Exam II Spring 2021

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University of Illinois, Urbana Champaign *

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432

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Statistics

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Jan 9, 2024

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pdf

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STAT 432 , Spring 2021 Name (Print): Midterm II , 05/04/2021 Net ID (Print): Time Limit: 9:30AM - 11AM This exam contains 6 pages (including this cover page) and 5 problems. Please read the following descriptions and requirements carefully. • You do not need to submit a hard copy of this exam. Instead, write all of your answers (clearly labeled) on a single file (MS word or txt) and submit it to Compass2g. Make sure to also write your name and NetID in the file. Your file should look like the following: Name: Ruoqing Zhu NetID: rqzhu Q1: ABC Q2: C Q3: BD ... • There are 20 questions. Each question worth 5 points. All questions may have multiple correct answers or even no correct answers. For each wrongly selected item (cor- rect but not selected, or incorrect but selected), you lose one point. For example, if the correct answer is AD, and your answer is AC, then you will lose two points, for not selecting D and wrongly selecting C. • This is an open-book exam and you can use your class notes, homework, calculator, PC, etc. or even google search. • You are NOT allowed to discuss the content of this exam to anyone else (except the instructor) until the end of May 4th. This includes posting any related questions on online discussion forums or social media during and after the exam. A violation of this policy will lead to an immediate F as your final score of this course! Section Points Score 1 20 2 20 3 25 4 25 5 10 Total: 100
STAT 432 Midterm II - Page 2 of 6 05/04/2021 1. Classifications (i) (5 points) Which of the following is true regarding linear and quadratic discriminate anal- ysis A. They both assume normal distributions B. They are based on the Bayes theorem C. LDA assumes all covaraince matrix to be the same D. LDA give a linear decision rule, which is the same as Logistic regression (ii) (5 points) Which of the following is true regrading a logistic regression A. If we need to make a hard classification rule based on the logistic regression, it would be based on a linear function of X B. Based on a logistic regression, if β 1 = 0 . 1 then for each unit increase of X 1 , the probability of Y being 1 will increase by 0.1. C. Logistic regression can be solved using gradient descent D. Logistic regression can be solved using coordinate descent (iii) (5 points) ROC and AUC A. ROC curve is a more sensible measure when one of the class labels dominates B. ROC curve is a more sensible measure when class proportions are similar C. AUC is a summary of the ROC curve D. ROC curve cannot be applied to a hard classification rule (iv) (5 points) Which of the following choices will affect the bias-variance trade-off (or the complexity) of the model A. Choosing LDA vs QDA B. Add a Lasso penalty on logistic regression C. Add a Ridge penalty on logistic regression D. Add a diagonal matrix to the covariance matrix in QDA
STAT 432 Midterm II - Page 3 of 6 05/04/2021 2. Splines (i) (5 points) The following R code is an example of l m f i t < - lm (Y ˜ s p l i n e s : : bs (X, degree = 2 , knots = c ( 1 , 2 , 3 ) ) ) A. Linear spline B. Piecewise linear C. Quadratic spline D. Piecewise quadratic (ii) (5 points) A researcher is fitting a univariate regression using cubic spline model with 3 knots. How many degrees of freedom this model has? A. 4 B. 5 C. 6 D. 7 (iii) (5 points) The main advantage of natural cubic spline compared with cubic spline is A. More flexible B. Easier to compute C. Less overfitting at the boundary D. Less overfitting at the interior (iv) (5 points) The main steps of fitting a multi-variate spline model involves A. Creating the spline basis and fitting a kernel regression B. Creating the spline basis and fitting a linear regression C. Creating the neighboring weights and fitting a weighted linear regression D. Creating the neighboring weights and fitting a weighted kernel regression
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