Likelihood & log-likelihood

Linear regression tries to optimize a "sum of squares" metric in order to find the best fit. That metric isn't applicable to logistic regression. Instead, logistic regression tries to optimize a metric called likelihood, or a related metric called log-likelihood.

The dashboard shows churn status versus time since last purchase from the churn dataset. The blue dotted line is the logistic regression prediction line. (That is, it's the "best fit" line.) The black solid line shows a prediction line calculated from the intercept and slope coefficients you specify as logistic.cdf(intercept + slope * time_since_last_purchase).

Change the intercept and slope coefficients and watch how the likelihood and log-likelihood values change.

As you get closer to the best fit line, what statement is true about likelihood and log-likelihood?