Logistic regression on titanic dataset

Importing our dataset from excel.

We assign a new variable for our dataset.

Structure(str) explains us the about variables whether they are numeric or character.

str(etit)

Classes ‘tbl_df’, ‘tbl’ and 'data.frame':   891 obs. of  12 variables:
 $ PassengerId: num  1 2 3 4 5 6 7 8 9 10 ...
 $ Survived   : num  0 1 1 1 0 0 0 0 1 1 ...
 $ Pclass     : num  3 1 3 1 3 3 1 3 3 2 ...
 $ Name       : chr  "Braund, Mr. Owen Harris" "Cumings, Mrs. John Bradley (Florence Briggs Thayer)" "Heikkinen, Miss. Laina" "Futrelle, Mrs. Jacques Heath (Lily May Peel)" ...
 $ Sex        : chr  "male" "female" "female" "female" ...
 $ Age        : num  22 38 26 35 35 NA 54 2 27 14 ...
 $ SibSp      : num  1 1 0 1 0 0 0 3 0 1 ...
 $ Parch      : num  0 0 0 0 0 0 0 1 2 0 ...
 $ Ticket     : chr  "A/5 21171" "PC 17599" "STON/O2. 3101282" "113803" ...
 $ Fare       : num  7.25 71.28 7.92 53.1 8.05 ...
 $ Cabin      : chr  NA "C85" NA "C123" ...
 $ Embarked   : chr  "S" "C" "S" "S" ...

Summary of the dataset gives us the minimum value,maximum value, quartile values,mean,median. This gives us the basic understanding of our dataset.

summary(etit)

  PassengerId       Survived          Pclass          Name               Sex           
 Min.   :  1.0   Min.   :0.0000   Min.   :1.000   Length:891         Length:891        
 1st Qu.:223.5   1st Qu.:0.0000   1st Qu.:2.000   Class :character   Class :character  
 Median :446.0   Median :0.0000   Median :3.000   Mode  :character   Mode  :character  
 Mean   :446.0   Mean   :0.3838   Mean   :2.309                                        
 3rd Qu.:668.5   3rd Qu.:1.0000   3rd Qu.:3.000                                        
 Max.   :891.0   Max.   :1.0000   Max.   :3.000                                        
                                                                                       
      Age            SibSp           Parch           Ticket               Fare       
 Min.   : 0.42   Min.   :0.000   Min.   :0.0000   Length:891         Min.   :  0.00  
 1st Qu.:20.12   1st Qu.:0.000   1st Qu.:0.0000   Class :character   1st Qu.:  7.91  
 Median :28.00   Median :0.000   Median :0.0000   Mode  :character   Median : 14.45  
 Mean   :29.70   Mean   :0.523   Mean   :0.3816                      Mean   : 32.20  
 3rd Qu.:38.00   3rd Qu.:1.000   3rd Qu.:0.0000                      3rd Qu.: 31.00  
 Max.   :80.00   Max.   :8.000   Max.   :6.0000                      Max.   :512.33  
 NA's   :177                                                                         
    Cabin             Embarked        
 Length:891         Length:891        
 Class :character   Class :character  
 Mode  :character   Mode  :character  
                                      
                                      
                                      
                                      

Head function gives the top 6 observations of our variables.

Now we check the na values columnwise.

colSums(is.na(etit))

PassengerId    Survived      Pclass        Name         Sex         Age       SibSp 
          0           0           0           0           0         177           0 
      Parch      Ticket        Fare       Cabin    Embarked 
          0           0           0         687           2 

We remove the variables PassengerId ,Name, Ticket,cabin from our dataset

Now we view our dataset.

we check the na values and omit it from our dataset

colSums(is.na(etit))

Survived   Pclass      Sex      Age    SibSp    Parch     Fare Embarked 
       0        0        0        0        0        0        0        0 

we have to factorise our character variable for further analysis.

Now we check the structure and we see that all variables are num or factor.

str(etit)

Classes ‘tbl_df’, ‘tbl’ and 'data.frame':   712 obs. of  8 variables:
 $ Survived: Factor w/ 2 levels "0","1": 1 2 2 2 1 1 1 2 2 2 ...
 $ Pclass  : num  3 1 3 1 3 1 3 3 2 3 ...
 $ Sex     : Factor w/ 2 levels "0","1": 2 1 1 1 2 2 2 1 1 1 ...
 $ Age     : num  22 38 26 35 35 54 2 27 14 4 ...
 $ SibSp   : num  1 1 0 1 0 0 3 0 1 1 ...
 $ Parch   : num  0 0 0 0 0 0 1 2 0 1 ...
 $ Fare    : num  7.25 71.28 7.92 53.1 8.05 ...
 $ Embarked: Factor w/ 2 levels "0","1": 2 1 2 2 2 2 2 2 1 2 ...
 - attr(*, "na.action")= 'omit' Named int  6 18 20 27 29 30 32 33 37 43 ...
  ..- attr(*, "names")= chr  "6" "18" "20" "27" ...

This dotplot shows the survived rate in different age.

We plot how many count in passenger class.

This plot shows how many survived in male and female.

We see the distribution of ages of passengers

We see the survival rate with age and sex.

We split the data into 80% train data and 20% test data.

split_etit

[1]  TRUE FALSE FALSE  TRUE  TRUE  TRUE  TRUE  TRUE

Spliting our Training data.

Splitting our test data.

Forming our model.

summary(model_etit)

Call:
glm(formula = Survived ~ ., family = "binomial", data = train_etit)

Deviance Residuals: 
    Min       1Q   Median       3Q      Max  
-2.6684  -0.7069  -0.3881   0.6738   2.4250  

Coefficients:
             Estimate Std. Error z value Pr(>|z|)    
(Intercept)  5.429803   0.724821   7.491 6.82e-14 ***
Pclass      -1.238310   0.189149  -6.547 5.88e-11 ***
Sex1        -2.431730   0.246964  -9.846  < 2e-16 ***
Age         -0.042573   0.009435  -4.512 6.42e-06 ***
SibSp       -0.451719   0.149039  -3.031  0.00244 ** 
Parch       -0.019863   0.135369  -0.147  0.88334    
Fare         0.001182   0.003054   0.387  0.69867    
Embarked1   -0.262844   0.276103  -0.952  0.34111    
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

(Dispersion parameter for binomial family taken to be 1)

    Null deviance: 716.62  on 533  degrees of freedom
Residual deviance: 488.65  on 526  degrees of freedom
AIC: 504.65

Number of Fisher Scoring iterations: 5

We remove our variables whose p values are greater.

summary(final_model)

Call:
glm(formula = Survived ~ . - Parch - Fare - Embarked, family = "binomial", 
    data = train_etit)

Deviance Residuals: 
    Min       1Q   Median       3Q      Max  
-2.6866  -0.6889  -0.3861   0.6593   2.4198  

Coefficients:
             Estimate Std. Error z value Pr(>|z|)    
(Intercept)  5.423446   0.629048   8.622  < 2e-16 ***
Pclass      -1.301043   0.163682  -7.949 1.89e-15 ***
Sex1        -2.445973   0.241339 -10.135  < 2e-16 ***
Age         -0.043269   0.009416  -4.595 4.32e-06 ***
SibSp       -0.454408   0.141757  -3.206  0.00135 ** 
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

(Dispersion parameter for binomial family taken to be 1)

    Null deviance: 716.62  on 533  degrees of freedom
Residual deviance: 489.91  on 529  degrees of freedom
AIC: 499.91

Number of Fisher Scoring iterations: 5

We predict our model.

predict_result

         1          2          3          4          5          6          7          8 
0.88326901 0.59756114 0.70947426 0.83379670 0.24249631 0.25053284 0.07724415 0.50261957 
         9         10         11         12         13         14         15         16 
0.90353584 0.66778840 0.87132253 0.10350865 0.14832816 0.26252322 0.11842914 0.58406267 
        17         18         19         20         21         22         23         24 
0.11181104 0.85370771 0.19849970 0.66401399 0.10553352 0.64831948 0.13772528 0.01841237 
        25         26         27         28         29         30         31         32 
0.34071313 0.13018811 0.33040634 0.34982489 0.14832816 0.40048084 0.93796816 0.03465286 
        33         34         35         36         37         38         39         40 
0.11398571 0.15959624 0.73548657 0.13772528 0.35969258 0.79367809 0.44798160 0.90190295 
        41         42         43         44         45         46         47         48 
0.15387784 0.80748947 0.13266682 0.28440911 0.31154919 0.04179059 0.10151821 0.10178857 
        49         50         51         52         53         54         55         56 
0.29329685 0.13266682 0.45291416 0.26770984 0.05349962 0.26347448 0.11842914 0.74025898 
        57         58         59         60         61         62         63         64 
0.10553352 0.16548559 0.95245648 0.94510514 0.14832816 0.76534564 0.10553352 0.12569121 
        65         66         67         68         69         70         71         72 
0.10968825 0.82102075 0.42743405 0.50804746 0.84822063 0.30234498 0.12776661 0.11618081 
        73         74         75         76         77         78         79         80 
0.39488945 0.08016667 0.67359786 0.50682080 0.09027544 0.89600153 0.04538981 0.93540236 
        81         82         83         84         85         86         87         88 
0.06829611 0.11398571 0.13772528 0.90379357 0.10151821 0.46365579 0.15959624 0.28060784 
        89         90         91         92         93         94         95         96 
0.14294483 0.07857999 0.16291192 0.59347457 0.41162978 0.15426369 0.63839183 0.17506016 
        97         98         99        100        101        102        103        104 
0.53501425 0.89600153 0.13772528 0.79107992 0.60901470 0.80114568 0.41162978 0.79416247 
       105        106        107        108        109        110        111        112 
0.65878634 0.06829611 0.94397604 0.95970801 0.82416631 0.05689586 0.83076570 0.87873321 
       113        114        115        116        117        118        119        120 
0.09027544 0.09051887 0.09027544 0.78333656 0.13266682 0.08016667 0.70559362 0.05575022 
       121        122        123        124        125        126        127        128 
0.34941829 0.08016667 0.35542125 0.09574250 0.14367177 0.04179059 0.14294483 0.95622531 
       129        130        131        132        133        134        135        136 
0.88518875 0.13772528 0.06559370 0.41162978 0.47020289 0.06577539 0.62437412 0.14294483 
       137        138        139        140        141        142        143        144 
0.96992027 0.47020289 0.06048488 0.94730726 0.46483689 0.95970801 0.83930780 0.08678434 
       145        146        147        148        149        150        151        152 
0.53992822 0.23852992 0.26677993 0.54041187 0.82102075 0.59866436 0.47302335 0.10553352 
       153        154        155        156        157        158        159        160 
0.16548559 0.81172462 0.15387784 0.78650253 0.67731693 0.04354479 0.54462256 0.09763900 
       161        162        163        164        165        166        167        168 
0.09389254 0.49723083 0.36425772 0.09574939 0.50804746 0.58711316 0.87873321 0.13772528 
       169        170        171        172        173        174        175        176 
0.06048488 0.08016667 0.67731693 0.84824111 0.73185326 0.76828961 0.76049752 0.70501132 
       177        178 
0.30234498 0.11842914 

we form a table to see our accuracy.

table(actual=test_etit$Survived,predicted=predict_result>0.64)

      predicted
actual FALSE TRUE
     0    99    2
     1    26   51

we check our accuaracy for our model.

my_accu

[1] 0.8426966

After our prediction we need check our accuracy of our prediction. library ROCR is used to plot out actual value and predicted value to test our perfomance. From our ROCR graph we can find out our threshold value for our accuracy prediction. Here for 0.64 threshold value we get 84% accuracy for prediction so our predicted model is good to use.