Make homework 5 public

homework/homework5/bivariate.py

@@ -0,0 +1,84 @@
+import matplotlib.pyplot as plt
+import math
+
+def linreg(X, Y):
+    assert len(X)==len(Y)
+    n = len(X)
+    EX = sum(X)
+    EY = sum(Y)
+    EX2 = sum([x * x for x in X])
+    EXY = sum([ X[i] * Y[i] for i in range(n)])
+    m = (n * EXY - EX * EY) / (n * EX2 - EX * EX)
+    b = (EY - m * EX) / float(n)
+    return (m, b)
+
+def corr(X, Y):
+    mux = sum(X)/float(len(X))
+    muy = sum(Y)/float(len(Y))
+    SUMXX = sum([(x - mux) * (x - mux) for x in X])
+    SUMYY = sum([(y - muy) * (y - muy) for y in Y])
+    SUMXY = sum([(X[i] - mux) * (Y[i] - muy) for i in range(len(X))])
+    return SUMXY/(SUMXX * SUMYY)**0.5
+
+def estimatedFit(X, m, b):
+    return [x * m + b for x in X]
+
+def bivariate(X, Y):
+    print "Linear Regression: "
+    print "Plot color: blue"
+    (m, b) = linreg(X, Y)
+    fit = estimatedFit(X, m, b)
+    r = corr(fit, Y)
+    print "M: %s" %(m)
+    print "B: %s" %(b)
+    print "R-squared: ", r*r
+    plt.plot(X, fit, "b-")
+
+    # y = (a/x)+b -> 1/X
+    print "\nInverse Regression: "
+    print "Plot color: red"
+    Xp = [1.0/float(x) for x in X]
+    (m,b) = linreg(Xp, Y)
+    fit = estimatedFit(Xp, m, b)
+    r = corr(fit, Y)
+    print "M: %s" %(m)
+    print "B: %s" %(b)
+    print "R-squared: ", r*r
+    plt.plot(X, fit, "r-")
+
+    # y = x^m + b    
+    print "\nPower Law: "
+    print "Plot color: green"
+    Xp = [math.log(x) for x in X]
+    Yp = [math.log(y) for y in Y]
+    (m,b) = linreg(Xp, Yp)
+    fit = estimatedFit(Xp, m, b)
+    r = corr(fit, Yp)
+    print "M: %s" %(m)
+    print "B: %s" %(b)
+    print "R-squared: ", r*r
+    plt.plot(X, [math.exp(y) for y in fit], "g-")
+
+    # y = a*sqrt(x)+b -> X*X
+    print "\nSquare root: "
+    print "Plot color: magenta"
+    Xp = [math.sqrt(x) for x in X]
+    (m,b) = linreg(Xp, Y)
+    fit = estimatedFit(Xp, m, b)
+    r = corr(fit, Y)
+    print "M: %s" %(m)
+    print "B: %s" %(b)
+    print "R-squared: ", r*r
+    plt.plot(X, fit, 'm-')
+
+    # y = a*log(x)+b -> e^X           
+    print "\nLogarithm: "
+    print "Plot color: cyan"
+    Xp = [math.log(x) for x in X]
+    (m,b) = linreg(Xp, Y)
+    fit = estimatedFit(Xp, m, b)
+    r = corr(fit, Y)
+    print "M: %s" %(m)
+    print "B: %s" %(b)
+    print "R-squared: ", r*r
+    plt.plot(X, fit, 'c-')

homework/homework5/diamond.py

@@ -0,0 +1,18 @@
+import numpy as np
+import matplotlib.pyplot as plt
+import bivariate
+import math
+
+carat = np.loadtxt('diamond.tab', delimiter='\t', skiprows=1,usecols=[0])
+price = np.loadtxt('diamond.tab', delimiter='\t', skiprows=1,usecols=[1])
+
+data = zip(carat, price) #sort
+data.sort()
+(carat, price) = zip(* data) # unzip
+bivariate.bivariate(carat,price)
+
+plt.plot(carat, price, 'k+')
+plt.xlabel("Carats")
+plt.ylabel("Price")
+plt.title("Price of Diamonds by Carat")
+plt.show()

homework/homework5/diamond.tab

@@ -0,0 +1,48 @@
+0.17	355
+0.16	328
+0.17	350
+0.18	325
+0.25	642
+0.16	342
+0.15	322
+0.19	485
+0.21	483
+0.15	323
+0.18	462
+0.28	823
+0.16	336
+0.2	498
+0.23	595
+0.29	860
+0.12	223
+0.26	663
+0.25	750
+0.27	720
+0.18	468
+0.16	345
+0.17	352
+0.16	332
+0.17	353
+0.18	438
+0.17	318
+0.18	419
+0.17	346
+0.15	315
+0.17	350
+0.32	918
+0.32	919
+0.15	298
+0.16	339
+0.16	338
+0.23	595
+0.23	553
+0.17	345
+0.33	945
+0.25	655
+0.35	1086
+0.18	443
+0.25	678
+0.25	675
+0.15	287
+0.26	693
+0.15	316