Aravind Titanic survival Analysis

The dataset used here is TitanicSurvival dataset in which we have to predict the survivors of the titanic disaster. Below code gives us the how to Import dataset and variable types. View function is used to view tour imported dataset.

titanicsurvival

Error: object 'titanicsurvival' not found

Assigning dataset to a new variable for our analysis

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

str(my_data_titanic)

Classes ‘tbl_df’, ‘tbl’ and 'data.frame':   261 obs. of  8 variables:
 $ obs        : num  1 2 3 4 5 6 7 8 9 10 ...
 $ 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 ...
 $ 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 ...

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(my_data_titanic)

      obs       PassengerId     Survived          Pclass     
 Min.   :  1   Min.   :  1   Min.   :0.0000   Min.   :1.000  
 1st Qu.: 66   1st Qu.: 66   1st Qu.:0.0000   1st Qu.:2.000  
 Median :131   Median :131   Median :0.0000   Median :3.000  
 Mean   :131   Mean   :131   Mean   :0.3487   Mean   :2.406  
 3rd Qu.:196   3rd Qu.:196   3rd Qu.:1.0000   3rd Qu.:3.000  
 Max.   :261   Max.   :261   Max.   :1.0000   Max.   :3.000  
                                                             
     Sex                 Age            SibSp           Parch       
 Length:261         Min.   : 0.83   Min.   :0.000   Min.   :0.0000  
 Class :character   1st Qu.:19.00   1st Qu.:0.000   1st Qu.:0.0000  
 Mode  :character   Median :28.00   Median :0.000   Median :0.0000  
                    Mean   :28.61   Mean   :0.636   Mean   :0.3985  
                    3rd Qu.:37.00   3rd Qu.:1.000   3rd Qu.:0.0000  
                    Max.   :71.00   Max.   :8.000   Max.   :5.0000  
                    NA's   :51                                      

View function is used to view our dataset.

Head function gives the top 6 observations of our variables

Missing values is filled with median of that variable as we cannnot carry out analysis with those missing values.

Considering our dependent variable as a factor will help us to plot graph based on our dependent variable.

ggplot2 library is used to plot graphs in a colourful way.Dotplot is used here to check the relationship between survived and age variables.

Here we split our data into 80% for train data, 20% for test data for prediction.Library catools is used to split data randomly into 80% for training and 20% for testing.

We train our model for prediction including all variables. We cannot remove variable based on p value and we should consider AIC value for removing variables.

summary(model_titanic)

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

Deviance Residuals: 
    Min       1Q   Median       3Q      Max  
-1.9882  -0.6168  -0.3831   0.6152   2.3366  

Coefficients: (1 not defined because of singularities)
             Estimate Std. Error z value Pr(>|z|)    
(Intercept)  5.166809   1.122195   4.604 4.14e-06 ***
obs         -0.001629   0.002577  -0.632 0.527388    
PassengerId        NA         NA      NA       NA    
Pclass      -1.043573   0.270168  -3.863 0.000112 ***
Sexmale     -2.970411   0.433374  -6.854 7.17e-12 ***
Age         -0.043542   0.017889  -2.434 0.014935 *  
SibSp       -0.615172   0.236748  -2.598 0.009365 ** 
Parch        0.213787   0.230008   0.929 0.352641    
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

(Dispersion parameter for binomial family taken to be 1)

    Null deviance: 250.92  on 194  degrees of freedom
Residual deviance: 165.64  on 188  degrees of freedom
AIC: 179.64

Number of Fisher Scoring iterations: 5

We need to remove variable seperately and check model overall AIC. 3 variables are removed one by one and AIC is checked. AIC should not decrease.

summary(model_calculation_1)

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

Deviance Residuals: 
    Min       1Q   Median       3Q      Max  
-1.9692  -0.6057  -0.3642   0.6151   2.3735  

Coefficients: (1 not defined because of singularities)
             Estimate Std. Error z value Pr(>|z|)    
(Intercept)  5.198737   1.116334   4.657 3.21e-06 ***
obs         -0.001535   0.002565  -0.598 0.549611    
PassengerId        NA         NA      NA       NA    
Pclass      -1.028297   0.268861  -3.825 0.000131 ***
Sexmale     -2.991456   0.432742  -6.913 4.75e-12 ***
Age         -0.043816   0.017796  -2.462 0.013813 *  
SibSp       -0.549252   0.222571  -2.468 0.013596 *  
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

(Dispersion parameter for binomial family taken to be 1)

    Null deviance: 250.92  on 194  degrees of freedom
Residual deviance: 166.50  on 189  degrees of freedom
AIC: 178.5

Number of Fisher Scoring iterations: 5

summary(model_calculation_2)

Call:
glm(formula = Survived ~ . - obs, family = "binomial", data = train_titanic)

Deviance Residuals: 
    Min       1Q   Median       3Q      Max  
-1.9882  -0.6168  -0.3831   0.6152   2.3366  

Coefficients:
             Estimate Std. Error z value Pr(>|z|)    
(Intercept)  5.166809   1.122195   4.604 4.14e-06 ***
PassengerId -0.001629   0.002577  -0.632 0.527388    
Pclass      -1.043573   0.270168  -3.863 0.000112 ***
Sexmale     -2.970411   0.433374  -6.854 7.17e-12 ***
Age         -0.043542   0.017889  -2.434 0.014935 *  
SibSp       -0.615172   0.236748  -2.598 0.009365 ** 
Parch        0.213787   0.230008   0.929 0.352641    
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

(Dispersion parameter for binomial family taken to be 1)

    Null deviance: 250.92  on 194  degrees of freedom
Residual deviance: 165.64  on 188  degrees of freedom
AIC: 179.64

Number of Fisher Scoring iterations: 5

summary(model_calculation_3)

Call:
glm(formula = Survived ~ . - PassengerId, family = "binomial", 
    data = train_titanic)

Deviance Residuals: 
    Min       1Q   Median       3Q      Max  
-1.9882  -0.6168  -0.3831   0.6152   2.3366  

Coefficients:
             Estimate Std. Error z value Pr(>|z|)    
(Intercept)  5.166809   1.122195   4.604 4.14e-06 ***
obs         -0.001629   0.002577  -0.632 0.527388    
Pclass      -1.043573   0.270168  -3.863 0.000112 ***
Sexmale     -2.970411   0.433374  -6.854 7.17e-12 ***
Age         -0.043542   0.017889  -2.434 0.014935 *  
SibSp       -0.615172   0.236748  -2.598 0.009365 ** 
Parch        0.213787   0.230008   0.929 0.352641    
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

(Dispersion parameter for binomial family taken to be 1)

    Null deviance: 250.92  on 194  degrees of freedom
Residual deviance: 165.64  on 188  degrees of freedom
AIC: 179.64

Number of Fisher Scoring iterations: 5

After seeing AIC we remove obs variable from our model.

summary(model_final_titanic)

Call:
glm(formula = Survived ~ . - obs, family = "binomial", data = train_titanic)

Deviance Residuals: 
    Min       1Q   Median       3Q      Max  
-1.9882  -0.6168  -0.3831   0.6152   2.3366  

Coefficients:
             Estimate Std. Error z value Pr(>|z|)    
(Intercept)  5.166809   1.122195   4.604 4.14e-06 ***
PassengerId -0.001629   0.002577  -0.632 0.527388    
Pclass      -1.043573   0.270168  -3.863 0.000112 ***
Sexmale     -2.970411   0.433374  -6.854 7.17e-12 ***
Age         -0.043542   0.017889  -2.434 0.014935 *  
SibSp       -0.615172   0.236748  -2.598 0.009365 ** 
Parch        0.213787   0.230008   0.929 0.352641    
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

(Dispersion parameter for binomial family taken to be 1)

    Null deviance: 250.92  on 194  degrees of freedom
Residual deviance: 165.64  on 188  degrees of freedom
AIC: 179.64

Number of Fisher Scoring iterations: 5

Now we predict our model using test data based on our trained model.

predict_result

         1          2          3          4          5          6 
0.71076730 0.07824510 0.80886019 0.13867549 0.51004099 0.19016744 
         7          8          9         10         11         12 
0.09997748 0.68345138 0.32332508 0.09852130 0.09765669 0.75685141 
        13         14         15         16         17         18 
0.02740911 0.78383854 0.92944878 0.12008716 0.84655226 0.29951068 
        19         20         21         22         23         24 
0.07945105 0.09288400 0.66412226 0.90033888 0.08744285 0.16565174 
        25         26         27         28         29         30 
0.83912949 0.65755090 0.72059595 0.05916360 0.75185989 0.01485273 
        31         32         33         34         35         36 
0.10703554 0.23356966 0.07013690 0.30107277 0.13500569 0.73396214 
        37         38         39         40         41         42 
0.08711358 0.21498113 0.08271845 0.74719077 0.08851373 0.02949691 
        43         44         45         46         47         48 
0.14408431 0.78740737 0.18413554 0.01849268 0.47430841 0.03275988 
        49         50         51         52         53         54 
0.86872796 0.07767353 0.06034641 0.11385083 0.08923421 0.09628556 
        55         56         57         58         59         60 
0.91475826 0.12015382 0.25203262 0.25970226 0.21106102 0.05690354 
        61         62         63         64         65         66 
0.17518991 0.06662949 0.07160154 0.12358793 0.89820044 0.07052627 

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 0.66 threshold value we get 84% accuracy for prediction so our predicted model is good to use.