Exercises - Basics of Programming… With Some Data Science

Basics of R for Data Science

• Write a for loop that runs 20 iterations, each time generating and printing a single random number from a distribution of your choice (e.g., rbinom(), rnorm(), rgamma(), rpois(), rlogis()).

• Write a for loop that runs 20 iterations, each time: 1) drawing a single number from a standard normal distribution (with rnorm()); 2) if the number is negative print it, else print the string "positive".

• Create a vector of 10 random numbers from a standard normal distribution (using rnorm()), then the ifelse function to convert the vector into a character one where each element is: "neg" if the number is negative, "pos" otherwise.

• Use a for loop to address the following task: We aim 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 \(N = 30\)

  • run thousands of iterations, each time generating two independent random variables (using rnorm()) with the above characteristics;
  • for each iteration, compute the estimated correlation coefficient with cor() and store it as an number in a vector;
  • after completing the iterations, visualize the distribution of estimated correlation coefficients with hist() or any other plotting method; also, compute the median() and the 95% confidence interval using the quantile methods (i.e., with quantile() setting the argument probs=c(.025,.975)).

• Write a custom function called describe_sign() that takes a number as input and returns "negative" if the input is below zero, "zero" if it is exactly zero, or "positive" if the input 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 a vector that has n_sim elements, all filled with NA;
  • runs 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 vector;
  • returns the vector filled with simulated correlation coefficients

• Extra for advanced users: Repeat one of the previous exercise that used the for loop, but without using the for loop (i.e., employing an alternative iterative method)

• Extra for super advanced users: Repeat the above exercise where you had to define 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 the mvrnorm() function from the MASS package