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DSC 324 Midterm
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Questions in this quiz (40)
1Matrix multiplication can be used for which of the following operations on tables of data:
- Aa) Computing the table's covariance matrix
- Bb) Adding purchases of stock to a table of stock portfolios
- Cc) Computing ordinary least-squares regression
- Dd) a and c
- Ee) All of these
2When conducting automatic selection of variables in a regression:
- Aa) Forward selection will give you the most important predictors because it starts with an empty model
- Bb) Backwards elimination/selection will produce a more complicated model
- Cc) It is often helpful to try several methods to see if they reach consensus on the model
- Dd) a and c
- Ee) a and b
3Naomi is attempting to model the dependence of overall sales for her company's management based on fifty variables that they have collected on advertising and product quality. One of her goals is model parsimony. Which of the following may be one reason for this?
- Aa) A model with fewer predictors will more accurately predict future sales performance
- Bb) A model with more variables will be more convincing to management
- Cc) A model with larger betas (slopes) will capture more of the variance in sales
- Dd) A model with fewer predictors will be easier to explain to management
- Ee) A ridge model can help capture more variance in the training set
4If X is a matrix of data with a column for each field in the data and a row for each sample, how can we use matrix operations to compute the covariance matrix of the variables in the data?
- AX−1
- BX * XT
- C(XT * X)−1XT
- DXT * X
- EX + XT
5What is the product of:
[0 2 3] [1]
[1 9 0] [4]- A[14 ]
[−35] - B[0 2 3]
[-4 -36 0] - C[−8 ]
[−35] - DThey cannot be multiplied
- A[14 ]
6What is
[3 1]T
[-1 2]- A[3 -1]
[1 2] - B[1/3 -1]
[1 1/2] - C[-1 3]
[2 1] - D7
- A[3 -1]
7What is [−51−2] ∘[−121] (dot product)
- Aa) [52−2]
- Bb) 5
- Cc) [−63−1]
- Dd) They cannot be multiplied
8Select all that apply:
Matrices and matrix operations are important in data analysis because they:- AAllow us to work with data mathematically in its most natural presentation, as a table, and work with them more concisely in equations.
- BAre a more efficient way of keeping track of long sums that occur in data analysis like in standard deviations and correlations
- CAllow us to hide the details of our calculations so that proprietary algorithms can be protected from copying
- DAllow Keanu Reeves to make lots of money in cinema
9Which of the following are true about matrix multiplication?
- AIt is distributive
- BIt is associative
- CIf M is a 3x3 matrix an N is a 2x3 matrix, then M*N is a 3x2 matrix
- DElement (i, j) in M*N is the dot product of row i in M with column j in N
- EIt is commutative
10Which of the following are true about automatic model building techniques?
- AThey automatically leverage the human eye to determine the important predictors
- BForward selection may result in some variables never getting considered
- CReverse selection may eliminate important predictors because of interactions
- DAll subsets selection will always provide the best model for a given dataset
- EGetting a similar answer from multiple techniques improves confidence in the result
11Cassie has determined is attempting to perform variable selection and counteract overfitting in her efforts to create a model for company profit. Which of the following techniques should she consider?
- AReverse elimination
- BRidge regression
- CLogistic regression
- DLasso regression
12Which of the following are true about ridge regression?
- Aa) It trades bias to reduce variance in the computed beta slopes
- Bb) It magnifies the values of the beta slopes using a penalty value l
- Cc) It is always more accurate than ordinary least-squares regression
- Da) and c)
- EAll of these
13Remi is studying employee performance at his company. Given the fact that the company only has 20 employees, he is concerned that his regression models might be experiencing overfitting. Which of the following symptoms might confirm his suspicions?
- AVery high multiple-R2 value near 1.0
- BHighly significant p-values for the beta slopes
- CLarge values for the slopes (betas) calculated compared to the range of values of the variables
- DMuch higher residual error on test sets vs training sets
- EExtremely accurate predictions on test sets
14When performing a Ridge regression, it is possible for some beta coefficients to be 0.
- ATrue
- BFalse
15When performing an elastic-net regression, which of the following are true of the alpha α term?
- AAlpha can be any integer value.
- BAn alpha value of 1 will perform a Lasso regression only.
- CThe alpha value should be equal to the lambda λ value.
- DDepending on the alpha value, we can perform a mix of Lasso and Ridge regression in a single equation.
16The bias-variance tradeoff is:
- AA way to minimize prediction error.
- BA balance between model complexity and error.
- CGuarantees the most predictive regression model possible.
- DEnsures the beta coefficients never exceed a set value.
- EAlways maximizes the variance of the model.
17Which regression model seeks to minimize the sum of the absolute values of the beta coefficients?
- ALogistic regression
- BLasso regression
- CRidge regression
- DElastic net regression
18In the following equation, what does the first summation represent?
- AThe sum of all beta coefficients of the independent variables.
- BThe RMSE of the model.
- CThe sum of squared error.
- DThe optimal value of alpha in elastic net regression
19When building a regression model, we always want to maximize the R^2 value.
- ATrue
- BFalse
20Jacob has created a regression model and created the following residual plot. Which of the following is true?
- AThe variance of the residuals is too high for a predictive model.
- BThe model is not capturing the full shape of the original data.
- CThe residuals display heteroscedasticity.
- DThe shape of the residuals shows the model Jacob created much have been a Ridge regression.
21The transpose of matrix [3 6 8] is:
[7 4 9]
[5 4 3]- A[7 4 9]
[5 4 3]
[3 6 8] - B[1 0 0]
[0 1 0]
[0 0 1] - C[3 7 5]
[6 4 4]
[8 9 3] - DUndefined
- A[7 4 9]
22What is the product of the following multiplication (dot product):
[ 6 4 1] o [3 2 4]- A30
- B[18 8 4]
- C48
- DCannot be multiplied
23Multicollinearity issues may be detected in a multiple regression analysis through:
- Aa) An abnormally low R2 value
- Bb) Regression coefficients signs that don't match scatterplots
- Cc) High VIF scores for one or more variables
- Da) and c)
- Eb) and c)
24Which of the following are true about the bias-variance tradeoff:
- AIt can allow us to improve estimates of beta slopes by introducing bias
- BWe can reduce both bias and variance simultaneously to increase the predictive power of the model
- CAdding variables to a model will often increase variance and reduce bias
- DAdding bias into the system will inevitably hurt the model's predictive power
25Which of the following are true about lasso regression?
- AIt computes a best fit circle or ellipse containing the data
- BIt seeks to reduce the variance of the betas at the expense of bias in the residuals
- CIt is computed by matrix multiplication much like ordinary least squares regression (OLS)
- DIt uses a parameter lambda that reduces the number of variables included in the model
26Which of the following are true about computing scaled PCA analysis?
- APrincipal components are computed from the covariance matrix of the data.
- BPrincipal components are computed from the correlation matrix of the data.
- CThe analysis is appropriate when variables use different units.
- DIt is always used in PCA when the goal is pure dimensionality reduction
27Which of the following are true about the Elastic Net regression technique?
- AIt is a flexible method of computing principal components allowing their sizes to stretch
- BIt mixes ridge and lasso regressions linearly to gain the advantages of both
- CIt performs variable selection while reducing overfitting
- DIt is applicable only if lasso fails to eliminate model overfitting
28Which of the following can indicate that a regression computation is overfitted?
- AThe R2 for the regression is very close to 1.
- BRMSE on the test set is significantly higher than on the training set.
- CThe residuals are heteroscedastic
- DThe computed beta coefficients are larger than we'd expect based on the range of the associated variable.
29What does this calculate?
( Z^T Z )^-1 Z^T Y- AThe covariance of a dataset
- BThe beta coefficients of an OLS regression
- CThe eigenvectors of a transformation matrix
- DThe optimal lambda value for a regularized regression
30Which of the following are true about factor analysis?
- AIts main purpose is dimensionality reduction
- BIts main purpose is revealing underlying influences on the variables in our dataset
- CThe factors are scaled to improve interpretability
- DThe factors are rotated to improve interpretability
- EWhen we conduct a factor analysis, we should preserve as much variance as we possibly can.
- FThe interpretation of the factors is the most important part of the analysis
31When using PCA to perform dimensionality reduction, what is our final result?
- AA matrix with fewer columns than our original dataset, but transformed values based on the loadings in the principal components.
- BA matrix of our original data with a subset of the original columns.
- CA matrix of our original data with a subset of the original rows.
- DA set of latent factors to be interpreted.
32Ridge regression seeks to:
- AReduce the number of variables in a model
- BMinimize the variance in a model
- CMinimize the square of the beta coefficients in a model
- DReduce overfitting
- EIncrease prediction accuracy
33As the lambda value increases in a lasso regression:
- AThe amount of bias in the model increases
- BThe amount of variance in the model decreases
- CThe overall fit of the model decreases
- DThe number of variables in the model decreases
34A scree plot:
- APlots the principal components against their RMSE
- BHelps us determine an optimal value for lambda
- CCan check for multicollinearity
- DCan help us determine the number of principal components we should choose in PCA.
35The principal components of a PCA:
- AAre eigenvectors of a transformation matrix
- BSeek to capture as much variance in the first few components as possible.
- CAre parallel to each other
- DAre rotated to lie along the primary axis of our coordinate system
- EAre made up of a linear combination of only highly correlated variables.
- FAre highly correlated with each other
36We might consider using the correlation matrix instead of the covariance matrix in a PCA if:
- AThe variables are all in the same units
- BSeveral variables have drastically different scales
- CTo see if we get a better results and keep whichever is best
- DIf we're computing a principal factor analysis
37Matrices can be used for:
- ACalculating sales data
- BTransforming linear space
- CRepresenting data sets
- DRepresenting summations
- ECalculating systems of equations
38In factor analysis, we often don't worry about the factors on the tail end of a scree plot because:
- AWe never want more than 4 factors to analyze for the sake of simplicity
- BThey represent an amount of unexplainable variance instead of meaningful information
- CThey usually have too many variables in their significant loadings
- DThey contain no information at all
39One of the most common uses for factor analysis is:
- AImage compression
- BPicturing projects of higher-order space onto lower-order space
- CAnalyzing survey data
- DPredicting housing prices
40Which of the following are true about matrix multiplication?
- AIt is commutative
- BIt is distributive
- CThe number of rows of the first matrix must equal the number of columns of the second.
- DThe resultant matrix is always the same dimensions as the first matrix
- EIt can be thought of as a series of vector multiplications (dot products)
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- Quiz on DSC 324 Midterm, created by E I on 08/10/2021.
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