KM Assignment 2

library(haven)
TEDS_2016 <- read_stata("https://github.com/datageneration/home/blob/master/DataProgramming/data/TEDS_2016.dta?raw=true")

summary(TEDS_2016)
    District         Sex             Age           Edu            Arear      
 Min.   : 201   Min.   :1.000   Min.   :1.0   Min.   :1.000   Min.   :1.000  
 1st Qu.:1401   1st Qu.:1.000   1st Qu.:2.0   1st Qu.:2.000   1st Qu.:1.000  
 Median :6406   Median :1.000   Median :3.0   Median :3.000   Median :3.000  
 Mean   :4661   Mean   :1.486   Mean   :3.3   Mean   :3.334   Mean   :2.744  
 3rd Qu.:6604   3rd Qu.:2.000   3rd Qu.:5.0   3rd Qu.:5.000   3rd Qu.:4.000  
 Max.   :6806   Max.   :2.000   Max.   :5.0   Max.   :9.000   Max.   :6.000  
                                                                             
     Career         Career8          Ethnic          Party      
 Min.   :1.000   Min.   :1.000   Min.   :1.000   Min.   : 1.00  
 1st Qu.:1.000   1st Qu.:2.000   1st Qu.:1.000   1st Qu.: 5.00  
 Median :2.000   Median :4.000   Median :1.000   Median : 7.00  
 Mean   :2.683   Mean   :3.811   Mean   :1.658   Mean   :13.02  
 3rd Qu.:4.000   3rd Qu.:5.000   3rd Qu.:2.000   3rd Qu.:25.00  
 Max.   :5.000   Max.   :8.000   Max.   :9.000   Max.   :26.00  
                                                                
    PartyID          Tondu           Tondu3           nI2       
 Min.   :1.000   Min.   :1.000   Min.   :1.000   Min.   : 1.00  
 1st Qu.:2.000   1st Qu.:3.000   1st Qu.:2.000   1st Qu.: 1.00  
 Median :2.000   Median :4.000   Median :2.000   Median : 3.00  
 Mean   :4.522   Mean   :4.127   Mean   :2.667   Mean   :35.13  
 3rd Qu.:9.000   3rd Qu.:5.000   3rd Qu.:3.000   3rd Qu.:98.00  
 Max.   :9.000   Max.   :9.000   Max.   :9.000   Max.   :98.00  
                                                                
    votetsai          green         votetsai_nm      votetsai_all   
 Min.   :0.0000   Min.   :0.0000   Min.   :0.0000   Min.   :0.0000  
 1st Qu.:0.0000   1st Qu.:0.0000   1st Qu.:0.0000   1st Qu.:0.0000  
 Median :1.0000   Median :0.0000   Median :1.0000   Median :1.0000  
 Mean   :0.6265   Mean   :0.3781   Mean   :0.6265   Mean   :0.5478  
 3rd Qu.:1.0000   3rd Qu.:1.0000   3rd Qu.:1.0000   3rd Qu.:1.0000  
 Max.   :1.0000   Max.   :1.0000   Max.   :1.0000   Max.   :1.0000  
 NA's   :429                       NA's   :429      NA's   :248     
  Independence     Unification           sq           Taiwanese     
 Min.   :0.0000   Min.   :0.0000   Min.   :0.0000   Min.   :0.0000  
 1st Qu.:0.0000   1st Qu.:0.0000   1st Qu.:0.0000   1st Qu.:0.0000  
 Median :0.0000   Median :0.0000   Median :1.0000   Median :1.0000  
 Mean   :0.2888   Mean   :0.1225   Mean   :0.5172   Mean   :0.6272  
 3rd Qu.:1.0000   3rd Qu.:0.0000   3rd Qu.:1.0000   3rd Qu.:1.0000  
 Max.   :1.0000   Max.   :1.0000   Max.   :1.0000   Max.   :1.0000  
                                                                    
      edu            female        whitecollar       lowincome    
 Min.   :1.000   Min.   :0.0000   Min.   :0.0000   Min.   :1.000  
 1st Qu.:2.000   1st Qu.:0.0000   1st Qu.:0.0000   1st Qu.:4.000  
 Median :3.000   Median :0.0000   Median :1.0000   Median :5.000  
 Mean   :3.301   Mean   :0.4864   Mean   :0.5373   Mean   :4.343  
 3rd Qu.:5.000   3rd Qu.:1.0000   3rd Qu.:1.0000   3rd Qu.:5.000  
 Max.   :5.000   Max.   :1.0000   Max.   :1.0000   Max.   :5.000  
 NA's   :10                                                       
     income         income_nm           age              KMT        
 Min.   : 1.000   Min.   : 1.000   Min.   : 20.00   Min.   :0.0000  
 1st Qu.: 3.000   1st Qu.: 2.000   1st Qu.: 35.00   1st Qu.:0.0000  
 Median : 5.500   Median : 5.000   Median : 49.00   Median :0.0000  
 Mean   : 5.324   Mean   : 5.281   Mean   : 49.11   Mean   :0.2296  
 3rd Qu.: 7.000   3rd Qu.: 8.000   3rd Qu.: 61.00   3rd Qu.:0.0000  
 Max.   :10.000   Max.   :10.000   Max.   :100.00   Max.   :1.0000  
                  NA's   :330                                       
      DPP              npp             noparty            pfp         
 Min.   :0.0000   Min.   :0.00000   Min.   :0.0000   Min.   :0.00000  
 1st Qu.:0.0000   1st Qu.:0.00000   1st Qu.:0.0000   1st Qu.:0.00000  
 Median :0.0000   Median :0.00000   Median :0.0000   Median :0.00000  
 Mean   :0.3497   Mean   :0.02544   Mean   :0.3716   Mean   :0.01893  
 3rd Qu.:1.0000   3rd Qu.:0.00000   3rd Qu.:1.0000   3rd Qu.:0.00000  
 Max.   :1.0000   Max.   :1.00000   Max.   :1.0000   Max.   :1.00000  
                                                                      
     South            north        Minnan_father    Mainland_father 
 Min.   :0.0000   Min.   :0.0000   Min.   :0.0000   Min.   :0.0000  
 1st Qu.:0.0000   1st Qu.:0.0000   1st Qu.:0.0000   1st Qu.:0.0000  
 Median :0.0000   Median :0.0000   Median :1.0000   Median :0.0000  
 Mean   :0.4947   Mean   :0.4799   Mean   :0.7225   Mean   :0.1024  
 3rd Qu.:1.0000   3rd Qu.:1.0000   3rd Qu.:1.0000   3rd Qu.:0.0000  
 Max.   :1.0000   Max.   :1.0000   Max.   :1.0000   Max.   :1.0000  
                                                                    
   Econ_worse       Inequality      inequality5      econworse5   
 Min.   :0.0000   Min.   :0.0000   Min.   :1.000   Min.   :1.000  
 1st Qu.:0.0000   1st Qu.:1.0000   1st Qu.:4.000   1st Qu.:3.000  
 Median :1.0000   Median :1.0000   Median :5.000   Median :4.000  
 Mean   :0.5544   Mean   :0.9355   Mean   :4.495   Mean   :3.644  
 3rd Qu.:1.0000   3rd Qu.:1.0000   3rd Qu.:5.000   3rd Qu.:4.000  
 Max.   :1.0000   Max.   :1.0000   Max.   :5.000   Max.   :5.000  
                                                                  
 Govt_for_public     pubwelf5     Govt_dont_care     highincome    
 Min.   :0.0000   Min.   :1.000   Min.   :0.0000   Min.   :0.0000  
 1st Qu.:0.0000   1st Qu.:2.000   1st Qu.:0.0000   1st Qu.:0.0000  
 Median :0.0000   Median :3.000   Median :0.0000   Median :1.0000  
 Mean   :0.4249   Mean   :2.877   Mean   :0.4988   Mean   :0.5765  
 3rd Qu.:1.0000   3rd Qu.:4.000   3rd Qu.:1.0000   3rd Qu.:1.0000  
 Max.   :1.0000   Max.   :5.000   Max.   :1.0000   Max.   :1.0000  
                                                   NA's   :330     
    votekmt         votekmt_nm          Blue       Green      No_Party
 Min.   :0.0000   Min.   :0.0000   Min.   :0   Min.   :0   Min.   :0  
 1st Qu.:0.0000   1st Qu.:0.0000   1st Qu.:0   1st Qu.:0   1st Qu.:0  
 Median :0.0000   Median :0.0000   Median :0   Median :0   Median :0  
 Mean   :0.2053   Mean   :0.2752   Mean   :0   Mean   :0   Mean   :0  
 3rd Qu.:0.0000   3rd Qu.:1.0000   3rd Qu.:0   3rd Qu.:0   3rd Qu.:0  
 Max.   :1.0000   Max.   :1.0000   Max.   :0   Max.   :0   Max.   :0  
                  NA's   :429                                         
    voteblue       voteblue_nm       votedpp_1        votekmt_1     
 Min.   :0.0000   Min.   :0.0000   Min.   :0.0000   Min.   :0.0000  
 1st Qu.:0.0000   1st Qu.:0.0000   1st Qu.:0.0000   1st Qu.:0.0000  
 Median :0.0000   Median :0.0000   Median :1.0000   Median :0.0000  
 Mean   :0.2787   Mean   :0.3735   Mean   :0.5256   Mean   :0.2309  
 3rd Qu.:1.0000   3rd Qu.:1.0000   3rd Qu.:1.0000   3rd Qu.:0.0000  
 Max.   :1.0000   Max.   :1.0000   Max.   :1.0000   Max.   :1.0000  
                  NA's   :429      NA's   :187      NA's   :187     
mod1.lm <- lm(Tondu ~ female+DPP+age+income+edu+Taiwanese+Econ_worse, data = TEDS_2016)
summary(mod1.lm)

Call:
lm(formula = Tondu ~ female + DPP + age + income + edu + Taiwanese + 
    Econ_worse, data = TEDS_2016)

Residuals:
    Min      1Q  Median      3Q     Max 
-4.0523 -1.1411 -0.2287  0.7986  6.1354 

Coefficients:
             Estimate Std. Error t value Pr(>|t|)    
(Intercept)  4.204138   0.274188  15.333  < 2e-16 ***
female       0.368598   0.082680   4.458 8.82e-06 ***
DPP          0.121223   0.091598   1.323    0.186    
age          0.001668   0.003143   0.531    0.596    
income      -0.025558   0.015862  -1.611    0.107    
edu         -0.181096   0.036824  -4.918 9.61e-07 ***
Taiwanese    0.768943   0.091437   8.410  < 2e-16 ***
Econ_worse  -0.248545   0.083640  -2.972    0.003 ** 
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 1.667 on 1672 degrees of freedom
  (10 observations deleted due to missingness)
Multiple R-squared:  0.1074,    Adjusted R-squared:  0.1036 
F-statistic: 28.73 on 7 and 1672 DF,  p-value: < 2.2e-16
mod2.lm <- lm(Tondu ~ votetsai, data = TEDS_2016)
summary(mod2.lm)

Call:
lm(formula = Tondu ~ votetsai, data = TEDS_2016)

Residuals:
    Min      1Q  Median      3Q     Max 
-3.3785 -1.3588 -0.3588  0.6215  5.6412 

Coefficients:
            Estimate Std. Error t value Pr(>|t|)    
(Intercept)  3.35881    0.06918   48.55   <2e-16 ***
votetsai     1.01967    0.08741   11.67   <2e-16 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 1.501 on 1259 degrees of freedom
  (429 observations deleted due to missingness)
Multiple R-squared:  0.09755,   Adjusted R-squared:  0.09683 
F-statistic: 136.1 on 1 and 1259 DF,  p-value: < 2.2e-16
TEDS_2016$Tondu<-as.numeric(TEDS_2016$Tondu,labels=c("Unificationnow”,“Statusquo,unif.infuture”,“Statusquo,decidelater","Statusquoforever","Statusquo,indep.infuture","Independencenow”,“Noresponse"))

library(descr)
freq(TEDS_2016$Tondu)

TEDS_2016$Tondu 
      Frequency Percent
1            27   1.598
2           180  10.651
3           546  32.308
4           328  19.408
5           380  22.485
6           108   6.391
9           121   7.160
Total      1690 100.000
hist(TEDS_2016$Tondu)

Lab 1:

Basic Commands

Create object using the assignment operator (<-, =)

x <- c(1,3,2,5)
x
[1] 1 3 2 5
x = c(1,6,2)
x
[1] 1 6 2
y = c(1,4,3)

Using function

length(x)  # What does length() do?
[1] 3
length(y)
[1] 3

Using +, -, *, /,^ operators

x+y
[1]  2 10  5
ls() # List objects in the environment
[1] "mod1.lm"   "mod2.lm"   "TEDS_2016" "x"         "y"        
rm(x,y) # Remove objects
ls()
[1] "mod1.lm"   "mod2.lm"   "TEDS_2016"
rm(list=ls()) # Danger! What does this do?  Not recommended! *This clears the console

Matrix operations

?matrix
x=matrix(data=c(1,2,3,4), nrow=2, ncol=2) # Create a 2x2 matrix object
x
     [,1] [,2]
[1,]    1    3
[2,]    2    4
x=matrix(c(1,2,3,4),2,2)
matrix(c(1,2,3,4),2,2,byrow=TRUE) # What about byrow=F?
     [,1] [,2]
[1,]    1    2
[2,]    3    4
sqrt(x) # What does x look like?
         [,1]     [,2]
[1,] 1.000000 1.732051
[2,] 1.414214 2.000000
x^2
     [,1] [,2]
[1,]    1    9
[2,]    4   16
x=rnorm(50) # Generate a vector of 50 numbers using the rnorm() function

y=x+rnorm(50,mean=50,sd=.1) # What does rnorm(50,mean=50,sd=.1) generate?

cor(x,y) # Correlation of x and y
[1] 0.9953722
set.seed(1303) # Set the seed for Random Number Generator (RNG) to generate values that are reproducible.
rnorm(50)
 [1] -1.1439763145  1.3421293656  2.1853904757  0.5363925179  0.0631929665
 [6]  0.5022344825 -0.0004167247  0.5658198405 -0.5725226890 -1.1102250073
[11] -0.0486871234 -0.6956562176  0.8289174803  0.2066528551 -0.2356745091
[16] -0.5563104914 -0.3647543571  0.8623550343 -0.6307715354  0.3136021252
[21] -0.9314953177  0.8238676185  0.5233707021  0.7069214120  0.4202043256
[26] -0.2690521547 -1.5103172999 -0.6902124766 -0.1434719524 -1.0135274099
[31]  1.5732737361  0.0127465055  0.8726470499  0.4220661905 -0.0188157917
[36]  2.6157489689 -0.6931401748 -0.2663217810 -0.7206364412  1.3677342065
[41]  0.2640073322  0.6321868074 -1.3306509858  0.0268888182  1.0406363208
[46]  1.3120237985 -0.0300020767 -0.2500257125  0.0234144857  1.6598706557
set.seed(3) # Try different seeds?
y=rnorm(100)

Simple descriptive statistics

mean(y)
[1] 0.01103557
var(y)
[1] 0.7328675
sqrt(var(y))
[1] 0.8560768
sd(y)
[1] 0.8560768

Graphics using R Graphics (without packages)

x=rnorm(100)
y=rnorm(100)
plot(x,y, pch=20, col = "blue") # Scatterplot for two numeric variables by default

plot(x,y, pch=20, col = "blue",xlab="this is the x-axis",ylab="this is the y-axis",main="Plot of X vs Y") # Add labels

pdf("Figure01.pdf") # Save as pdf, add a path or it will be stored on the project directory
plot(x,y,pch=20, col="forestgreen") # Try different colors?
dev.off() # Close the file using the dev.off function
quartz_off_screen 
                2 
x=seq(1,10) # Same as x=c(1:10)
x
 [1]  1  2  3  4  5  6  7  8  9 10
x=1:10
x
 [1]  1  2  3  4  5  6  7  8  9 10
x=seq(-pi,pi,length=50)
y=x

Lab 2:

R Programmng Basic Commands

(Adapted from ISLR Chapter 3 Lab: Introduction to R)

Indexing Data using []

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[2,3]
[1] 10
A[c(1,3),c(2,4)]
     [,1] [,2]
[1,]    5   13
[2,]    7   15
A[1:3,2:4]
     [,1] [,2] [,3]
[1,]    5    9   13
[2,]    6   10   14
[3,]    7   11   15
A[1:2,]
     [,1] [,2] [,3] [,4]
[1,]    1    5    9   13
[2,]    2    6   10   14
A[,1:2]
     [,1] [,2]
[1,]    1    5
[2,]    2    6
[3,]    3    7
[4,]    4    8
A[1,]
[1]  1  5  9 13
A[-c(1,3),]
     [,1] [,2] [,3] [,4]
[1,]    2    6   10   14
[2,]    4    8   12   16
A[-c(1,3),-c(1,3,4)]
[1] 6 8
dim(A)
[1] 4 4

Loading Data from GitHub

Auto=read.table("https://raw.githubusercontent.com/karlho/knowledgemining/gh-pages/data/Auto.data")
# fix(Auto) # Starting the X11 R data editor
Auto=read.table("https://raw.githubusercontent.com/karlho/knowledgemining/gh-pages/data/Auto.data",header=T,na.strings="?")
# fix(Auto)
Auto=read.csv("https://raw.githubusercontent.com/karlho/knowledgemining/gh-pages/data/Auto.csv",header=T,na.strings="?")
# fix(Auto)
dim(Auto)
[1] 397   9
Auto[1:4,]
  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
                       name
1 chevrolet chevelle malibu
2         buick skylark 320
3        plymouth satellite
4             amc rebel sst
Auto=na.omit(Auto)
dim(Auto)
[1] 392   9
names(Auto)
[1] "mpg"          "cylinders"    "displacement" "horsepower"   "weight"      
[6] "acceleration" "year"         "origin"       "name"

Load data from ISLR website

Auto=read.table("https://www.statlearning.com/s/Auto.data",header=T,na.strings="?")
dim(Auto)
[1] 397   9

Additional Graphical and Numerical Summaries

# plot(cylinders, mpg)
plot(Auto$cylinders, Auto$mpg)

attach(Auto)
plot(cylinders, mpg)

cylinders=as.factor(cylinders)
plot(cylinders, mpg)

plot(cylinders, mpg, col="red")

plot(cylinders, mpg, col="red", varwidth=T)

plot(cylinders, mpg, col="red", varwidth=T,horizontal=T)

plot(cylinders, mpg, col="red", varwidth=T, xlab="cylinders", ylab="MPG")

hist(mpg)

hist(mpg,col=2)

hist(mpg,col=2,breaks=15)

#pairs(Auto)
pairs(~ mpg + displacement + horsepower + weight + acceleration, Auto)

plot(horsepower,mpg)

# identify(horsepower,mpg,name) # Interactive: point and click the dot to identify cases
summary(Auto)
      mpg          cylinders      displacement     horsepower        weight    
 Min.   : 9.00   Min.   :3.000   Min.   : 68.0   Min.   : 46.0   Min.   :1613  
 1st Qu.:17.50   1st Qu.:4.000   1st Qu.:104.0   1st Qu.: 75.0   1st Qu.:2223  
 Median :23.00   Median :4.000   Median :146.0   Median : 93.5   Median :2800  
 Mean   :23.52   Mean   :5.458   Mean   :193.5   Mean   :104.5   Mean   :2970  
 3rd Qu.:29.00   3rd Qu.:8.000   3rd Qu.:262.0   3rd Qu.:126.0   3rd Qu.:3609  
 Max.   :46.60   Max.   :8.000   Max.   :455.0   Max.   :230.0   Max.   :5140  
                                                 NA's   :5                     
  acceleration        year           origin          name          
 Min.   : 8.00   Min.   :70.00   Min.   :1.000   Length:397        
 1st Qu.:13.80   1st Qu.:73.00   1st Qu.:1.000   Class :character  
 Median :15.50   Median :76.00   Median :1.000   Mode  :character  
 Mean   :15.56   Mean   :75.99   Mean   :1.574                     
 3rd Qu.:17.10   3rd Qu.:79.00   3rd Qu.:2.000                     
 Max.   :24.80   Max.   :82.00   Max.   :3.000                     
                                                                   
summary(mpg)
   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
   9.00   17.50   23.00   23.52   29.00   46.60

Linear Regression

ptbu=c("MASS","ISLR")
install.packages(ptbu, repos='http://cran.us.r-project.org')

The downloaded binary packages are in
    /var/folders/_3/frftztsd0jg3dcmlwqcnbkc00000gn/T//RtmpOx99IX/downloaded_packages
lapply(ptbu, require, character.only = TRUE)
Loading required package: MASS
Loading required package: ISLR

Attaching package: 'ISLR'
The following object is masked _by_ '.GlobalEnv':

    Auto
[[1]]
[1] TRUE

[[2]]
[1] TRUE
library(MASS)
library(ISLR)

# Simple Linear Regression

# fix(Boston)
names(Boston)
 [1] "crim"    "zn"      "indus"   "chas"    "nox"     "rm"      "age"    
 [8] "dis"     "rad"     "tax"     "ptratio" "black"   "lstat"   "medv"   
# lm.fit=lm(medv~lstat)
attach(Boston)
lm.fit=lm(medv~lstat,data=Boston)
attach(Boston)
The following objects are masked from Boston (pos = 3):

    age, black, chas, crim, dis, indus, lstat, medv, nox, ptratio, rad,
    rm, tax, zn
lm.fit=lm(medv~lstat)
lm.fit

Call:
lm(formula = medv ~ lstat)

Coefficients:
(Intercept)        lstat  
      34.55        -0.95  
summary(lm.fit)

Call:
lm(formula = medv ~ lstat)

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 ***
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"        
coef(lm.fit)
(Intercept)       lstat 
 34.5538409  -0.9500494 
confint(lm.fit)
                2.5 %     97.5 %
(Intercept) 33.448457 35.6592247
lstat       -1.026148 -0.8739505
predict(lm.fit,data.frame(lstat=(c(5,10,15))), interval="confidence")
       fit      lwr      upr
1 29.80359 29.00741 30.59978
2 25.05335 24.47413 25.63256
3 20.30310 19.73159 20.87461
predict(lm.fit,data.frame(lstat=(c(5,10,15))), interval="prediction")
       fit       lwr      upr
1 29.80359 17.565675 42.04151
2 25.05335 12.827626 37.27907
3 20.30310  8.077742 32.52846
# What is the differnce between "conference" and "prediction" difference?

plot(lstat,medv)
abline(lm.fit)
abline(lm.fit,lwd=3)
abline(lm.fit,lwd=3,col="red")

plot(lstat,medv,col="red")

plot(lstat,medv,pch=16)

plot(lstat,medv,pch="+")

plot(1:20,1:20,pch=1:20)

par(mfrow=c(2,2))
plot(lm.fit)

plot(predict(lm.fit), residuals(lm.fit))
plot(predict(lm.fit), rstudent(lm.fit))
plot(hatvalues(lm.fit))
which.max(hatvalues(lm.fit))
375 
375

Multiple Linear Regression

lm.fit=lm(medv~lstat+age,data=Boston)
summary(lm.fit)

Call:
lm(formula = medv ~ lstat + 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 ***
lstat       -1.03207    0.04819 -21.416  < 2e-16 ***
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.fit=lm(medv~.,data=Boston)
summary(lm.fit)

Call:
lm(formula = 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
library(car)
Loading required package: carData
vif(lm.fit)
    crim       zn    indus     chas      nox       rm      age      dis 
1.792192 2.298758 3.991596 1.073995 4.393720 1.933744 3.100826 3.955945 
     rad      tax  ptratio    black    lstat 
7.484496 9.008554 1.799084 1.348521 2.941491 
lm.fit1=lm(medv~.-age,data=Boston)
summary(lm.fit1)

Call:
lm(formula = medv ~ . - age, 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
lm.fit1=update(lm.fit, ~.-age)

Non-linear Transformations of the Predictors

lm.fit2=lm(medv~lstat+I(lstat^2))
summary(lm.fit2)

Call:
lm(formula = medv ~ lstat + I(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 ***
lstat       -2.332821   0.123803  -18.84   <2e-16 ***
I(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
lm.fit=lm(medv~lstat)
anova(lm.fit,lm.fit2)
Analysis of Variance Table

Model 1: medv ~ lstat
Model 2: medv ~ lstat + I(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.fit2)

lm.fit5=lm(medv~poly(lstat,5))
summary(lm.fit5)

Call:
lm(formula = medv ~ poly(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(lstat, 5)1 -152.4595     5.2148 -29.236  < 2e-16 ***
poly(lstat, 5)2   64.2272     5.2148  12.316  < 2e-16 ***
poly(lstat, 5)3  -27.0511     5.2148  -5.187 3.10e-07 ***
poly(lstat, 5)4   25.4517     5.2148   4.881 1.42e-06 ***
poly(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
summary(lm(medv~log(rm),data=Boston))

Call:
lm(formula = medv ~ log(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(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

Qualitative Predictors

# fix(Carseats)
names(Carseats)
 [1] "Sales"       "CompPrice"   "Income"      "Advertising" "Population" 
 [6] "Price"       "ShelveLoc"   "Age"         "Education"   "Urban"      
[11] "US"         
lm.fit=lm(Sales~.+Income:Advertising+Price:Age,data=Carseats)
summary(lm.fit)

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
attach(Carseats)
contrasts(ShelveLoc)
       Good Medium
Bad       0      0
Good      1      0
Medium    0      1

Interaction Terms (including interaction and single effects)

summary(lm(medv~lstat*age,data=Boston))

Call:
lm(formula = medv ~ lstat * 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 ***
lstat       -1.3921168  0.1674555  -8.313 8.78e-16 ***
age         -0.0007209  0.0198792  -0.036   0.9711    
lstat: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