The Question Of Order And Chaos

Data, How Are You Related?

Life goes in cycles, it seems to mess up, but it ends perfectly well-rounded. — Re: 4 circles, each delineated with squares, 1 encircling the other, 2011–10.27

To detect if 2 sets of data are correlated, we can use some statistics as decisional logic.

# this illustrates detecting data sets as +ve correlated, -ve correlated, or non-correlated.
from numpy import mean
from numpy import std
from numpy.random import randn
from numpy.random import seed
from matplotlib import pyplot
from scipy.stats import pearsonr # import the correlation function
from scipy.stats import linregress
def compute_statistics_correlation_and_plot(data1, data2):
    # summarize
    print('data1: mean=%.3f stdv=%.3f' % (mean(data1), std(data1)))
    print('data2: mean=%.3f stdv=%.3f' % (mean(data2), std(data2)))
    # calculate Pearson's correlation
    corr, _ = pearsonr(data1, data2)
    print('Pearsons correlation: %.3f' % corr)
    # plot the data
    pyplot.scatter(data1, data2)
    pyplot.title('Scatter plot of data1 vs data2')
    pyplot.xlabel('data1')
    pyplot.ylabel('data2')
    # show the plot
    pyplot.show()
    return
def compute_gradient_and_plot(data1, data2):
    # calculate linear regression
    slope, intercept, r_value, p_value, std_err = linregress(data1, data2)
    print('slope=%.3f, intercept=%.3f, r_value=%.3f' % (slope, intercept, r_value))
    # plot the data and regression line
    pyplot.scatter(data1, data2)
    pyplot.title('Scatter plot of data1 vs data2')
    pyplot.xlabel('data1')
    pyplot.ylabel('data2')
    pyplot.plot(data1, intercept + slope * data1, 'r')
    # show the plot
    pyplot.show()
    return
def generate_positive_correlated_2_data_sets(seed_initial = 1, length_data = 1000):
    seed(seed_initial)  # seed random number generator
    # prepare data
    data1 = 20 * randn(length_data) + 100
    data2 = data1 + (10 * randn(length_data) + 50)
bound_upper, bound_lower = get_upper_and_lower_bounds_of_data(data1)
    print(f"data 1 bounds…