Finding values for parameters
Use this diagram to explain how the 3 parameters affect the linear regression model.
Drag the 3 arrows to adjust the parameters. Explain, in particular, how σ defines the spread of crosses round the regn line.
Discuss how the parameters might be set to match the crosses on an actual scatterplot — in particular, the band should include about 95% of crosses.
It is relatively easy to find suitable parameter values for the artificial data set but, when the sample size is smaller or the relationship weaker, mention that it is harder to decide on the 'best' values by eye. (The Best values button sets the parameters to least squares line and the root mean residual sum of squares as will be described later.)
The data set below shows the body and heart weights of 47 female cats. The data might be used to predict heart weight from body weight since the latter can be easily measured from live cats!