Does the response depend on X?

Testing for a relationship between Y and X is equivalent to testing whether the regression line's slope, β1, is zero.

It is important to remember that a single data set can provide evidence about whether β1 = 0, but it usually does not allow a definite conclusion to be reached.

Model for the effect of a drug in reducing heart rate


The diagram below shows the same range of models, but allows us to see typical data from the models.