Review Jeopardy. Blue vs. Orange. Review Jeopardy
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1 Review Jeopardy Blue vs. Orange Review Jeopardy
2 Jeopardy Round Lectures 0-3 Jeopardy Round
3 $200 How could I measure how far apart (i.e. how different) two observations, y 1 and y 2, are from each other? A. Compute y 1 y 2 B. Compute y 2 y 1 C. Compute y 1 y 2 D. Compute covariance(y 1, y 2 ) E. Either (A) or (B) Jeopardy Round
4 How could I measure how far apart (i.e. how different) two observations, y 1 and y 2, are from each other? A. Compute y 1 y 2 B. Compute y 2 y 1 C. Compute y 1 y 2 D. Compute covariance(y 1, y 2 ) E. Either (A) or (B) Jeopardy Round
5 $200 What is the span of one vector in R 3? A. A plane B. A line C. The whole 3-dimensional space D. A point E. A vector Jeopardy Round
6 $200 What is the span of one vector in R 3? A. A plane B. A line C. The whole 3-dimensional space D. A point E. A vector Jeopardy Round
7 $400 What is the span of two linearly independent vectors in R 3? A. A plane B. A line C. The whole 3-dimensional space D. A point E. A vector Jeopardy Round
8 $400 What is the span of two linearly independent vectors in R 3? A. A plane B. A line C. The whole 3-dimensional space D. A point E. A vector Jeopardy Round
9 $400 For 3 vectors, x, y and z, suppose that 2x + 3y + 5z = 0 A. Then x, y and z are linearly independent B. Then x, y and z are linearly dependent C. Then x, y and z are orthogonal D. None of the above Jeopardy Round
10 $400 For 3 vectors, x, y and z, suppose that 2x + 3y + 5z = 0 A. Then x, y and z are linearly independent B. Then x, y and z are linearly dependent C. Then x, y and z are orthogonal D. None of the above Jeopardy Round
11 $600 If a collection of vectors is mutually orthogonal, then those vectors are linearly independent. A. True B. False Jeopardy Round
12 $600 If a collection of vectors is mutually orthogonal, then those vectors are linearly independent. A. True B. False Jeopardy Round
13 $800 If U is an orthogonal matrix, then: A. U T U = UU T = I B. U T is the inverse of U C. U is a covariance matrix. D. U T U = 0 E. Both (A) and (B). Jeopardy Round
14 $800 If U is an orthogonal matrix, then: A. U T U = UU T = I B. U T is the inverse of U C. U is a covariance matrix. D. U T U = 0 E. Both (A) and (B). Jeopardy Round
15 $1000 If the span of 3 vectors x, y, and z is a 2-dimensional subspace (a plane) then... A. x, y, and z are linearly dependent B. x, y, and z are linearly independent C. x, y, and z are orthogonal D. x, y, and z are all multiples of the same vector Jeopardy Round
16 $1000 If the span of 3 vectors x, y, and z is a 2-dimensional subspace (a plane) then... A. x, y, and z are linearly dependent B. x, y, and z are linearly independent C. x, y, and z are orthogonal D. x, y, and z are all multiples of the same vector Jeopardy Round
17 $1000 In order for a matrix to have eigenvalues and eigenvectors, what must be true? A. All matrices have eigenvalues and eigenvectors B. The matrix must be square C. The matrix must be orthogonal D. The matrix must be a covariance matrix Jeopardy Round
18 $1000 In order for a matrix to have eigenvalues and eigenvectors, what must be true? A. All matrices have eigenvalues and eigenvectors B. The matrix must be square C. The matrix must be orthogonal D. The matrix must be a covariance matrix Jeopardy Round
19 $1000 If I multiply a matrix A by its eigenvector x, what can I say about the result, Ax? A. The result is a unit vector B. The result is a scalar, which is called the eigenvalue C. The result is a scalar multiple of x D. The result is orthogonal Jeopardy Round
20 $1000 If I multiply a matrix A by its eigenvector x, what can I say about the result, Ax? A. The result is a unit vector B. The result is a scalar, which is called the eigenvalue C. The result is a scalar multiple of x D. The result is orthogonal Jeopardy Round
21 Double Jeopardy Round Lectures 4-7 Double Jeopardy Round
22 $400 If your data matrix has 1,000 observations on 40 variables, then how many principal components exist? A. Impossible to tell from this information B. 40,000 C. 1,000 D. 40 Double Jeopardy Round
23 $400 If your data matrix has 1,000 observations on 40 variables, then how many principal components exist? A. Impossible to tell from this information B. 40,000 C. 1,000 D. 40 Double Jeopardy Round
24 $400 The first principal component is... A. A statistic that tells you how much multicollinearity is in your data B. A scalar that tells you how much total variance is in the data C. The first column in your data matrix D. A vector that points in the direction of maximum variance in the data Double Jeopardy Round
25 $400 The first principal component is... A. A statistic that tells you how much multicollinearity is in your data B. A scalar that tells you how much total variance is in the data C. The first column in your data matrix D. A vector that points in the direction of maximum variance in the data Double Jeopardy Round
26 $800 The loadings on a principal component tell you A. The variance of each variable on that principal component B. How correlated each variable is with that principal component C. Absolutely nothing D. How much each observation weighs along that principal component Double Jeopardy Round
27 $800 The loadings on a principal component tell you A. The variance of each variable on that principal component B. How correlated each variable is with that principal component C. Absolutely nothing D. How much each observation weighs along that principal component Double Jeopardy Round
28 $1200 The principal component scores are... A. Statistics which tell you the importance of each principal component B. The coordinates of your data in the new basis of principal components C. Statistics which tell you how each variable relates to each principal component D. Relatively random Double Jeopardy Round
29 $1200 The principal component scores are... A. Statistics which tell you the importance of each principal component B. The coordinates of your data in the new basis of principal components C. Statistics which tell you how each variable relates to each principal component D. Relatively random Double Jeopardy Round
30 $1200 The eigenvalues of the covariance matrix... A. Are always orthogonal B. Add up to 1 C. Tell you how much variance exists along each principal component D. Tell you the proportion of variance explained by each principal component Double Jeopardy Round
31 $1200 The eigenvalues of the covariance matrix... A. Are always orthogonal B. Add up to 1 C. Tell you how much variance exists along each principal component D. Tell you the proportion of variance explained by each principal component Double Jeopardy Round
32 $1600 The total amount of variance in a data set is... A. The sum of all the entries in the covariance matrix B. The sum of the eigenvalues of the covariance matrix C. The sum of the variances of each variable D. Both (B) and (C) Double Jeopardy Round
33 $1600 The total amount of variance in a data set is... A. The sum of all the entries in the covariance matrix B. The sum of the eigenvalues of the covariance matrix C. The sum of the variances of each variable D. Both (B) and (C) Double Jeopardy Round
34 $1600 PCA is a special case of the Singular Value Decomposition, when your data is either centered or standardized. A. True B. False Double Jeopardy Round
35 $1600 PCA is a special case of the Singular Value Decomposition, when your data is either centered or standardized. A. True B. False Double Jeopardy Round
36 $1600 Principal Component Regression... A. Can give you meaningful beta parameters for your original variables B. Attempts to solve the problem of severe multicollinearity in predictor variables C. Is a biased regression technique and should be used only as a last resort when you cannot omit correlated variables. D. All of the above Double Jeopardy Round
37 $1600 Principal Component Regression... A. Can give you meaningful beta parameters for your original variables B. Attempts to solve the problem of severe multicollinearity in predictor variables C. Is a biased regression technique and should be used only as a last resort when you cannot omit correlated variables. D. All of the above Double Jeopardy Round
38 $1600 Principal components with eigenvalues close to zero are correlated with the intercept in a linear regression model A. True B. False Double Jeopardy Round
39 $1600 Principal components with eigenvalues close to zero are correlated with the intercept in a linear regression model A. True B. False Double Jeopardy Round
40 Final Jeopardy Category: PCA Rotations Final Jeopardy
41 Wager $2000 $3000 $4000 $5000 Final Jeopardy
42 Final Jeopardy Question What is the purpose or motivation behind the rotations of principal components in Factor Analysis? A. The original principal components were not orthogonal, so we need to adjust them B. The first principal component does not explain enough variance. By rotating, we can explain more variance. C. The loadings of the variables are difficult to interpret, by rotating we get new factors which more clearly represent combinations of original variables D. The rotation helps spread the observations out so that we can more clearly see different groups or classes in the data Final Jeopardy
43 Final Jeopardy Question What is the purpose or motivation behind the rotations of principal components in Factor Analysis? A. The original principal components were not orthogonal, so we need to adjust them B. The first principal component does not explain enough variance. By rotating, we can explain more variance. C. The loadings of the variables are difficult to interpret, by rotating we get new factors which more clearly represent combinations of original variables D. The rotation helps spread the observations out so that we can more clearly see different groups or classes in the data Final Jeopardy
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