MajorCourseassig1

import pandas as pd import numpy as np import matplotlib.pyplot as plt np.random.seed(5) x = np.random.randint(10,70,10) y = np.random.randint(20,40,10) x.sort() y.sort()

x

y

def calc_mean(dataset): ''' Def : Mean is defined as the arithmetic average of a population. Formula : (sum of obesrvations)∕(No. of observations) ''' return dataset.sum()/len(dataset)

def calc_variance(dataset,mean): ''' Def : Variance is the degree of variation∕spread in the dataset. Formula : 1) Σ((X - X_mean)^2) ∕ n ''' squared_diff = np.square(dataset-mean) return calc_mean(squared_diff)

def calc_SD(variance): ''' Def : 1) Standard deviation is the amount of deviation of points around the mean. 2) Variation but in terms of the actual dataset. Formula : √(variance) ''' return np.sqrt(variance)

def calc_covariance(dataset1,dataset2): ''' Def : Covariance measures the relationship trend between two sets of data. Formula : 1) Σ((X - X_mean)*(Y - Y_mean)) ∕ n ''' mean1 = calc_mean(dataset1) mean2 = calc_mean(dataset2) return np.sum(np.multiply(dataset1-mean1,dataset2-mean2))/len(dataset1)

def calc_correlation(dataset1,dataset2): ''' Def : Covariance measures the relationship trend between two sets of data. Formula : 1) Σ((X - X_mean)*(Y - Y_mean)) ∕ √(Σ(X - X_mean)^2*Σ(Y - Y_mean)^2) ''' mean1 = calc_mean(dataset1) mean2 = calc_mean(dataset2) num = np.sum(np.multiply(dataset1-mean1,dataset2-mean2)) de = np.multiply(np.sum(np.square(dataset1-mean1)),np.sum(np.square(dataset2-mean2))) return num/np.sqrt(de)

def calc_SE(dataset,sd): ''' Def : The standard error is a statistical term that easures the accuracy with which a sample distribution represents a population by using standard deviation. Formula : Standard_deviation ∕ √(n) ''' return sd/np.sqrt(len(dataset))

mean = calc_mean(x) mean2 = calc_mean(y) variance = calc_variance(x,mean) S_D = calc_SD(variance) covariance = calc_covariance(x,y) correlation = calc_correlation(x,y) S_E = calc_SE(x,S_D) print(mean,mean2,variance,S_D,covariance,correlation,S_E)

plt.plot(x,"mo:",label="dataset 1") plt.plot(y,"go:",label = "dataset 2") plt.legend(loc="upper left")

plt.plot(x,"mo:",label="Dataset 1") plt.axhline(mean,color='b',marker= 'o', linestyle=':',label="Mean") plt.legend(loc="upper left")

plt.plot(y,"ro:",label="Dataset 2") plt.axhline(mean2,color='g',marker= 'o', linestyle=':',label="Mean") plt.legend(loc="upper left")

corr = np.correlate(x, y, "same") plt.plot(list(corr),"go:",label = "Correlation")

plt.plot(x,"mo:",label="Dataset 1") plt.axhline(mean,color='g',marker= 'o', linestyle=':',label="Mean") plt.axhline(variance,color='b',marker= 'o', linestyle=':',label="Variance") plt.legend(loc="upper left")

plt.plot(y,"ro:",label="Dataset 2") plt.plot(x,"go:",label="Daraset 1") plt.axhline(covariance,color='b',marker= 'o', linestyle=':',label="covariance")