Statistics 305a
Practice Midterm Exam
统计考试代做 The questions carry UNEQUAL weight. Remember that the graders will favor concise, readable, well structured solutions.
Practice midterm:
Duration: 60 mins = 45 (solve) + 15 (submit) mins
Total points: 15 On real midterm:
Duration: 135 mins = 120 (solve) + 15 (submit) mins
Total points: 35
The questions carry UNEQUAL weight. Remember that the graders will favor concise, readable, well structured solutions. Books and class notes are allowed, including online. You may not communicate with anyone via any media during the exam period.
1.(3 pts) 统计考试代做
I wish to fit a linear regression model using observations (xi , yi ), i = 1, . . . , N with xi ∈ Rp and p large. I decide to use principal component regression using the first two PCs. So to this end, I center and standardize the columns of my X matrix, and compute its SVD UDV T to get the principal components, the first two columns Z of UD. I then fit my model. How do I use my model to make a prediction at a new vector x0? Be precise.
2.(2 pts) 统计考试代做
Mark which of the following linear regression methods is equivariant to scaling of the predictor variables Xj ? (This means the fit does not change, but the coefficients may).
(a) Quadratic polynomial regression
(b) Lasso regression.
(c) Principal component regression.
(d) Forward stepwise regression
where cov means covariance matrix, and for two symmetric matrices A and B, A ⊱ B means A − B is positive definite. (This is also true as long as the rank of X is bigger than 0, but no need to go there)
4.(5 pts) 统计考试代做
You have a dataset with p = 10, 000 gene expression values per subject, and a response y that is quantitative. You want to run best-subset regression, but your resources allow a maximum of 45 variables. You decide to first filter the genes, by thresholding their absolute cor-relation with y, picking the threshold to leave you with 45 genes. Now you can run best-subsets regression. Describe briefly how you will use 10-fold cross-validation to select the subset size.
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