Regression

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

 Error

 Bias

 Lambda

 Variance

2. 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?

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

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

 Linearity between outcome and predictor variable

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

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

 Feature/ variable

 Lambda

 Noise

 Complexity

4. 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

 Overfit

 Cross validation

 Small dataset

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

 Working with models that are underfit

 Determining if a model can be generalized for a broader group

 Working with models with large amounts of data

 Working with models with small amounts of data

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

 Normal

 Approximately Normal

 Standard Normal

 Non-Normal

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

 Computational errors have been made

 Important regressors’ have not been included in the model

 Multicollinearity is present

 The range of some of the regressors is too small

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

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

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

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

 Simple linear regression

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

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

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

 If there is non-constant variance then there will be an equal 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

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

 t-test

 Chi-Square test

 Durbin M-test

 F-test

11. A testing set is —————.

 Multiple data sets that have been run on the model

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

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

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

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

 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

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

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

13. A training set is ————–.

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

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

 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

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

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

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

 Neither option

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

 Use regularization

 Reduce the number of features in the training data

 Reduce model complexity

 Increase model complexity

16. 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

 Multiple Correlation Coefficient

 Coefficient of Variation

 Coefficient of Partial Correlation

17. 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?

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

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

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

 False

 True

19. 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 $\sim Normal (0, 1)$

 Residuals $\sim Normal (1, 0)$

 Residuals $\sim Uniform (0, 1)$

 Residuals $\sim Normal (0, σ^2)$

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

 High bias

 High generalizability

 High complexity

 High variance

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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?

Performing Statistical Models in R

The post is about MCQs correlation and regression Quiz. There are 20 multiple-choice questions covering topics related to the basics of correlation and regression analysis, best-fitting trend, least square regression line, interpretation of correlation and regression coefficients, and regression plot. Let us start with the MCQs correlation and regression Quiz now.

Please go to MCQs Correlation and Regression 10 to view the test

MCQs Correlation and Regression

• Which of the following statement(s) about correlations is/are right? I. When dealing with a positive Pearson’s r, the line goes up. II. When the observations cluster around a straight line, we deal with a linear relation between the variables. III. The steeper the line, the smaller the correlation.
• Suppose you have collected the following data about how much chocolate people eat and how happy these people are. Amount of chocolate bars a week: 2, 4, 1.5, 2, 3. Grades for happiness: 7, 3, 8, 8, 6. (Note that the data follows paired observations) The Pearson Correlation between these two variables will be
• Suppose, you have investigated how eating chocolate bars influences the grades of students. For this purpose, you keep track of their chocolate intake (in bars per week) and assess their exam results one day later. Which statement(s) about the regression line $\hat{y} = 0.66x + 1.99$ is/are true?
• A professor uses the following formula to grade a statistics exam: $\hat{y} = 0.5 + 0.53x$. After obtaining the results the professor realizes that the grades are very low, so he might have been too strict. He decides to level up all results by one point. What will be the new grading equation?
• What is the explained variance? And how can you measure it?
• A teacher asks his students to fill in a form about how many cigarettes they smoke every week and how much they weigh. After obtaining the data/results, he makes a scatterplot and analyses the data points. Pearson’s r is computed to assess the correlation and found to of 0.80. From the correlation results, it is concluded that smoking more cigarettes causes high body weight. What is wrong with this analysis?
• What can you conclude about a Pearson’s r that is bigger than 1?
• Why do we use squared residuals when computing the regression line?
• What technique is used to help identify the nature of the relationship between two variables?
• Regression is a form of this?
• The correlation coefficient is used to determine
• If there is a very strong correlation between two variables then the correlation coefficient must be
• Regression modeling is a statistical framework for developing a mathematical equation that describes how
• In the least squares regression, which of the following is not a required assumption about the error term $\varepsilon$?
• In a regression analysis if $R^2=1$ then
• In a regression analysis, the variable that is used to explain the change in the outcome of an experiment, or some natural process, is called
• For a mathematical model related to a straight line, if a value for the x variable is specified, then
• When a regression line passes through the origin then
• The range of the multiple correlation coefficient is
• In regression analysis, the variable that is being predicted is

Computer MCQs Online Test

MCQs in Statistics

The post is about MCQs Linear Regression and correlation Quiz. There are 20 multiple-choice questions covering topics related to the basics of correlation and regression analysis, best-fitting trend, least square regression line, interpretation of correlation and regression coefficients, and regression plot. Let us start with the MCQs about Linear Regression and Correlation Quiz now.

Please go to Linear Regression and Correlation Quiz 9 to view the test

Linear Regression and Correlation Quiz with Answers

• A regression analysis is run between two continuous variables “amount of food eaten” vs “the amount of calories burnt”. The coefficient value is $-0.33$ for “the amount of food eaten” and an R-square value of 0.81. What is the correlation coefficient?
• In the simple linear regression equation, the term $B_0$ represents the
• In model development, one can develop more accurate models when one has which of the following?
• How should one interpret an R-squared if it is 0.89?
• When comparing linear regression models, when will the mean squared error (MSE) be smaller?
• Which of the following is NOT true about a model?
• Which of the following is NOT a method for evaluating a regression model?
• Which of the following is NOT true about a model?
• What type of model would you use if you wanted to find the relationship between a set of variables?
• Pearson correlation are concerned with
• Which of the following statements describes a positive correlation between two variables?
• When using the Pearson method to evaluate the correlation between two variables, which set of numbers indicates a strong positive correlation?
• What are the key reasons to develop a model for your data analysis?
• There are four assumptions associated with a linear regression model. What is the definition of the assumption of homoscedasticity?
• Which performance metric for regression is the mean of the square of the residuals (error)?
• When comparing the MSE of different models, do you want the highest or lowest value of MSE?
• Which is NOT true for comparing multiple linear regression (MLR) and simple linear regression (SLR)?
• One can visualize the correlation between two variables by plotting them on a scatter plot and then doing which of the following?
• When using the Pearson method to evaluate the correlation between two variables, how can one know that there is a strong certainty in the result?
• The method of least squares finds the best-fit line that ————– the error between observed and estimated points on the line.

Simulation in R for Sampling

Model Selection Criteria