Asssessing slope from a single data set

Use this page to show that the randomness of the LS slope implies uncertainty about whether β1 is zero when b1 is close to zero.

Change the slope to zero then take a few samples.

The least squares slope is usually non-zero, so a single data set cannot immediately tell you whether β1 is zero.


The context of the model is the effect of a drug (mg) in lowering the heart rate of adults. The response is the reduction in heart rate (before minus after receiving the drug) in beats per minute.