Paper 3, Section I, K

Statistical Modelling
Part II, 2016

The RR command

>boxcox(>\operatorname{boxcox}( rainfall \sim month+elnino+month:elnino)

performs a Box-Cox transform of the response at several values of the parameter λ\lambda, and produces the following plot:

We fit two linear models and obtain the Q-Q plots for each fit, which are shown below in no particular order:

Define the variable on the yy-axis in the output of boxcox, and match each Q-Q plot to one of the models.

After choosing the model fit.2, the researcher calculates Cook's distance for the ii th sample, which has high leverage, and compares it to the upper 0.010.01-point of an Fp,npF_{p, n-p} distribution, because the design matrix is of size n×pn \times p. Provide an interpretation of this comparison in terms of confidence sets for β^\hat{\beta}. Is this confidence statement exact?