Laboratorio Capítulo 3

Libraries

library (MASS)
library (ISLR)

Simple Linear Regression

fix(Boston)
names(Boston)

 [1] "crim"    "zn"      "indus"   "chas"    "nox"    
 [6] "rm"      "age"     "dis"     "rad"     "tax"    
[11] "ptratio" "black"   "lstat"   "medv"   

lm.fit<-lm(medv~lstat,data=Boston)
lm.fit

Call:
lm(formula = medv ~ lstat, data = Boston)

Coefficients:
(Intercept)        lstat  
      34.55        -0.95  

summary(lm.fit)

Call:
lm(formula = medv ~ 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 ***
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"    
 [3] "effects"       "rank"         
 [5] "fitted.values" "assign"       
 [7] "qr"            "df.residual"  
 [9] "xlevels"       "call"         
[11] "terms"         "model"        

lm.fit$coefficients

(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

plot(Boston$lstat,Boston$medv,col="blue",pch=20)
abline(lm.fit,col="red",lwd=3)

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

par(mfrow =c(1,2))
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
(Intercept) 33.22276    0.73085  45.458
lstat       -1.03207    0.04819 -21.416
age          0.03454    0.01223   2.826
            Pr(>|t|)    
(Intercept)  < 2e-16 ***
lstat        < 2e-16 ***
age          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
(Intercept)  3.646e+01  5.103e+00   7.144
crim        -1.080e-01  3.286e-02  -3.287
zn           4.642e-02  1.373e-02   3.382
indus        2.056e-02  6.150e-02   0.334
chas         2.687e+00  8.616e-01   3.118
nox         -1.777e+01  3.820e+00  -4.651
rm           3.810e+00  4.179e-01   9.116
age          6.922e-04  1.321e-02   0.052
dis         -1.476e+00  1.995e-01  -7.398
rad          3.060e-01  6.635e-02   4.613
tax         -1.233e-02  3.760e-03  -3.280
ptratio     -9.527e-01  1.308e-01  -7.283
black        9.312e-03  2.686e-03   3.467
lstat       -5.248e-01  5.072e-02 -10.347
            Pr(>|t|)    
(Intercept) 3.28e-12 ***
crim        0.001087 ** 
zn          0.000778 ***
indus       0.738288    
chas        0.001925 ** 
nox         4.25e-06 ***
rm           < 2e-16 ***
age         0.958229    
dis         6.01e-13 ***
rad         5.07e-06 ***
tax         0.001112 ** 
ptratio     1.31e-12 ***
black       0.000573 ***
lstat        < 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

summary(lm.fit)$sigma

[1] 4.745298

library (car)
vif(lm.fit)

    crim       zn    indus     chas      nox 
1.792192 2.298758 3.991596 1.073995 4.393720 
      rm      age      dis      rad      tax 
1.933744 3.100826 3.955945 7.484496 9.008554 
 ptratio    black    lstat 
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
(Intercept)  36.436927   5.080119   7.172
crim         -0.108006   0.032832  -3.290
zn            0.046334   0.013613   3.404
indus         0.020562   0.061433   0.335
chas          2.689026   0.859598   3.128
nox         -17.713540   3.679308  -4.814
rm            3.814394   0.408480   9.338
dis          -1.478612   0.190611  -7.757
rad           0.305786   0.066089   4.627
tax          -0.012329   0.003755  -3.283
ptratio      -0.952211   0.130294  -7.308
black         0.009321   0.002678   3.481
lstat        -0.523852   0.047625 -10.999
            Pr(>|t|)    
(Intercept) 2.72e-12 ***
crim        0.001075 ** 
zn          0.000719 ***
indus       0.737989    
chas        0.001863 ** 
nox         1.97e-06 ***
rm           < 2e-16 ***
dis         5.03e-14 ***
rad         4.75e-06 ***
tax         0.001099 ** 
ptratio     1.10e-12 ***
black       0.000544 ***
lstat        < 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)
summary(lm.fit1)

Call:
lm(formula = 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
(Intercept)  36.436927   5.080119   7.172
crim         -0.108006   0.032832  -3.290
zn            0.046334   0.013613   3.404
indus         0.020562   0.061433   0.335
chas          2.689026   0.859598   3.128
nox         -17.713540   3.679308  -4.814
rm            3.814394   0.408480   9.338
dis          -1.478612   0.190611  -7.757
rad           0.305786   0.066089   4.627
tax          -0.012329   0.003755  -3.283
ptratio      -0.952211   0.130294  -7.308
black         0.009321   0.002678   3.481
lstat        -0.523852   0.047625 -10.999
            Pr(>|t|)    
(Intercept) 2.72e-12 ***
crim        0.001075 ** 
zn          0.000719 ***
indus       0.737989    
chas        0.001863 ** 
nox         1.97e-06 ***
rm           < 2e-16 ***
dis         5.03e-14 ***
rad         4.75e-06 ***
tax         0.001099 ** 
ptratio     1.10e-12 ***
black       0.000544 ***
lstat        < 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

Interaction Terms

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
(Intercept) 36.0885359  1.4698355  24.553
lstat       -1.3921168  0.1674555  -8.313
age         -0.0007209  0.0198792  -0.036
lstat:age    0.0041560  0.0018518   2.244
            Pr(>|t|)    
(Intercept)  < 2e-16 ***
lstat       8.78e-16 ***
age           0.9711    
lstat:age     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

Non-Linear Transformations of predictors

lm.fit2<-lm(medv~lstat+I(lstat^2),data=Boston)
summary (lm.fit2)

Call:
lm(formula = medv ~ lstat + I(lstat^2), data = Boston)

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,data=Boston)
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),data=Boston)
summary (lm.fit5)

Call:
lm(formula = medv ~ poly(lstat, 5), data = Boston)

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
                   
(Intercept)     ***
poly(lstat, 5)1 ***
poly(lstat, 5)2 ***
poly(lstat, 5)3 ***
poly(lstat, 5)4 ***
poly(lstat, 5)5 ***
---
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"     
 [4] "Advertising" "Population"  "Price"      
 [7] "ShelveLoc"   "Age"         "Education"  
[10] "Urban"       "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
(Intercept)         6.5755654  1.0087470   6.519
CompPrice           0.0929371  0.0041183  22.567
Income              0.0108940  0.0026044   4.183
Advertising         0.0702462  0.0226091   3.107
Population          0.0001592  0.0003679   0.433
Price              -0.1008064  0.0074399 -13.549
ShelveLocGood       4.8486762  0.1528378  31.724
ShelveLocMedium     1.9532620  0.1257682  15.531
Age                -0.0579466  0.0159506  -3.633
Education          -0.0208525  0.0196131  -1.063
UrbanYes            0.1401597  0.1124019   1.247
USYes              -0.1575571  0.1489234  -1.058
Income:Advertising  0.0007510  0.0002784   2.698
Price:Age           0.0001068  0.0001333   0.801
                   Pr(>|t|)    
(Intercept)        2.22e-10 ***
CompPrice           < 2e-16 ***
Income             3.57e-05 ***
Advertising        0.002030 ** 
Population         0.665330    
Price               < 2e-16 ***
ShelveLocGood       < 2e-16 ***
ShelveLocMedium     < 2e-16 ***
Age                0.000318 ***
Education          0.288361    
UrbanYes           0.213171    
USYes              0.290729    
Income:Advertising 0.007290 ** 
Price:Age          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

LoadLibraries

Error: object 'LoadLibraries' not found

LoadLibraries=function (){
  library (ISLR)
  library (MASS)
  print (" The libraries have been loaded .")
}

LoadLibraries

function (){
  library (ISLR)
  library (MASS)
  print (" The libraries have been loaded .")
}

function (){
library (ISLR)
library (MASS)
print ("The libraries have been loaded .")
}

function (){
library (ISLR)
library (MASS)
print ("The libraries have been loaded .")
}

LoadLibraries()

[1] " The libraries have been loaded ."