In-Class Midterm (2015)

# In-Class Midterm (2015) - MS&E 226 Small Data In-Class...

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MS&E 226 In-Class Midterm Examination “Small” Data October 20, 2015 Instructions (a) You have 80 minutes to complete the exam. (b) No aids of any kind are allowed – only pencil or pen, and paper. (c) There are 13 questions. Each will be graded “correct” or “incorrect”; not providing an answer will be counted as “incorrect.” (d) Include a signed acknowledgment of the honor code (on the other side of this page). (e) Record your answers on the other side of this page. 1

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Honor Code In taking this examination, I acknowledge and accept the Stanford University Honor Code. NAME (signed) NAME (printed) Answers PROBLEM ANSWER 1 2 3 4 5 6 7 8 9 10 11 12 13 2
PROBLEM 1. Alice uses ordinary least squares to fit a linear regression model on a dataset containing outcome data Y and covariates X (assume all numeric covariates are numeric). She shares her results with Bob. Bob wants to replicate the results, and also uses ordinary least squares to fit a linear regression model, but does so after standardizing each column of data (the outcome as well as all covariates). When they compare the sum of squared residuals, they notice that they are wildly different. This catches Alice and Bob by surprise, because they were taught that standardizing doesn’t change anything for linear regression. Why was the sum of squared residuals so different in their respective fitted models? (a) Because the intercept is not scaled. (b) Because the outcome is measured on a different scale. (c) Because they should have compared the square root of the sum of squared residuals, instead of just the sum of squared residuals. (d) One of them must have made a coding mistake, because the sum of squared residuals should have been the same. PROBLEM 2. Suppose we have data with covariates X and outcome Y , and we build a linear regression model of Y against the covariates X . Let A be the resulting R 2 value. Now suppose we add new covariates to X . However, assume these covariates are just random noise (e.g., they might be i.i.d. N (0 , 1) random variables), without any relationship to X or Y .

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