STAT443 Study Guide - Quiz Guide: Projection Matrix, Seasonality, Identity Matrix

• School: University of Waterloo
• Department: Statistics
• Course: STAT443
• Professor: Diana Skrzydlo

Document Summary

These are some practice questions to prepare you for the midterm and the nal exam. Use the commands qqnorm() and qqline() in r and comment on the plot: consider the multiple regression model y = x + , in which the least-squares estimator of is. = (x t x) 1x t y . De ning h = x(x t x) 1x t , we can see that = x = hy . To show this, notice that e = = y = (i h)y . Now prove that the estimated residuals e = and are orthogonal (their covariance is zero). Explain why the results would be misleading: prove the bias-variance decomposition of the prediction mse for a single new observation, showing all steps: e[(ynew ynew)2] = 2 + bias( new)2 + v ar( new). 1: perform a complete residual analysis based on the following residual plots and information.