How logistic regression works

Intermediate Regression in R

Richie Cotton

Data Evangelist at DataCamp

Sum of squares doesn't work

sum((y_pred - y_actual) ^ 2)

y_actual is always 0 or 1.

y_pred is between 0 and 1.

There is a better metric than sum of squares.

    y_pred * y_actual

    y_pred * y_actual + (1 - y_pred) * (1 - y_actual)

sum(y_pred * y_actual + (1 - y_pred) * (1 - y_actual))

When y_actual = 1

y_pred * 1 + (1 - y_pred) * (1 - 1) = y_pred

When y_actual = 0

y_pred * 0 + (1 - y_pred) * (1 - 0) = 1 - y_pred

Computing likelihood involves adding many very small numbers, leading to numerical error.
Log-likelihood is easier to compute.

log(y_pred) * y_actual + log(1 - y_pred) * (1 - y_actual)

Both equations give the same answer.

Maximizing log-likelihood is the same as minimizing negative log-likelihood.

-sum(log_likelihoods)

calc_neg_log_likelihood <- function(coeffs) {

  intercept <- coeffs[1]
  slope <- coeffs[2]

  # More calculation!

}

optim(
  par = ???,
  fn = ???
)

Intermediate Regression in R