STATS 415 001 FA 2021 Quizzes Mock midterm! Mock midterm Started: Oct 13 at 9:11pm Quiz Instruc!ons Quiz saved at 9:11pm This exam has 5 T/F ques!ons, 5 single-choice ques!ons, 3 mul!ple-choice ques!ons and 2 data analysis ques!ons. The final two data analysis ques!ons require submission of rmd files that answer all the ques!ons. 2 ptsQues!on 1 True False The larger K you choose in the K-nearest-neighbors (KNN) method, the more accurate the resul!ng classifier will become. 2 ptsQues!on 2 True False A credit card company would like to hire you to build an automa!c system that tells whether a given applicant should be issued with a credit card. This task is an unsupervised learning problem. 2 ptsQues!on 3 True False The more covariates you recruit in your linear regression model, the less training error you will get. 2 ptsQues!on 4 True False The sample median of solves a least square problem in the sense that () { } ∈[] () = ∈(−∞, ∞) ∑=1 ( − ) 2 2 ptsQues!on 5 True False The sample mean is sensi!ve to outliers. 3 ptsQues!on 6 The ordinary least squares (OLS) es!mator does not have any bias. The higher the on the training data is, the stronger generaliza!on capabitlity of the learned model has. The residuals are independent across the observa!ons. The residuals are uncorrelated across the observa!ons. Which of the following is true about linear regression? 2 3 ptsQues!on 7 It will not change It will increase by 1 It will increase by some amount, but we do not have enough informa!on to determine by how much Suppose I have a sample of 100 data points, all of them unique posi!ve numbers. If I mul!ply 10 largest values by 100, how will the sample mean change? 3 ptsQues!on 8 It is a discrimina!ve method rather than a genera!ve one in the sense that it does not involve the data genera!on mechanism. It can be applied to prac!cal data that are not exactly Gaussian. It is mo!vated by the Bayes Rule. Compared with general QDA, LDA requires fewer parameters to be es!mated. Which of the following is false about the linear discriminant analysis (LDA)? 3 ptsQues!on 9 The smaller K is, the lower the training MSE The larger K is, the more robust the resul!ng classifier is. The larger K is, the lower the tes!ng error is. The smaller K is, the more sensi!ve the resul!ng classifier is. Which of the following is false about KNN? 3 ptsQues!on 10 A sca"er plot Side-by-side boxplots of Y for each level of X Side-by-side boxplots of X for different ranges of Y Suppose you have two variables, X and Y, and are interested in visualizing their rela!onship. X is categorical with three levels, and Y is a con!nuous variable that takes values between 0 and 1. What is the most appropriate plot to make? 5 ptsQues!on 11 In a two-class classifica!on task, the feature vectors from the two classes are Gaussian and share the same covariance structure. Method (A): LDA v.s. Model (B): QDA. In a two-class classifica!on task, the feature vectors from the two classes are Gaussian and have different means. Method (A): LDA v.s. Model (B): QDA. In a classifica!on problem, the features are independent of each other. Method (A): QDA v.s. Method (B): Naive Bayes In a regression problem with a con!nuous response Y and a single covariate , the sca"er plot of and is presented as follows: Method (A): KNN v.s. Method (B): Linear regression In each of the following setups, !ck the box if Method (A) is preferred to Method (B). 5 ptsQues!on 12 (M3) is problema!c because we need to introduce extra dummy variables to express , which is discrete. In (M1), must be non-nega!ve. According to (M2), one unit increase in , given all the other predictors fixed, implies increase in . In words, one more USD expense on produc!on will improve the ra!ng by on average. The in-sample of (M3) will be smaller than that of (M1) and (M2). Suppose you are trying to predict the average ra!ng ( , a con!nuous response variable ranging from 0 to 10) of a movie based on whether the movie is a roman!c movie ( : 1 if yes and 0 otherwise), its produc!on cost ( : con!nuous, in USD) and the number of views ( : a discrete non-nega!ve variable). Consider the following three models under the fixed design setup: (M1): (M2): (M3): where . Which of the following arguments is true? 1 2 3 = + + ,0 1 1 = + + + + ,0 11 2 2 312 = + + + + + ,0 11 2 2 33 412 () = 0 3 0 2 2 2 2 5 ptsQues!on 13 The projec!on matrix is symmetric. The projec!on matrix is always full-rank and thus inver!ble. Given a design matrix , whose rows correspond to the feature vectors of observa!ons, and a response vector , which of the following arguments is true? ∈ ℝ × ∈ ℝ = ( ∈⊤ )−1⊤ ℝ× ( − = − )2 ( − = 0)100 100 ( − ) ≥ 0⊤ ≥ 0⊤ 30 ptsQues!on 14 Upload Our goal in this problem is to predict the housing price using its different features. Download and read "housing.csv" in the folder "Mock midterm datasets" using R. Submit your R markdown file to answer the following ques!ons. (1) Choose the first 10,000 observa!ons of the loaded data frame as the training data and the rest as the tes!ng data. Build a linear model on the training data by regressing the housing price on these variables: bedrooms, bathrooms, sq$_living and sq$_lot, including an intercept term. Report the coefficients you obtained. What are the training and tes!ng MSEs? (2) Add the zipcode to your linear model. Report the training and tes!ng MSEs of your new model. How many parameters are there in this new model? (Hint: Pay a"en!on to the data type of the zipcode.) Choose a File 30 ptsQues!on 15 Upload Download and read "iris.csv" in the folder "Mock midterm datasets" using R. Submit a R markdown file that answers the following ques!ons. (1) Give the sca"er plot of the features "Petal.Width" and "Petal.Length" of all the observa!ons. Use three different colors to represent the three species, and describe correpondence between the colors and species in the legend of the plot. (2) Choose the first 100 observa!ons of the loaded data frame as the training data and the rest as the tes!ng data. Apply LDA and QDA using only the features "Petal.Width" and "Petal.Length". Report the training and tes!ng predic!on accuracy of the LDA and QDA methods respec!vely. (3) Apply the K-NN method on the same training and tes!ng dataset as in (2). Give the plot of the tes!ng MSE with respect to choice of K. Choose a File Submit Quiz Ques!ons Time Running: Hide 1 Hour, 19 Minutes, 42 Seconds ? Ques!on 1 ? 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