First, the key terms.

Intercept
The starting value of a linear score when its inputs are zero.
Threshold
A cutoff used to convert a score or probability into a decision.

The idea, explained

A linear model adds weighted features and an intercept. In logistic regression, a sigmoid transformation keeps the output between zero and one. A threshold then converts that probability into a decision. Despite its name, logistic regression is commonly used for classification. Neither method establishes causation merely because a coefficient is large. Feature selection, correlated inputs and the population being studied matter when interpreting results.

STEP 1

Read a linear equation

In predicted minutes = 5 + 2 × kilometres, 5 is the intercept and 2 is the distance coefficient. An additional kilometre changes the prediction by 2 minutes within this simplified model. That interpretation depends on the model and measured inputs.

STEP 2

Understand the probability step

A logistic model first computes a score, then applies a sigmoid transformation to place it between zero and one. You need not calculate the sigmoid to understand the distinction: its result is a probability estimate, whereas a linear estimate has no built-in zero-to-one boundary.

STEP 3

Choose the decision separately

If estimated late-arrival probability is 0.4, a threshold of 0.5 predicts “not late.” A threshold of 0.3 predicts “late.” Neither threshold changes the underlying probability or model weights. Their suitability depends on the costs of missed and false warnings.

Follow a worked example.

A simplified linear estimate predicts trip time as 5 minutes plus 2 minutes per kilometre. A logistic model instead estimates the probability of arriving late. Choosing a 0.3 rather than 0.5 decision threshold changes how often the service flags a trip.

Walk it through, one step at a time

  1. For a 4 km trip, the linear prediction is 5 + 2 × 4 = 13 minutes.
  2. For a different logistic model, assume the output probability is 0.4. Out of 100 similar cases, calibration would concern how often the event actually occurs.
  3. Apply the chosen 0.3 warning threshold: this case is flagged. Then evaluate whether such warnings help users, rather than assuming a warning is correct because it was issued.

Where people get stuck

A probability estimate is not a guaranteed outcome, and changing a decision threshold does not retrain the model.

Now try it yourself.

Pause before opening each answer. Explain your reasoning in your own words.

1. Check the core idea

Can a linear prediction be used directly as a valid probability in every case?

Reveal the answer & reasoning

No. It may fall below zero or above one. Logistic regression uses a transformation designed to produce values in the probability range.

2. Apply what you learned

Is a logistic probability of 0.8 the same as “the event will definitely happen”?

Reveal the answer & reasoning

No. It is an estimated likelihood. Outcomes can differ, and the estimate itself can be poorly calibrated or unsuitable for the current population.