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 calculated by ggplot2's geom_smooth(). (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 plogis(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?