# Prediction interval vs. confidence interval in linear regression analysis

I know such a problem is explained many times, but I have still a problem with the concept and interpretation:

I would like to estimate export weight for 2016

• The red point is estimated point
• red lines are prediction interval
• blue lines are confidence interval

As I understand the actual export weight for 2016 is between the red lines with probability 0.95 (95% prediction interval)

and the parameter of fitted model: (here $\beta_0$ and $\beta_1$)

$$\mathit{Y}=\beta_0+\beta_1X_1+\varepsilon$$

are between both blue lines confidence interval. That means possible green lines are between both blue lines (confidence interval)

My Question:

If all possible green lines are between confidence interval, then there is not possible to have the estimated point outside the confidence interval. But we have determined, it is possible to have an estimated point between red line or prediction interval. How can I interpret it correctly

• Your interpretation "all possible green lines are between confidence interval," is not correct – Glen_b Jul 26 '16 at 11:14

$$\mathit{Y}=\beta_0+\beta_1X_1+\varepsilon$$
Where $\beta_0$ and $\beta_1$ are unknown parameters we only can estimate and $\varepsilon$ is a random variable.
The blue lines are confidence intervals for $\beta_0+\beta_1X_1$, that is, intervals for the green line, but please notice that that is not the future observation (that is just your point estimation of it). Your future observation will include an $\varepsilon$ term which will cause more variability, and the red lines account for that extra variability.