population 0.0001592 0.0003679 0.433 0.665330
## Price -0.1008064 0.0074399 -13.549 < 2e-16 ***
## ShelveLocGood 4.8486762 0.1528378 31.724 < 2e-16 ***
## ShelveLocMedium 1.9532620 0.1257682 15.531 < 2e-16 ***
## Age -0.0579466 0.0159506 -3.633 0.000318 ***
## Education -0.0208525 0.0196131 -1.063 0.288361
## UrbanYes 0.1401597 0.1124019 1.247 0.213171
## USYes -0.1575571 0.1489234 -1.058 0.290729
## Income:Advertising 0.0007510 0.0002784 2.698 0.007290 **
## Price:Age 0.0001068 0.0001333 0.801 0.423812
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.011 on 386 degrees of freedom
## Multiple R-squared: 0.8761, Adjusted R-squared: 0.8719
## F-statistic: 210 on 13 and 386 DF, p-value: < 2.2e-16
contrasts(Carseats$ShelveLoc)
## Good Medium
## Bad 0 0
## Good 1 0
## Medium 0 1