Prediction vs Confidence intervals in Regression Analysis

Do you know the difference between prediction intervals and confidence intervals in regression analysis?!

Today, as part of the #DataDrivenPitfalls series, we uncover another common yet critical mistake in data science and data-driven decision-making: 𝐂𝐨𝐧𝐟𝐮𝐬𝐢𝐧𝐠 𝐏𝐫𝐞𝐝𝐢𝐜𝐭𝐢𝐨𝐧 𝐈𝐧𝐭𝐞𝐫𝐯𝐚𝐥𝐬 𝐰𝐢𝐭𝐡 𝐂𝐨𝐧𝐟𝐢𝐝𝐞𝐧𝐜𝐞 𝐈𝐧𝐭𝐞𝐫𝐯𝐚𝐥𝐬

Both types of intervals provide important but distinct information about the data and the model’s predictions. Understanding the difference is crucial for accurate data interpretation and decision-making.

𝐏𝐫𝐞𝐝𝐢𝐜𝐭𝐢𝐨𝐧 𝐈𝐧𝐭𝐞𝐫𝐯𝐚𝐥𝐬:

➡ Prediction intervals are used to estimate the range within which a single new observation is expected to fall, with a certain level of confidence.

These intervals take into account not only the uncertainty of the model’s parameters (like the mean) but also the inherent variability (or noise) in the data itself.

For example, if we use a regression model to predict house prices based on certain features, a prediction interval for a new house’s price would give us a range that, with a certain level of confidence (e.g., 95%), includes the true selling price of this house, 𝐜𝐨𝐧𝐬𝐢𝐝𝐞𝐫𝐢𝐧𝐠 𝐛𝐨𝐭𝐡 𝐭𝐡𝐞 𝐦𝐨𝐝𝐞𝐥’𝐬 𝐮𝐧𝐜𝐞𝐫𝐭𝐚𝐢𝐧𝐭𝐲 𝐚𝐧𝐝 𝐭𝐡𝐞 𝐧𝐚𝐭𝐮𝐫𝐚𝐥 𝐯𝐚𝐫𝐢𝐚𝐛𝐢𝐥𝐢𝐭𝐲 𝐨𝐟 𝐡𝐨𝐮𝐬𝐞 𝐩𝐫𝐢𝐜𝐞𝐬.

𝐂𝐨𝐧𝐟𝐢𝐝𝐞𝐧𝐜𝐞 𝐈𝐧𝐭𝐞𝐫𝐯𝐚𝐥𝐬:

➡ Confidence intervals, on the other hand, are used to estimate the range within which we expect the average outcome to fall, for a given set of conditions or inputs, with a certain level of confidence.

Unlike prediction intervals, confidence intervals do not account for the variability of individual observations; they only reflect the uncertainty in estimating the mean response.

Continuing with the house price example, a confidence interval might tell us the range within which we expect the average price of houses with certain features to lie, with a given level of confidence.

It does not, however, give us information about the variability of prices for individual houses with those features.

▶ In summary, while confidence intervals focus on the uncertainty of estimating population parameters (like the mean response), prediction intervals consider the additional variability of individual outcomes, making them generally wider than confidence intervals, as shown below.

Understanding the distinction between these two types of intervals is crucial for correctly interpreting the uncertainty in statistical estimates and predictions.

#datascience #decisionmaking