Summary

Once the values of the intercept and slope have been estimated, linear regression models can be used to predict the values of $y$ from $x$. In this case, we can estimate timber hardness based on its relationship with wood density. The uncertainty in the predicted values can be quantified by a prediction interval (PI). These are similar to confidence intervals, but they’re wider because they contain the inferential uncertainty about the regression line. This uncertainty is captured by the confidence interval plus the predictive uncertainty due to the scatter of points around the regression line.