Question

So Jacques starts up his JavaScript interpreter and sets up the environment he needs to keep his journal.

var journal = [];

function addEntry(events, didITurnIntoASquirrel) {
  journal.push({
    events: events,
    squirrel: didITurnIntoASquirrel
  });
}

And then, every evening at ten—or sometimes the next morning, after climbing down from the top shelf of his bookcase—he records the day.

addEntry(["work", "touched tree", "pizza", "running",
          "television"], false);
addEntry(["work", "ice cream", "cauliflower", "lasagna",
          "touched tree", "brushed teeth"], false);
addEntry(["weekend", "cycling", "break", "peanuts",
          "beer"], true);

Once he has enough data points, he intends to compute the correlation between his squirrelification and each of the day’s events and ideally learn something useful from those correlations.

Correlation is a measure of dependence between variables (“variables” in the statistical sense, not the JavaScript sense). It is usually expressed as a coefficient that ranges from -1 to 1. Zero correlation means the variables are not related, whereas a correlation of one indicates that the two are perfectly related—if you know one, you also know the other. Negative one also means that the variables are perfectly related but that they are opposites—when one is true, the other is false.

For binary (Boolean) variables, the phi coefficient (ϕ) provides a good measure of correlation and is relatively easy to compute. To compute ϕ, we need a table n that contains the number of times the various combinations of the two variables were observed. For example, we could take the event of eating pizza and put that in a table like this:

ϕ can be computed using the following formula, where n refers to the table:

ϕ =	n11n00 - n10n01 √ n1•n0•n•1n•0

The notation n₀₁ indicates the number of measurements where the first variable (squirrelness) is false (0) and the second variable (pizza) is true (1). In this example, n₀₁ is 9.

The value n_1• refers to the sum of all measurements where the first variable is true, which is 5 in the example table. Likewise, n_•0 refers to the sum of the measurements where the second variable is false.

So for the pizza table, the part above the division line (the dividend) would be 1×76 - 4×9 = 40, and the part below it (the divisor) would be the square root of 5×85×10×80, or √340000. This comes out to ϕ ≈ 0.069, which is tiny. Eating pizza does not appear to have influence on the transformations.

This is a book about getting computers to do what you want them to do. Computers are about as common as screwdrivers today, but they contain a lot more hidden complexity and thus are harder to operate and understand. To many, they remain alien, slightly threatening things.