Predicting if a student will get admission or not

In [33]:
import pandas as pd
import numpy as np
In [34]:
admission = pd.read_csv( "admission.csv" )
In [35]:
admission.head()
Out[35]:
admit gre gpa rank
0 0 380 3.61 3
1 1 660 3.67 3
2 1 800 4.00 1
3 1 640 3.19 4
4 0 520 2.93 4
In [36]:
admission.columns = ["admit", "gre", "gpa", "ranking" ]

Does the ranking of the college impact the admissions and how much

In [37]:
pd.crosstab( admission.admit, admission.ranking )
Out[37]:
ranking 1 2 3 4
admit
0 28 97 93 55
1 33 54 28 12
In [38]:
admit_by_rankings = pd.crosstab( admission.admit, admission.ranking ).apply( lambda x: x/x.sum(), axis = 0 )
In [39]:
admit_by_rankings
Out[39]:
ranking 1 2 3 4
admit
0 0.459016 0.642384 0.768595 0.820896
1 0.540984 0.357616 0.231405 0.179104
In [40]:
admit_by_rankings = pd.DataFrame( admit_by_rankings.unstack() ).reset_index()
In [41]:
admit_by_rankings
Out[41]:
ranking admit 0
0 1 0 0.459016
1 1 1 0.540984
2 2 0 0.642384
3 2 1 0.357616
4 3 0 0.768595
5 3 1 0.231405
6 4 0 0.820896
7 4 1 0.179104
In [42]:
admit_by_rankings.columns = ["ranking", "admit", "total" ]
In [43]:
import matplotlib as plt
import seaborn as sn
%matplotlib inline
In [44]:
sn.barplot( admit_by_rankings.ranking, admit_by_rankings.total, hue = admit_by_rankings.admit )
Out[44]:
<matplotlib.axes._subplots.AxesSubplot at 0x97ecdd8>

Is the mean GRE and GPA score different for student who got admitted and who did not?

In [45]:
gre_0 = admission[admission.admit == 0]["gre"]
In [46]:
sn.distplot( gre_0 )
Out[46]:
<matplotlib.axes._subplots.AxesSubplot at 0x98ae048>
In [47]:
gre_1 = admission[admission.admit == 1]["gre"]
In [ ]:
sn.distplot( gre_1 )
In [ ]:
g = sn.FacetGrid(admission, col="admit", size = 10)
g.map(sn.distplot, "gre")
In [ ]:
g = sn.FacetGrid(admission, col="admit", size = 10)
g.map(sn.distplot, "gpa")
In [51]:
sn.pairplot( admission[["gre", "gpa"]], size = 4 )
Out[51]:
<seaborn.axisgrid.PairGrid at 0xad2ab70>
In [ ]:
g = sn.FacetGrid(admission, row="ranking", size = 6)
g.map(sn.distplot, "gre")
In [53]:
sn.boxplot( "ranking", "gre", data = admission )
Out[53]:
<matplotlib.axes._subplots.AxesSubplot at 0xc8eaeb8>

Building a Classification Model

Convert the categorical variables into dummy variables

In [54]:
def create_dummies( df, colname ):
  col_dummies = pd.get_dummies(df[colname], prefix=colname)
  col_dummies.drop(col_dummies.columns[0], axis=1, inplace=True)
  df = pd.concat([df, col_dummies], axis=1)
  df.drop( colname, axis = 1, inplace = True )
  return df
In [55]:
admission_new = create_dummies( admission, "ranking" )
In [56]:
admission_new.head()
Out[56]:
admit gre gpa ranking_2 ranking_3 ranking_4
0 0 380 3.61 0 1 0
1 1 660 3.67 0 1 0
2 1 800 4.00 0 0 0
3 1 640 3.19 0 0 1
4 0 520 2.93 0 0 1
In [57]:
from sklearn.linear_model import LogisticRegression
In [58]:
logreg = LogisticRegression()
In [59]:
admission_new.columns
Out[59]:
Index(['admit', 'gre', 'gpa', 'ranking_2', 'ranking_3', 'ranking_4'], dtype='object')
In [60]:
feature_cols = ['gre', 'gpa', 'ranking_2', 'ranking_3', 'ranking_4']
In [61]:
logreg.fit( admission_new[feature_cols], admission_new.admit )
Out[61]:
LogisticRegression(C=1.0, class_weight=None, dual=False, fit_intercept=True,
        intercept_scaling=1, max_iter=100, multi_class='ovr',
        penalty='l2', random_state=None, solver='liblinear', tol=0.0001,
        verbose=0)
In [62]:
list( zip( feature_cols, logreg.coef_ ) )
Out[62]:
[('gre',
array([ 0.00181821,  0.24353836, -0.60583825, -1.1749243 , -1.37839861]))]
In [63]:
logreg.coef_
Out[63]:
array([[ 0.00181821,  0.24353836, -0.60583825, -1.1749243 , -1.37839861]])
In [64]:
logreg.intercept_
Out[64]:
array([-1.8727875])
In [65]:
admission_new["predicted_class"] = logreg.predict( admission_new[feature_cols] )
In [66]:
admission_new = pd.concat( [admission_new, pd.DataFrame( logreg.predict_proba( admission_new[feature_cols] ) )], axis = 1 )
In [67]:
admission_new.head()
Out[67]:
admit gre gpa ranking_2 ranking_3 ranking_4 predicted_class 0 1
0 0 380 3.61 0 1 0 0 0.814212 0.185788
1 1 660 3.67 0 1 0 0 0.721900 0.278100
2 1 800 4.00 0 0 0 1 0.364488 0.635512
3 1 640 3.19 0 0 1 0 0.787621 0.212379
4 0 520 2.93 0 0 1 0 0.830918 0.169082

Evaluating the model - Confusion Matrix

In [70]:
from sklearn import metrics
In [71]:
cm = metrics.confusion_matrix( admission_new.admit, admission_new.predicted_class )
In [72]:
cm
Out[72]:
array([[259,  14],
     [103,  24]])
In [73]:
sn.heatmap(cm, annot=True,  fmt='.2f' );

Accuracy Score

In [77]:
score = metrics.accuracy_score( admission_new.admit, admission_new.predicted_class )
In [79]:
score
Out[79]:
0.70750000000000002

ROC Curve

http://blog.yhathq.com/posts/roc-curves.html

In [80]:
auc_score = metrics.roc_auc_score( admission_new.admit, admission_new.predicted_class )
In [81]:
auc_score
Out[81]:
0.56884716333535223
In [82]:
fpr, tpr, _ = metrics.roc_curve( admission_new.admit, admission_new.predicted_class )
In [83]:
import matplotlib.pyplot as pyplt
pyplt.figure()
pyplt.plot( fpr, tpr, label='ROC curve (area = %0.2f)' % auc_score )
pyplt.plot([0, 1], [0, 1], 'k--')
pyplt.xlim([0.0, 1.0])
pyplt.ylim([0.0, 1.05])
pyplt.xlabel('False Positive Rate')
pyplt.ylabel('True Positive Rate')
pyplt.title('Receiver operating characteristic example')
pyplt.legend(loc="lower right")
pyplt.show()
In [91]:
print( metrics.classification_report( admission_new.admit, admission_new.predicted_class ) )

             precision    recall  f1-score   support

        0       0.72      0.95      0.82       273
        1       0.63      0.19      0.29       127

avg / total       0.69      0.71      0.65       400

Cross validating the model

In [87]:
from sklearn.cross_validation import cross_val_score
In [88]:
logreg = LogisticRegression()
X = admission_new[feature_cols]
y = admission_new.admit
scores = cross_val_score(logreg, X, y, cv=10, scoring='accuracy')
In [89]:
scores
Out[89]:
array([ 0.82926829,  0.6097561 ,  0.73170732,  0.675     ,  0.725     ,
      0.675     ,  0.7       ,  0.66666667,  0.74358974,  0.66666667])
In [90]:
scores.mean()
Out[90]:
0.70226547842401499