Simulation from model with β1  = 0.75

This page demonstrates the most important property of confidence intervals:

In 95% of samples, the 95% CI will include the population slope, but in 5% of samples it will not.

Click Accumulate then take about 100 samples. Approximately 95% of the resulting CIs include β1 = 0.75.

Click on any interval to see the data set that produced it.

We cannot tell whether or not our single data set is one of the 'lucky' ones.