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.