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 give the yield of Pima cotton (pounds per acre) and irrigation levels (water applied in feet per acre) in the Salt River Valley for different plots of land. Each plot was on Maricopa sandy loam soil.