plot student attrition in course

student_numbers.py

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+from __future__ import division
+import math, re
+import numpy as NP
+import matplotlib.pyplot as plt
+
+summary = '''
+Preregistered: ~70,000
+Registered: 42,223
+Watched at least 1 video: 24,287
+Watched all videos: 4,030
+Got a statement of achievement: 1,466
+
+Total number of videos downloaded: 860,854
+
+# of students submitting PS's and average scores
+PS1 8425 3.8
+PS2 4527 4.1
+PS3 3721 3.1
+PS4 2994 3.7
+PS5 2529 3.2
+PS6 2005 3.6
+PS7 1911 2.9
+PS8 1654 3.8
+
+Programming Assignment statistics:
+
+PA # sub Max Avg Std
+PA1 Spamlord: Train 6042 16.00 11.61 4.34
+PA1 Spamlord: Test 5989 8.00 4.92 1.35 
+PA2 Autocorrect: Laplace Unigram Dev 3576 3.00 2.87 0.48
+PA2 Autocorrect: Laplace Unigram Test 3560 3.00 2.93 0.34
+PA2 Autocorrect: Laplace Bigram Dev 3543 3.00 2.89 0.46
+PA2 Autocorrect: Laplace Bigram Test 3532 3.00 2.83 0.49
+PA2 Autocorrect: Stupid Backoff Dev 3481 3.00 2.77 0.57
+PA2 Autocorrect: Stupid Backoff Test 3467 3.00 2.66 0.60
+PA2 Autocorrect: Custom Dev 3374 3.00 2.67 0.72 
+PA2 Autocorrect: Custom Test 3367 3.00 2.51 0.71
+PA3 Sentiment: Development All Words 3184 10.00 9.02 1.76
+PA3 Sentiment: Testing All Words 3177 10.00 9.29 1.41
+PA3 Sentiment: Dev without Stop Words 3173 10.00 8.96 1.51
+PA3 Sentiment: Test Without Stop Words 3170 10.00 9.26 1.39 
+PA4 NER: Development Set F-Score 2770 10.00 6.46 2.43
+PA4 NER: Test Set F-Score 2755 10.00 7.07 2.61
+PA5 PCFG: Development Set 2246 16.00 11.01 5.45
+PA5 PCFG: Test Set 2221 8.00 2.29 2.29
+PA6 Parsing: Development Set 1357 12.00 7.97 4.28
+PA6 Parsing: Test Set 1324 12.00 8.71 3.40
+PA 7 IR: Development Postings 1710 3.00 2.81 0.71
+PA 7 IR: Test Postings 1708 3.00 2.92 0.48
+PA 7 IR: Development Boolean Retrieval 1707 3.00 2.86 0.61 
+PA 7 IR: Test Boolean Retrieval 1706 3.00 2.90 0.53
+PA 7 IR: Development TFIDF 1703 3.00 2.72 0.85
+PA 7 IR: Test TFIDF 1700 3.00 2.79 0.73
+PA 7 IR: Dev Cosine Ranked Retrieval 1670 3.00 2.19 1.31 
+PA 7 IR: Test Cosine Ranked Retrieval 1662 3.00 2.29 1.26 
+PA8 Jeopardy: Development Wiki 1477 6.00 3.74 1.83
+PA8 Jeopardy: Testing Wiki 1449 7.00 2.97 2.02
+PA8 Jeopardy: Development Googling 1363 5.00 3.48 1.88
+PA8 Jeopardy: Testing Googling 1340 6.00 2.47 1.75
+'''
+
+# Use number of students submitting PS's (problem sets) and PA's 
+# (programming assignments) as proxies for participation. 
+# proxy for participation
+weekly_ps = [(int(m.group(1)), int(m.group(2))) for m in re.finditer(r'PS\s*(\d+)\s+(\d+)', summary)]
+weekly_pa = [(int(m.group(1)), int(m.group(2))) for m in re.finditer(r'PA\s*(\d+).+?(\d+)', summary)]
+
+# Weeks by number in summary: 1-8
+weeks = sorted(set(w for w,_ in weekly_ps) | set(w for w,_ in weekly_pa))  
+
+# ps_numbers = {week : number students completing PS for week}
+ps_numbers = dict(weekly_ps)
+
+# pa_numbers = {week : average number students completing PAs for week}
+pa_numbers = {}
+for k,v in weekly_pa:
+    pa_numbers[k] = pa_numbers.get(k,[]) + [v]
+pa_numbers = dict((k,sum(v)/len(v)) for k,v in pa_numbers.items())
+
+#
+# Data looks close enough to a power law with week 1 as an outlier
+# So compute a least squares fit of log of all weeks but 1
+#
+
+# Variable for least squares fit 
+x = NP.array(weeks)
+A = NP.vstack([x, NP.ones(len(x))]).T
+y_ps = NP.array([ps_numbers[w] for w in weeks])
+y_pa = NP.array([pa_numbers[w] for w in weeks])
+
+# Compute least squares of log(y) vs x
+# First point looks like an outlier so omit it
+m1,c1 = NP.linalg.lstsq(A[1:,:], NP.log(y_ps[1:]))[0]
+m2,c2 = NP.linalg.lstsq(A[1:,:], NP.log(y_pa[1:]))[0]
+print 'm1=%.2f, c1=%.2f, week = %.2f x prev week' % (m1, c1, NP.exp(m1))
+print 'm2=%.2f, c2=%.2f, week = %.2f x prev week' % (m2, c2, NP.exp(m1))
+
+# Plot the data and fitted lines
+# and save as attrition.png in current directory
+plt.plot(x, y_ps, 'or', label='By problem sets', markersize=10)
+plt.plot(x, y_pa, 'ob', label='By programming assignment', markersize=10)
+plt.plot(x, NP.exp(m1*x+c1), 'r', label='Best fit - problems')
+plt.plot(x, NP.exp(m2*x+c2), 'b', label='Best fit - assignments')
+plt.xlabel('Week')
+plt.ylabel('Number of students')
+plt.title('NLP-Class Attrition by Week')
+plt.legend()
+#plt.show()
+plt.savefig('attrition.png', dpi=200)
+