Exercises - Basics of Programming

Basics of Python for Data Science

First of all
import numpy as np
import matplotlib.pyplot as plt
then:

• Write a for loop that runs 20 iterations, each time generating and printing a single random number, rounded to the 3^rd decimal point, and drawn from a distribution of your choice (e.g., np.random.binomial(), np.random.normal(), np.random.gamma(), np.random.poisson(), np.random.logistic()).

• Write a for loop that runs 20 iterations, each time:

  • drawing a single number from a standard normal distribution (with np.random.normal());
  • if the number is negative print it, else print the string "positive".

• Create an array of 10 random numbers from a standard normal distribution (using np.random.normal()), then use np.where() to create a new character array where each element is: "neg" if the number is negative, "pos" otherwise.

• We want to examine the sampling variability of the correlation between two normally distributed but unrelated variables (i.e., their underlying true correlation is \(r = 0\)), when the sample size is \(N = 30\); so write a for loop that:

  • runs thousands of iterations, each time generating two independent random variables (using np.random.normal()) with \(N = 30\);
  • at each iteration, compute the estimated correlation coefficient with np.corrcoef() and store it as a number in a list or array (warning: np.corrcoeff() returns a small 2x2 matrix, so you have to extract the coefficient of interest from there before storing it);
  • after completing all the iterations, visualize the distribution of estimated correlation coefficients with plt.hist() (hint: then also call plt.show()) or any other plotting method; also, compute the np.median() and the 95% confidence interval using the quantile method (i.e., with np.quantile() setting q=[.025,.975]).

• Write a custom function called describe_sign() that takes a number as input and returns as output: "negative" if the input value is below zero, "zero" if it is exactly zero, or "positive" if it is greater than zero.

• Write a custom function called simulate_correlations() that does the following (this is a bit advanced but funny 🙂):

  • take two numeric arguments as input: N and n_sim;
  • initializes an empty array (np.empty()) that has n_sim elements, all filled with np.nan;
  • run a for loop n_sim times;
  • inside the loop, at each iteration it generates two independent normally distributed variables each with N observations, computes the correlation coefficient between them, and stores it in the appropriate position of the previously initialized array (hint: this had already been done in the exercise above);
  • return as output the array filled with simulated correlation coefficients

• Extra for advanced users: Repeat the above exercise on the simulate_correlations() custom function, but now adding a third numeric argument as input, called r, which defines the true correlation between the two normally distributed variables. To generate correlated variables, you can use np.random.multivariate_normal() (first of all, see and understand the documentation!)

• You are working with standardized test scores and you want to label each score as "low" (below −1), "average" (between −1 and +1), or "high" (above +1):

  • Generate an array of 50 standard normal scores;
  • Use np.select() to transform the scores into the above labels.