Regression Multiple Choice Questions and Answers

1 In a linear regression problem, we are using “R-squared” to measure goodness-of-fit. We add a feature in linear regression model and retrain the same model. Which of the following option is true?

A If R Squared increases, this variable is significant

B If R Squared decreases, this variable is not significant

C Individually R squared cannot tell about variable importance. We can’t say anything about it right now

D None of these

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Answer: Individually R squared cannot tell about variable importance. We can’t say anything about it right now

2 Which one of the statement is true regarding residuals in regression analysis?

A Mean of residuals is always zero

B Mean of residuals is always less than zero

C Mean of residuals is always greater than zero

D There is no such rule for residuals.

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Answer: Mean of residuals is always zero

3 Which of the one is true about Heteroskedasticity?

A Linear Regression with varying error terms

B Linear Regression with constant error terms

C Linear Regression with zero error terms

D All of the above

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Answer: Linear Regression with varying error terms

4 The correlation coefficient is used to determine:

A A specific value of the y-variable given a specific value of the x-variable

B A specific value of the x-variable given a specific value of the y-variable

C The strength of the relationship between the x and y variables

D All of the above

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Answer: The strength of the relationship between the x and y variables

5 Suppose, we are using Logistic regression model for n-class classification problem. In this case, we can use One-vs-rest method. Choose which of the following option is true regarding this?

A We need to fit n model in n-class classification problem

B We need to fit n-1 models to classify into n classes

C We need to fit only 1 model to classify into n classes

D All of these

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Answer: We need to fit n model in n-class classification problem

6 Logistic Regression transforms the output probability to be in a range of [0, 1]. Which of the following function is used by logistic regression to convert the probability in the range between [0,1].

A Sigmoid

B Mode

C Square

D All of the above

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Answer: Sigmoid

7 Which of the following method(s) does not have closed form solution for its coefficients?

A Ridge regression

B Lasso

C Both Ridge and Lasso

D None of both

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Answer: Lasso

8 To test linear relationship of y(dependent) and x(independent) continuous variables, which of the following plot best suited?

A Scatter plot

B Barchart

C Histograms

D All of the above

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Answer: Scatter plot

9 Which of the following indicates a fairly strong relationship between X and Y?

A Correlation coefficient = 0.9

B The p-value for the null hypothesis Beta coefficient =0 is 0.0001

C The t-statistic for the null hypothesis Beta coefficient=0 is 30

D None of the above

View Answer

Answer: Correlation coefficient = 0.9

10 Generally, which of the following method(s) is used for predicting continuous dependent variable?

1. Linear Regression 2. Logistic Regression

A 1 and 2

B only 1

C only 2

D None of these

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Answer: only 1

11 Suppose we have generated the data with help of polynomial regression of degree 3 (degree 3 will perfectly fit this data). Now consider below points and choose the option based on these points.

1. Simple Linear regression will have high bias and low variance 2. Simple Linear regression will have low bias and high variance 3. polynomial of degree 3 will have low bias and high variance 4. Polynomial of degree 3 will have low bias and Low variance

A Only 1

B 1 and 3

C 1 and 4

D 2 and 4

View Answer

Answer: 1 and 4

12 Suppose we fit “Lasso Regression” to a data set, which has 100 features (X1,X2…X100). Now, we rescale one of these feature by multiplying with 10 (say that feature is X1), and then refit Lasso regression with the same regularization parameter. Now, which of the following option will be correct?

A It is more likely for X1 to be excluded from the model

B It is more likely for X1 to be included in the model

C Can’t say

D All of these

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Answer: It is more likely for X1 to be included in the model

13 Which of the following is true about “Ridge” or “Lasso” regression methods in case of feature selection?

A Ridge regression uses subset selection of features

B Lasso regression uses subset selection of features

C Both use subset selection of features

D None of the above

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Answer: Lasso regression uses subset selection of features

14 Q18. Which of the following statement(s) can be true post adding a variable in a linear regression model?

1. R-Squared and Adjusted R-squared both increase 2. R-Squared increases and Adjusted R-squared decreases 3. R-Squared decreases and Adjusted R-squared decreases 4. R-Squared decreases and Adjusted R-squared increases

A 1 and 2

B 1 and 3

C 2 and 4

D None of the above

View Answer

Answer: 1 and 2

15 Which of the following option is true regarding “Regression” and “Correlation” ? Note: y is dependent variable and x is independent variable.

A The relationship is symmetric between x and y in both

B The relationship is not symmetric between x and y in both

C The relationship is not symmetric between x and y in case of correlation but in case of regression it is symmetric

D The relationship is symmetric between x and y in case of correlation but in case of regression it is not symmetric

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Answer: The relationship is symmetric between x and y in case of correlation but in case of regression it is not symmetric

16 Suppose you have fitted a complex regression model on a dataset. Now, you are using Ridge regression with tuning parameter lambda to reduce its complexity. Choose the option(s) below which describes relationship of bias and variance with lambda.

A In case of very large lambda; bias is low, variance is low

B In case of very large lambda; bias is low, variance is high

C In case of very large lambda; bias is high, variance is low

D In case of very large lambda; bias is high, variance is high

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Answer: In case of very large lambda; bias is high, variance is low

17 Suppose you have fitted a complex regression model on a dataset. Now, you are using Ridge regression with tuning parameter lambda to reduce its complexity. Choose the option(s) below which describes relationship of bias and variance with lambda.

A In case of very small lambda; bias is low, variance is low

B In case of very small lambda; bias is low, variance is high

C In case of very small lambda; bias is high, variance is low

D In case of very small lambda; bias is high, variance is high

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Answer: In case of very small lambda; bias is low, variance is high

18 In a simple linear regression model (One independent variable), If we change the input variable by 1 unit. How much output variable will change?

A By 1

B No change

C By its Slope

D None of the above

View Answer

Answer: By its Slope

19 Which of the following statement is true about partial derivative of the cost functions w.r.t weights / coefficients in linear-regression and logistic-regression?

A Both will be different

B Both will be same

C Can’t say

D All of the above

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