AnalyticsCal-Online/correlation_coefficient.py at master · AnalyticsCal/AnalyticsCal-Online · GitHub

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import math
from math import sqrt
import matplotlib.pyplot as plt

# Calculate Mean

def mean(values):
	return sum(values) / float(len(values))

def variance(values, mean):
        n = len(values)
        return sum([(x - mean) ** 2 for x in values]) / (n - 1)# n - 1: is used as sample data points are considered


# Calculate Covariance

# Calculate covariance between x and y
def covariance(x, mean_x, y, mean_y):
        n = len(x)
        covar = 0.0
        for i in range(len(x)):
                covar += (x[i] - mean_x) * (y[i] - mean_y)
        return covar / (n - 1)

#correlationCoefficient
def correlationCoefficient(X,Y) :
        n = len(X)
        sum_X = 0
        sum_Y = 0
        sum_XY = 0
        squareSum_X = 0
        squareSum_Y = 0

        i = 0
        while i < n :
                # sum of elements of array X.
                sum_X = sum_X + X[i]

                # sum of elements of array Y.
                sum_Y = sum_Y + Y[i]

                # sum of X[i] * Y[i].
                sum_XY = sum_XY + X[i] * Y[i]

                # sum of square of array elements.
                squareSum_X = squareSum_X + X[i] * X[i]
                squareSum_Y = squareSum_Y + Y[i] * Y[i]

                i = i + 1

        # use formula for calculating correlation coefficient.
        corr = (float)(n * sum_XY - sum_X * sum_Y)/(float)(math.sqrt((n * squareSum_X - sum_X * sum_X)* (n * squareSum_Y - sum_Y * sum_Y)))
        return corr


        """
print("number of observation: ",n)
print("mean of x: ", "%.2f"% mean_x, "mean of y: ", "%.2f"% mean_y)
print("variance of x: ", "%.2f"% var_x , "variance of y: ","%.2f"% var_y)
print("SD of x: ", "%.2f"% sqrt(var_x), "SD of y: ", "%.2f"% sqrt(var_y))
print("covariance of x & y: ", "%.2f"% covar)
print("b0: ","%.2f"% b0, "b1: ", "%.2f"% b1)
print("Best fit line:")
print("y = ""%.2f"% +(b1)+"*x+"+"%.2f"% (b0))
print('RMSE: %.3f' % (rmse))
print ('Correlation Coefficient between x & y is ','{0:.6f}'.format(correlationCoefficient(X, Y)))
plt.scatter(x, y, s=50, alpha=1)
plt.title('Scatter plot of predicted_y & y')
plt.xlabel('predicted_y')
plt.ylabel('y')
plt.show()
#===================================================================
print("number of observation: ",n)
print("mean of x: ", "%.2f"% mean_x, "mean of y: ", "%.2f"% mean_y)
print("variance of x: ", "%.2f"% (var_x/n), "variance of y: ","%.2f"% (var_y/n-1))
print("SD of x: ", "%.2f"% sqrt(var_x/n), "SD of y: ", "%.2f"% sqrt(var_y/n-1))
print("covariance of x & y: ", covar/n-1)
print("b0: ","%.2f"% b0, "b1: ", "%.2f"% b1)
print("Best fit line:")
print("y = ""%.2f"% +(b1)+"*x+"+"%.2f"% (b0))
print('RMSE: %.3f' % (rmse))
print ('Correlation Coefficient between x & y is ','{0:.6f}'.format(correlationCoefficient(X,Y)))

#====================================================================
"""

def display(data):
    dataset=data
    #dataset = [[165349.2,192261.83],[162597.7,191792.06],[153441.51,191050.39],[144372.41,182901.99],[142107.34,166187.94],[131876.9,156991.12],[134615.46,156122.51],[130298.13,155752.6],[120542.52,152211.77],[123334.88,149759.96],[101913.08,146121.95],[100671.96,144259.4],[93863.75,141585.52],[91992.39,134307.35],[119943.24,132602.65],[114523.61,129917.04],[78013.11,126992.93],[94657.16,125370.37],[91749.16,124266.9],[86419.7,122776.86],[76253.86,118474.03],[78389.47,111313.02],[73994.56,110352.25],[67532.53,108733.99],[77044.01,108552.04],[64664.71,107404.34],[75328.87,105733.54],[72107.6,105008.31],[66051.52,103282.38],[65605.48,101004.64],[61994.48,99937.59],[61136.38,97483.56],[63408.86,97427.84],[55493.95,96778.92],[46426.07,96712.8],[46014.02,96479.51],[28663.76,90708.19],[44069.95,89949.14],[20229.59,81229.06],[38558.51,81005.76],[28754.33,78239.91],[27892.92,77798.83],[23640.93,71498.49],[15505.73,69758.98],[22177.74,65200.33],[1000.23,64926.08],[1315.46,49490.75],[0,42559.73],[542.05,35673.41],[0,14681.4]]
    x = [row[0] for row in dataset]
    y = [row[1] for row in dataset]
    # Load a CSV file
    n=len(x)
    #print(y)
    mean_x=mean(x)
    mean_y=mean(y)
    var_x, var_y = variance(x, mean_x), variance(y, mean_y)
    covar = covariance(x, mean_x, y, mean_y)
    X = x
    Y = y
    n = len(X)
    r=correlationCoefficient(X,Y)
    return r