Regression Analysis: A Comprehensive Guide for Nursing Students

Question 1

Which of the following is NOT an assumption of linear regression?

Accepted Answer

The data must be sampled randomly.

Answer

The errors are normally distributed.

Answer

The variance of the errors is constant.

Answer

The independent variables are linearly related to the dependent variable.

Question 2

Which of the following is **not** an assumption of linear regression?

Accepted Answer

Multivariate normality of residuals

Answer

Linearity

Answer

Homoscedasticity

Answer

Independence of observations

Question 3

Which of the following is NOT a key assumption of linear regression?

Accepted Answer

Perfectly correlated independent variables (multicollinearity)

Answer

Linear relationship between variables

Answer

Constant variance of residuals (homoscedasticity)

Answer

No correlation between error terms (independence of errors)

Question 4

Which assumption is NOT required for the validity of linear regression results?

Accepted Answer

Errors are normally distributed

Answer

Linearity

Answer

Independence of errors

Answer

Homoscedasticity

Question 5

Which assumption is **not** commonly associated with linear regression?

Accepted Answer

Multivariate normality

Answer

Linearity

Answer

Homoscedasticity

Answer

Independence

Question 6

Which assumption is NOT typically made in linear regression?

Accepted Answer

High correlation among independent variables

Answer

Linear relationship between variables

Answer

Normally distributed errors

Answer

Constant error variance

Question 7

Which of the following is NOT an assumption of linear regression?

Accepted Answer

Independent variables are uncorrelated.

Answer

Errors are normally distributed.

Answer

Error variance is constant.

Answer

Relationship between variables is linear.

Question 8

Which assumption of linear regression ensures that the residuals have constant variance?

Accepted Answer

Homoscedasticity

Answer

Linearity

Answer

Independence

Answer

Normality

Question 9

Which assumption of linear regression specifies that the residuals should follow a particular distribution?

Accepted Answer

Normality of residuals

Answer

Independence of independent variables

Answer

Continuity of the dependent variable

Answer

Error-free measurement of independent variables

Question 10

In multiple regression analysis, the value of the dependent variable is influenced by:

Accepted Answer

Multiple independent variables

Answer

A single independent variable

Answer

The regression model's intercept

Answer

The regression line's slope

Question 11

What is the primary goal of multiple regression analysis?

Accepted Answer

Predict a continuous outcome variable using one or more independent variables.

Answer

Predict a categorical outcome variable using one or more independent variables.

Answer

Test the significance of the relationship between variables.

Answer

Determine the best subset of independent variables for a regression model.

Question 12

Which of the following is NOT an assumption of linear regression?

Accepted Answer

Presence of autocorrelation in the residuals

Answer

Linear relationship between the dependent and independent variables

Answer

Normally distributed residuals

Answer

Constant variance of the residuals

Question 13

Which model selection technique divides the dataset into training and testing sets, trains the model on the training set, and assesses its performance on the testing set?

Accepted Answer

Cross-validation

Answer

Bootstrapping

Answer

Bayesian model selection

Answer

Regularization

Question 14

In residual analysis, which plot is used to verify the assumption of linearity in a linear regression model?

Accepted Answer

Scatter Plot of Residuals vs. Fitted Values

Answer

Normal Probability Plot

Answer

Histogram of Residuals

Answer

QQ Plot of Residuals

Question 15

In regression analysis, which techniques are employed for regularization?

Accepted Answer

Ridge Regression

Accepted Answer

Lasso Regression

Accepted Answer

Elastic Net Regression

Answer

Forward Selection

Question 16

In regression analysis, how does the sample size affect the width of the confidence interval?

Accepted Answer

The confidence interval narrows as the sample size increases.

Answer

The confidence interval widens as the sample size increases.

Answer

The confidence interval remains unchanged regardless of the sample size.

Answer

The impact of sample size on the confidence interval depends on the specific regression model.

Question 17

In multiple regression, which variable selection method starts with a model that includes all variables and then removes variables one at a time until only significant variables remain?

Accepted Answer

Backward elimination

Answer

Forward selection

Answer

Stepwise selection

Answer

LASSO regression

Question 18

Which assumption is fundamental to Poisson regression?

Accepted Answer

Poisson distribution of the response variable

Answer

Equal mean and variance of the response variable

Answer

Linear relationship between independent and response variables

Question 19

In regression analysis, what term describes the variation in the dependent variable that remains unexplained by the independent variables?

Accepted Answer

Residual variation

Answer

Explained variation

Answer

Total variation

Answer

Independent variation

Question 20

In regression analysis, what does the coefficient of determination (R-squared) measure?

Accepted Answer

The proportion of variation in the dependent variable explained by the independent variable.

Answer

The strength of the relationship between the dependent and independent variables.

Answer

The amount of error in the regression model.

Answer

The significance of the regression model.

Question 21

In regression analysis, which null hypothesis is tested to assess the significance of the relationship between the independent and dependent variables?

Accepted Answer

There is no statistically significant linear relationship between the variables.

Answer

The slope of the regression line is zero.

Answer

The intercept of the regression line is zero.

Answer

The coefficient of determination (R-squared) is zero.

Question 22

In regression analysis, how can outliers and influential points potentially affect the outcomes and conclusions drawn from the model?

Accepted Answer

Be identified and their impact assessed using diagnostic tools

Answer

Enhance the accuracy and reliability of the model

Answer

Be removed before analysis to ensure accurate results

Answer

Be ignored as they do not affect the interpretation of results

Question 23

Which of the following are assumptions of linear regression models?

Accepted Answer

Independence of errors

Accepted Answer

Normally distributed errors

Accepted Answer

Constant variance of errors

Answer

No outliers or influential points

Question 24

Which assumption of linear regression is violated when the relationship between the dependent variable and one or more independent variables is non-linear?

Accepted Answer

Linearity

Answer

Independence of residuals

Answer

Homoscedasticity

Answer

Normally distributed errors

Question 25

In a linear regression model, what is the primary purpose of the coefficient of determination (R-squared)?

Accepted Answer

Explaining the proportion of variance in the dependent variable

Answer

Measuring the strength and direction of the relationship between variables

Answer

Predicting the dependent variable accurately

Answer

Identifying outliers or influential points

Question 26

In regression analysis, what does the coefficient of determination (R-squared) value represent?

Accepted Answer

The percentage of variation in the dependent variable explained by the independent variables

Answer

The number of independent variables in the regression model

Answer

The average value of the dependent variable

Answer

The standard error of the regression model

Question 27

In linear regression, the primary purpose of conducting a test for homoscedasticity is to:

Accepted Answer

Evaluate the assumption of equal variance of errors.

Answer

Check the linear relationship between independent and dependent variables.

Answer

Assess the statistical significance of regression coefficients.

Answer

Verify if the residuals are normally distributed.

Question 28

In linear regression, what happens if the assumption of linearity is not met?

Accepted Answer

The model becomes invalid, and the results cannot be trusted.

Answer

The model remains valid, but the results may be inaccurate.

Answer

The model remains valid, but interpreting the results may be more difficult.

Question 29

In regression analysis, what is the main goal of using ridge regression?

Accepted Answer

To reduce the variance of the regression coefficients, potentially at the cost of a slight increase in bias, to alleviate multicollinearity and improve model performance.

Answer

To eliminate the impact of outliers within the dataset.

Question 30

To assess the homoscedasticity assumption in linear regression, which graphical method is employed?

Accepted Answer

Plot residuals against fitted values

Answer

Plot residuals against independent variables

Answer

Create a scatterplot of the data

Question 31

In the context of multiple regression analysis, when analyzing a dependent variable with non-continuous characteristics (e.g., binary, categorical), which type of regression is most appropriate?

Accepted Answer

Logistic regression

Answer

Linear regression

Answer

Poisson regression

Question 32

What are the potential consequences of violating the assumption of linearity in linear regression analysis?

Accepted Answer

Incorrect results, unreliable predictions, and misleading inferences

Answer

Simplified interpretation of regression coefficients

Answer

Unaffected predictive ability with monotonic relationships

Question 33

To detect and address overfitting and underfitting in regression analysis, which techniques can be employed?

Accepted Answer

Utilize cross-validation to assess various models and choose the one with optimal predictive performance.

Accepted Answer

Apply a regularization technique like L1 or L2 regularization to penalize model complexity.

Answer

Increase model complexity to minimize residual variance.

Answer

Disregard the issue and presume the model will generalize effectively to new data.

Question 34

How can regression analysis be applied to make predictions and draw inferences about the larger population represented by the sample data?

Accepted Answer

Regression analysis can be used to make predictions and draw inferences about the population, provided the sample size is adequately large.

Answer

Regression analysis cannot be used for making predictions or drawing inferences about the population.

Answer

Regression analysis can be used to make predictions about the population, but not to draw inferences.

Answer

Regression analysis can be used to draw inferences about the population, but not to make predictions.

Question 35

In regression analysis, which variable selection technique strikes a balance between including relevant predictors and avoiding overfitting?

Accepted Answer

LASSO

Answer

Best subsets

Answer

Forward selection

Answer

Backward elimination

Question 36

Which assumption of linear regression requires the residuals to have a constant variance?

Accepted Answer

Homoscedasticity

Answer

Linearity

Answer

Independence

Answer

Normality

Question 37

In a multiple regression equation, what do the intercept and slope coefficients represent, respectively?

Accepted Answer

The mean value of the dependent variable and the change in the dependent variable for a one-unit change in the independent variable

Answer

The standard deviation of the dependent variable and the correlation between the dependent and independent variables

Answer

The probability of the dependent variable being equal to zero and the significance of the regression model

Answer

The minimum and maximum values of the dependent variable

Question 38

Which condition necessitates the use of a logarithmic transformation in regression analysis?

Accepted Answer

The dependent variable is skewed

Answer

The relationship between the variables is non-linear

Answer

The data points are clustered together

Answer

The independent variable is a categorical variable

Question 39

What is the primary purpose of the F-test in regression analysis?

Accepted Answer

To assess the overall significance of the regression model

Answer

To test the significance of individual independent variables

Answer

To verify the assumption of homoscedasticity

Answer

To calculate the correlation between the dependent and independent variables

Question 40

Which limitation of regression analysis is related to the potential influence of extreme values?

Accepted Answer

Sensitivity to outliers and influential points

Answer

Requirement of only quantitative variables

Answer

Inability to predict relationships

Answer

Necessity of a large sample size

Question 41

What does the coefficient of determination (R-squared) signify?

Accepted Answer

The proportion of variation in the dependent variable explained by the regression model

Answer

The correlation between the dependent and independent variables

Answer

The significance of the regression model

Answer

The standard deviation of the dependent variable

Question 42

In regression analysis, which technique goes beyond basic linear regression models?

Accepted Answer

Nonlinear regression

Answer

Time series analysis

Answer

Cluster analysis

Answer

Factor analysis

Question 43

Why is checking the normality assumption important in linear regression?

Accepted Answer

It helps ensure the validity of statistical inferences and can be assessed using methods like histograms, Q-Q plots, and the Shapiro-Wilk test.

Answer

It's only crucial for multiple regression, not simple linear regression.

Answer

It's not particularly important in linear regression.

Question 44

Which techniques can be used to extend regression analysis to model non-linear relationships between variables?

Accepted Answer

Applying transformations to create a linear relationship

Accepted Answer

Fitting a polynomial regression model of appropriate degree

Accepted Answer

Employing non-parametric regression techniques, such as kernel smoothing

Answer

Ignoring the non-linearity and using linear regression

Question 45

In regression analysis, diagnostic plots like residual plots and influence plots serve what purpose, and how can they enhance the model's validity?

Accepted Answer

Diagnostic plots help spot influential points that can skew the regression line and weaken the model.

Accepted Answer

Residual plots display the spread of residuals, helping detect patterns or trends that may indicate model issues.

Accepted Answer

Influence plots, like Cook's Distance and DFBETA, measure how much each data point affects the regression coefficients, allowing researchers to assess their impact on the model.

Answer

Diagnostic plots are only good for finding outliers, not influential points.

Question 46

In multiple regression, which variable selection method evaluates all possible combinations of variables to find the subset that minimizes prediction error?

Accepted Answer

Exhaustive Search

Answer

Forward Selection

Answer

Backward Elimination

Question 47

Which of the following diagnostic tools is used to detect non-linearity in regression analysis?

Accepted Answer

Scatterplot of residuals versus fitted values

Answer

Q-Q plot of residuals

Answer

Analysis of variance table

Answer

Collinearity diagnostics

Question 48

What is the key difference between simple linear regression and multiple regression?

Accepted Answer

Simple linear regression involves one independent variable, while multiple regression involves two or more independent variables.

Answer

Multiple regression is used when the relationship between the variables is non-linear, while simple linear regression is used when it is linear.

Answer

Simple linear regression assumes that the residuals are normally distributed, while multiple regression does not.

Answer

There is no difference between simple linear regression and multiple regression.

Question 49

What is the purpose of a p-value in regression analysis?

Accepted Answer

To determine if the regression model is statistically significant

Answer

To test the null hypothesis that the coefficient is equal to zero

Answer

To measure the strength of the relationship between the variables

Answer

To identify outliers in the data

Question 50

Which of the following is NOT an assumption of simple linear regression?

Accepted Answer

Normal distribution of the residuals (errors)

Answer

Linearity of the relationship between the dependent variable and independent variable

Answer

Independence of observations

Answer

Homoscedasticity (constant variance of residuals)

Question 51

Which of the following is a measure of goodness-of-fit in multiple regression?

Accepted Answer

Adjusted R-squared

Answer

Mean squared error

Answer

t-statistic

Answer

F-statistic

Question 52

What is the null hypothesis for a t-test in regression analysis?

Accepted Answer

The coefficient of the independent variable is zero

Answer

The regression line has a slope of zero

Answer

The correlation coefficient is zero

Answer

The model is not significant

Question 53

In the context of regression analysis, which practice is considered unethical?

Accepted Answer

Altering data to achieve desired outcomes

Answer

Maintaining participant confidentiality

Answer

Disclosing potential conflicts of interest

Answer

Obtaining informed consent before data collection

Question 54

The equation for a simple linear regression model is:

Accepted Answer

y = a + bx

Answer

y = bx + a

Answer

y = a + b/x

Answer

y = b/x + a

Question 55

In hypothesis testing for the significance of a regression coefficient, the null hypothesis is:

Accepted Answer

β = 0

Answer

β ≠ 0

Answer

β > 0

Answer

β < 0

Question 56

Which of the following is not an assumption of linear regression?

Accepted Answer

Multicollinearity

Answer

Linearity

Answer

Homoscedasticity

Answer

Independence

Question 57

The statistic used to measure the strength of the relationship between the independent and dependent variables in multiple regression is:

Accepted Answer

R-squared

Answer

F-statistic

Answer

t-statistic

Answer

p-value

Question 58

The difference between simple and multiple regression is that:

Accepted Answer

Simple regression has one independent variable, while multiple regression has multiple independent variables.

Answer

Multiple regression predicts a single dependent variable, while simple regression predicts multiple dependent variables.

Answer

Simple regression uses ANOVA to test significance, while multiple regression uses t-tests.

Answer

There is no difference between simple and multiple regression.

Question 59

When interpreting a regression coefficient, a positive sign indicates that:

Accepted Answer

The independent variable is positively correlated with the dependent variable.

Answer

The independent variable is negatively correlated with the dependent variable.

Answer

The independent variable has no effect on the dependent variable.

Answer

The sign of the coefficient is irrelevant.

Question 60

What is the primary purpose of the coefficient of determination (R-squared) in multiple regression?

Accepted Answer

To quantify the variance in the dependent variable explained by the independent variables.

Answer

To determine the statistical significance of the regression model.

Question 61

What is the key distinction between simple linear regression and multiple regression?

Accepted Answer

Simple linear regression involves one independent variable, while multiple regression involves two or more independent variables.

Answer

Simple linear regression assumes a linear relationship, while multiple regression assumes a nonlinear relationship.

Question 62

Which statistical test is commonly used to assess the significance of a regression model?

Accepted Answer

F-test

Answer

Z-test

Answer

t-test

Answer

Chi-square test

Question 63

How do you interpret a negative slope coefficient in a regression equation?

Accepted Answer

As the independent variable increases, the dependent variable decreases.

Answer

There is no relationship between the independent and dependent variables.

Answer

As the independent variable increases, the dependent variable increases.

Question 64

What is a key advantage of using regression analysis in research?

Accepted Answer

It can help identify potential causal relationships between variables.

Answer

It is easy to interpret and comprehend.

Answer

It always provides precise predictions.