Evaluating Regression Models Quiz 11

The post is about Evaluating Regression Models Quiz with answers. There are 20 multiple-choice questions about regression models and their evaluation, covering regression analysis, assumptions of regression, coefficient of determination, predicted and predictor variables, etc. Let us start with the Evaluating Regression Models Quiz now.

Online MCQs about Evaluating Regression Models

1. What does regularization introduce into a model that results in a drop in variance?

 Lambda

 Complexity

 Noise

 Feature/ variable

2. When evaluating models, what is the term used to describe a situation where a model fits the training data very well but performs poorly when predicting new data?

 Underfit

 Small dataset

 Cross validation

 Overfit

3. What is the difference between Ridge and Lasso regression?

 Lasso regression increases or decreases the value of Lambda to penalize complex models more or less

 Ridge regression penalizes the sum of the absolute values of the coefficients while Lasso regression penalizes the sum of squared coefficients

 There is no major difference between Ridge and Lasso regression

 Lasso regression penalizes the sum of the absolute values of the coefficients while Ridge regression penalizes the sum of squared coefficients

4. Parveen previously fitted a linear regression model to quantify the relationship between age and lung function measured by FEV1. After she fitted her linear regression model she decided to assess the validity of the linear regression assumptions. She knew she could do this by assessing the residuals and so produced the following plot known as a QQ plot.

How can she use this plot to see if her residuals satisfy the requirements for a linear regression?

 If the variance is constant across the predictor values the observations will lie on a straight line

 It is impossible that observations lie on a straight line

 If the residuals have uniform distribution then the observations will lie on a straight line

 If the residuals have a normal distribution then the observations will lie on a straight line

5. When tuning a model, a grid search attempts to find the value of a parameter that has the smallest —————-.

 Bias

 Variance

 Lambda

 Error

6. The residuals are the distance between the observed values and the fitted regression line. If the assumptions of linear regression hold how would we expect the residuals to behave?

 Residuals $\sim Normal (0, σ^2)$

 Residuals $\sim Normal (0, 1)$

 Residuals $\sim Normal (1, 0)$

 Residuals $\sim Uniform (0, 1)$

7. The ratio of explained variation to the total variation of the following regression model is called $y_i = \beta_0 + \beta_1 x_{1i} + \beta_2x_{2i} + \varepsilon_i, \quad i=1,2,\cdots, n$.

 Coefficient of Multiple Determination

 Coefficient of Partial Correlation

 Coefficient of Variation

 Multiple Correlation Coefficient

8. One cannot apply test of significance if $\varepsilon_i$ in the model $y_i = \alpha + \beta X_i+\varepsilon_i$ are

 Approximately Normal

 Normal

 Standard Normal

 Non-Normal

9. Let the value of the $R^2$ for a model is 0.0104. What does this tell?

 The residuals explain 1.04% of the total variability in the data

 The regression line explains 1.04% of the total variability in the data

 Neither option

10. Regression coefficients may have the wrong sign for the following reasons

 Important regressors’ have not been included in the model

 The range of some of the regressors is too small

 Multicollinearity is present

 Computational errors have been made

11. How can the following plot be used to see if residuals satisfy the requirements for a linear regression?

 If the residuals are normal then the observations will fall on the $y=0$ line

 If there is constant variance then there will be an uneven scatter of residual values around the mean value of zero

 If there is constant variance across predicted values then there will be an equal scatter of residual values around the mean value of zero

 If there is non-constant variance then there will be an equal scatter of residual values around the mean value of zero

12. A third-order polynomial regression model is described as which of the following?

 Squared, meaning that the predictor variable in the model is squared

 Cubic, meaning that the predictor variable in the model is cubed

 Simple linear regression

 Quadratic, meaning that the predictor variable in the model is squared

13. The test used to test the individual partial coefficient in the multiple regression is

 F-test

 Chi-Square test

 t-test

 Durbin M-test

14. What is a strategy you can employ to address an underfit model?

 Reduce model complexity

 Reduce the number of features in the training data

 Increase model complexity

 Use regularization

15. Which situations are helped by using the cross-validation method to train your model?

 Working with models with large amounts of data

 Working with models with small amounts of data

 Determining if a model can be generalized for a broader group

 Working with models that are underfit

16. A training set is ————–.

 A selected portion of the data set that is known to function well within the model

 A small portion of the data used to evaluate the performance of a model

 Multiple data sets that have been run on the model

 A large portion of a data set that is used to build a sound model

17. An underfit model is said to have which of the following?

 High generalizability

 High bias

 High complexity

 High variance

18. A testing set is —————.

 A large portion of a data set that is used to build a sound model

 A small portion of a data set that is used to see whether a model works

 Multiple data sets that have been run on the model

 A selected portion of the data set that is known to function well within the model

19. When using the poly() function to fit a polynomial regression model, you must specify “raw = FALSE” so you can get the expected coefficients.

 True

 False

20. When we fit a linear regression model we make strong assumptions about the relationships between variables and variance. These assumptions need to be assessed to be valid if we are to be confident in estimated model parameters. The questions below will help ascertain that you know what assumptions are made and how to verify these.

Which of these is not assumed when fitting a linear regression model?

 Variance of the outcome is constant across values of the predictor variable

 Linearity between outcome and predictor variable

 The outcome variable is normally distributed across values of the predictor variable

 The predictor variable is normally distributed across values of the outcome variable

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MCQs Evaluating Regression Models Quiz with Answers

• When using the poly() function to fit a polynomial regression model, you must specify “raw = FALSE” so you can get the expected coefficients.
• A third-order polynomial regression model is described as which of the following?
• When evaluating models, what is the term used to describe a situation where a model fits the training data very well but performs poorly when predicting new data?
• An underfit model is said to have which of the following?
• What does regularization introduce into a model that results in a drop in variance?
• When tuning a model, a grid search attempts to find the value of a parameter that has the smallest —————-.
• Which situations are helped by using the cross-validation method to train your model?
• What is a strategy you can employ to address an underfit model?
• What is the difference between Ridge and Lasso regression?
• A training set is ————–.
• A testing set is —————.
• Regression coefficients may have the wrong sign for the following reasons
• The ratio of explained variation to the total variation of the following regression model is called $y_i = \beta_0 + \beta_1 x_{1i} + \beta_2x_{2i} + \varepsilon_i, \quad i=1,2,\cdots, n$.
• One cannot apply test of significance if $\varepsilon_i$ in the model $y_i = \alpha + \beta X_i+\varepsilon_i$ are
• The test used to test the individual partial coefficient in the multiple regression is
• When we fit a linear regression model we make strong assumptions about the relationships between variables and variance. These assumptions need to be assessed to be valid if we are to be confident in estimated model parameters. The questions below will help ascertain that you know what assumptions are made and how to verify these. Which of these is not assumed when fitting a linear regression model?
• Parveen previously fitted a linear regression model to quantify the relationship between age and lung function measured by FEV1. After she fitted her linear regression model she decided to assess the validity of the linear regression assumptions. She knew she could do this by assessing the residuals and so produced the following plot known as a QQ plot. How can she use this plot to see if her residuals satisfy the requirements for a linear regression?
• How can the following plot be used to see if residuals satisfy the requirements for a linear regression?
• Let the value of the $R^2$ for a model is 0.0104. What does this tell?
• The residuals are the distance between the observed values and the fitted regression line. If the assumptions of linear regression hold how would we expect the residuals to behave?

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