Confidence Interval and Prediction Interval Are Not The Same

Here's the difference and what makes them important.

Contrary to common belief, linear regression NEVER predicts an actual value.

Instead, it models the relationship between the input and an average related to the outcome.

Thus, there's always some uncertainty involved, and it is important to communicate it.

Confidence interval and prediction interval help us capture this uncertainty.

Confidence interval:

• tells the range of mean outcome at a given input.

• answers the question: "If we know the input, what is the uncertainty around the average value of the outcome."

Thus, a 95% confidence interval says:

• given an input, we are 95% confident that the actual mean will lie in that region.

Confidence interval and prediction interval (Image Source: Here)

Prediction interval, however:

• tells the range of possible values the outcome variable may take.

• answers the question: "If we know the input, what is the actual range of the outcome variable that we may observe."

For instance, a 95% prediction interval tells us that:

• given an input, 95% of observed values will lie in that region.

So remember...

• Confidence interval and prediction interval are NOT the same.

• They depict different uncertainties of the outcome variable.

• Confidence interval captures the range of the mean outcome around an input.

• Prediction interval captures the range of the actual values of the outcome around an input.

• Prediction interval is typically wider than confidence interval.

👉 Over to you: What does a 100% confidence interval and prediction interval will look like?

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