(10 pts) Prove that I – H is the orthogonal projection onto the orthogonal complement of the col space of X. 2 Lab projects 6. (10 pts) Analyze the O-ring failure data using a linear regression. Identify any trends. Fit a model according to Y = 0 +1X, and perform analysis of this model, including examination of residuals. What stands out? Also, a link to a relevant paper is posted on the course website; this paper gives a lot of detail on the source and relevance of the data we’re modeling. Note: Challenger data can be loaded into R via the following commands: > install.packages(“alr3”) > library(alr3) > data(challeng) 7. (30 pts) Analyze the Drosophila Enhancer datasets. First, try linear regression. Is there an obvious reason to use some of the covariates and not others? Think about Fox. problem 6.9 in this problem set. Next, suggest a way to prioritize covariates for inclusion in the model. What’s the most predictive linear model you can build? Do most covariates matter or only a few? Next, try an alternative means of regression such as Support Vector Regression, LOESS, or Random Forests, or anything else you like. Is it trivial to outperform the linear model? Generate a plot that might explain why or why not. What intuition can you gather from the plot?