Regression Analysis for Nursing: Online Learning Quizzes

Question 1

What is the mathematical equation for a simple linear regression line?

Accepted Answer

y = mx + b

Answer

y = b + mx

Answer

y = mx - b

Answer

y = b - mx

Question 2

Which statistical measure describes the strength and direction of the linear association between two variables?

Accepted Answer

Correlation coefficient

Answer

Regression coefficient

Answer

Coefficient of determination

Answer

Standard error

Question 3

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

Accepted Answer

To evaluate the overall significance of the regression model

Answer

To assess the significance of individual predictor variables

Answer

To determine the optimal subset of predictor variables

Answer

To predict the value of the dependent variable

Question 4

What is the main goal of stepwise regression?

Accepted Answer

To identify the optimal combination of predictor variables for a regression model

Answer

To maximize the R-squared value

Answer

To minimize the standard error of the estimate

Answer

To enhance the interpretability of the regression model

Question 5

Which of the following is NOT a characteristic of a strong linear relationship?

Accepted Answer

Points scattered randomly around the regression line

Answer

High correlation coefficient

Answer

Low standard error of the estimate

Answer

Predictability of the dependent variable

Question 6

The coefficient of determination (R-squared) indicates the:

Accepted Answer

Amount of variation in the dependent variable explained by the independent variables

Answer

Strength of the relationship between the variables

Answer

Standard error of the estimate

Answer

Statistical significance of the regression model

Question 7

In a hypothesis test for regression, the null hypothesis states that:

Accepted Answer

The regression coefficients are all zero

Answer

The regression coefficients are all non-zero

Answer

The regression model is statistically significant

Answer

There is no relationship between the variables

Question 8

What does the coefficient of determination (R2) in regression analysis most accurately represent?

Accepted Answer

The proportion of variation in the dependent variable explained by the independent variable(s)

Answer

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

Answer

The ability to predict the dependent variable for any given value of the independent variable

Answer

A measure with no practical interpretation, used only for statistical testing

Question 9

What proportion of the variation in the dependent variable is explained by the model if the coefficient of determination (R-squared) is 0.64?

Accepted Answer

64%

Answer

26%

Answer

40%

Answer

80%

Question 10

Identify and explain the key assumptions of simple linear regression. Discuss how violations of these assumptions can impact the validity of the regression analysis.

Accepted Answer

Linearity, Homoscedasticity, Independence, and Normality

Answer

Linearity, Multicollinearity, Independence, and Normality

Answer

Non-linearity, Heteroscedasticity, Dependence, and Normality

Question 11

In a simple linear regression model, the slope coefficient (b1) represents:

Accepted Answer

The **change** in the dependent variable for a one-unit **increase** in the independent variable

Answer

The value of the dependent variable when the independent variable is equal to zero

Answer

The correlation coefficient between the dependent and independent variables

Question 12

What is a **primary** purpose of residual analysis in regression?

Accepted Answer

To identify potential violations of model assumptions and to assess model fit

Answer

To calculate the regression coefficients

Answer

To predict the values of the dependent variable

Question 13

The intercept coefficient (b0) in a regression model represents:

Accepted Answer

The value of the dependent variable when the **independent variable** is equal to zero

Answer

The correlation coefficient between the dependent and independent variables

Answer

The change in the dependent variable for a one-unit increase in the independent variable

Question 14

The coefficient of determination (R-squared) and the correlation coefficient (r) are **related** as follows:

Accepted Answer

R-squared is the square of the correlation coefficient

Answer

R-squared is the inverse of the correlation coefficient

Answer

R-squared is independent of the correlation coefficient

Question 15

A **primary benefit** of multiple regression analysis is that it:

Accepted Answer

Allows for the prediction of a dependent variable based on **multiple** independent variables

Answer

Is more precise than simple linear regression

Answer

Is simpler to interpret than simple linear regression

Question 16

To determine if there is a linear relationship between two variables, which graphical representation is most effective?

Accepted Answer

Scatterplot

Answer

Histogram

Answer

Pie Chart

Answer

Bar Graph

Question 17

In the formula for the slope of the regression line, what does 'r' represent?

Accepted Answer

Correlation coefficient

Answer

Standard deviation of the independent variable

Answer

Coefficient of determination

Answer

Mean of the dependent variable

Question 18

Which of the following is a key assumption of simple linear regression?

Accepted Answer

The relationship between the variables is linear.

Answer

The sample size is large.

Answer

The independent variable is manipulated by the researcher.

Question 19

What is the coefficient of determination primarily used to indicate?

Accepted Answer

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

Answer

The slope of the regression line

Question 20

One advantage of using multiple regression over simple linear regression is that it:

Accepted Answer

Examines the relationship between a dependent variable and multiple independent variables.

Answer

Is always more accurate.

Question 21

What is the primary purpose of examining a residual plot?

Accepted Answer

To evaluate the assumptions of regression analysis.

Answer

To predict the value of the dependent variable.

Answer

To determine the equation of the regression line.

Answer

To calculate the coefficient of determination.

Question 22

Which of the following is a widely used statistical software package for conducting regression analysis?

Accepted Answer

SPSS

Answer

Microsoft Excel

Answer

Google Sheets

Question 23

What is the primary purpose of the coefficient of determination (R^2) in multiple regression analysis?

Accepted Answer

To represent the proportion of variation in the dependent variable that can be explained by the independent variables.

Answer

To evaluate the significance of each individual regression coefficient.

Answer

To predict the value of the dependent variable for a given set of independent variables.

Question 24

In multiple regression analysis, which of the following is a potential consequence of high multicollinearity among the independent variables?

Accepted Answer

It can result in inflated standard errors for the regression coefficients.

Answer

It can increase the predictive accuracy of the regression model.

Answer

It can decrease the significance of the regression coefficients.

Question 25

What is the primary purpose of a residual plot in regression analysis?

Accepted Answer

To assess whether the assumptions of the regression model are met, such as linearity and homoscedasticity.

Answer

To predict the value of the dependent variable for new data points.

Answer

To calculate the coefficient of determination (R^2).

Answer

To identify the most significant independent variables in the regression equation.

Question 26

What is the primary difference between a scatterplot and a residual plot in regression analysis?

Accepted Answer

A scatterplot depicts the relationship between the independent and dependent variables, while a residual plot displays the differences between the predicted values and the actual observed values of the dependent variable.

Answer

A scatterplot shows the distribution of the independent variable, while a residual plot shows the distribution of the dependent variable.

Question 27

What is the main objective of a hypothesis test in regression analysis?

Accepted Answer

To determine whether the relationship between the independent and dependent variables is statistically significant.

Answer

To predict the value of the dependent variable for new data points.

Question 28

Which of the following is a potential advantage of using regression analysis in healthcare research?

Accepted Answer

It allows researchers to investigate the simultaneous effects of multiple independent variables on a single dependent variable.

Answer

Regression analysis is simple to conduct and interpret, requiring minimal statistical expertise.

Question 29

What is the distinction between the intercept and the slope in a regression equation?

Accepted Answer

The intercept represents the value of the dependent variable when all independent variables are equal to zero, while the slope indicates the change in the dependent variable for a one-unit increase in any single independent variable, assuming all other independent variables remain constant.

Answer

The intercept is the average value of the dependent variable, and the slope is the standard deviation of the dependent variable.

Question 30

What is the function of a confidence interval in regression analysis?

Accepted Answer

To provide a range of plausible values within which the true value of a population parameter, such as the slope or intercept, is likely to fall.

Answer

To determine whether the overall regression model is statistically significant.

Question 31

In a simple linear regression model, what does the slope represent?

Accepted Answer

The change in the dependent variable for a one-unit increase in the independent variable.

Answer

The average value of the dependent variable.

Answer

The strength and direction of the linear relationship between the variables.

Question 32

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

Accepted Answer

The independent variable must be normally distributed.

Answer

Linearity between the variables.

Answer

Homoscedasticity of residuals (errors have equal variance).

Question 33

What does the R-squared value in a regression model represent?

Accepted Answer

The proportion of variance in the dependent variable explained by the independent variable(s).

Answer

The probability of a Type I error.

Answer

The strength of the linear relationship between the variables.

Question 34

A researcher wants to study the relationship between hours of sleep and patient recovery time. Which type of regression analysis is most appropriate?

Accepted Answer

Simple linear regression.

Answer

Logistic regression (for predicting categorical outcomes).

Answer

Time series regression (for data with a time component).

Answer

Multiple regression (for examining multiple independent variables).

Question 35

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

Accepted Answer

To explain the proportion of variance in the dependent variable that is accounted for by all independent variables.

Answer

To measure the strength of the relationship between each independent variable and the dependent variable.

Question 36

What is the purpose of a residual plot in regression analysis?

Accepted Answer

To assess the assumptions of linearity, homoscedasticity, and independence of residuals.

Answer

To calculate the R-squared value.

Answer

To identify the best fit regression line.

Question 37

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

Accepted Answer

F-test.

Answer

T-test (for comparing means of two groups).

Answer

Chi-square test (for analyzing categorical data).

Answer

ANOVA (for comparing means of multiple groups).

Question 38

A researcher is investigating the relationship between medication dosage and patient blood pressure. The regression analysis reveals a significant p-value. What does this indicate?

Accepted Answer

There is a statistically significant relationship between medication dosage and patient blood pressure.

Answer

The regression model is a perfect fit for the data.

Question 39

Which of the following is an advantage of using multiple regression over simple linear regression?

Accepted Answer

It allows for the examination of the relationship between a dependent variable and multiple independent variables simultaneously.

Answer

It is easier to interpret the results.

Question 40

A nurse researcher wants to predict patient satisfaction scores based on factors like length of stay, nurse-to-patient ratio, and patient age. Which type of regression analysis should she use?

Accepted Answer

Multiple regression.

Answer

Time series regression (for data with a time component).

Answer

Simple linear regression (for examining the relationship between one dependent and one independent variable).

Answer

Logistic regression (for predicting categorical outcomes).

Question 41

Which of the following is NOT a core assumption of simple linear regression?

Accepted Answer

The relationship between the variables is perfectly linear.

Answer

The errors have a mean of zero.

Answer

The errors are independent of each other.

Question 42

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

Accepted Answer

The proportion of the dependent variable's variance explained by the independent variable.

Answer

The slope of the regression line.

Answer

The intercept of the regression line.

Question 43

Which of these is a commonly used method for selecting independent variables in a multiple regression model?

Accepted Answer

Stepwise regression

Answer

Cluster analysis

Answer

Factor analysis

Answer

Principal component analysis

Question 44

What is the primary purpose of a residual in regression analysis?

Accepted Answer

To represent the difference between the actual value and the predicted value.

Answer

To test the significance of the regression model.

Answer

To estimate the slope of the regression line.

Question 45

Which of the following is NOT a type of multiple regression analysis?

Accepted Answer

Logistic regression

Answer

Ordinary least squares regression

Answer

Weighted least squares regression

Answer

Ridge regression

Question 46

What is a significant benefit of using regression analysis in nursing research?

Accepted Answer

It can help identify risk factors for various health conditions.

Answer

It is a non-parametric test, suitable for all data types.

Answer

It is a simple and straightforward technique to understand.

Question 47

In regression analysis, what is the purpose of hypothesis testing?

Accepted Answer

To determine if the observed relationship between variables is statistically significant.

Answer

To estimate the errors in the model.

Answer

To determine the slope of the regression line.

Question 48

What is the key difference between the population regression line and the sample regression line?

Accepted Answer

The population regression line represents the true relationship between variables, while the sample regression line is an estimate based on a sample from the population.

Answer

The population regression line has a higher R-squared value than the sample regression line.

Question 49

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

Accepted Answer

The errors are normally distributed.

Answer

The variance of the errors is constant.

Answer

The relationship between the variables is linear.

Answer

Linear relationship between variables

Question 50

In regression analysis, what is the purpose of a scatterplot?

Accepted Answer

To visualize the relationship between the variables.

Answer

To calculate the slope and intercept of the regression line.

Answer

To determine the statistical significance of the regression model.

Question 51

Which measure is used to evaluate how well a regression model fits the data?

Accepted Answer

Coefficient of determination (R-squared)

Answer

Adjusted R-squared

Answer

Root mean square error (RMSE)

Answer

Standard error of the estimate (SEE)

Question 52

What does a positive regression coefficient indicate?

Accepted Answer

As the independent variable increases, the dependent variable also tends to increase.

Answer

The sign of the coefficient does not provide information about the direction of the relationship.

Answer

As the independent variable increases, the dependent variable tends to decrease.

Question 53

Which step is NOT involved in conducting multiple regression analysis?

Accepted Answer

Plotting the residuals against a variable of interest

Answer

Calculating the correlation matrix.

Answer

Fitting the regression model.

Answer

Examining diagnostic plots.

Question 54

What type of bias can occur when an important variable is excluded from a regression model?

Accepted Answer

Omitted variable bias

Answer

Selection bias

Answer

Multicollinearity

Answer

Measurement error

Question 55

What is the primary purpose of a residual plot?

Accepted Answer

To identify patterns in the residuals and check model assumptions.

Answer

To estimate the predicted values.

Answer

To determine the significance of the regression coefficients.

Question 56

Which type of regression model is appropriate when there is only one predictor variable?

Accepted Answer

Simple linear regression

Answer

Logistic regression

Answer

Poisson regression

Answer

Multiple regression

Question 57

In regression analysis, what is the distinction between dependent and independent variables?

Accepted Answer

The dependent variable is influenced by the independent variable.

Answer

Both variables are influenced by a third variable.

Answer

The independent variable is influenced by the dependent variable.

Question 58

What is a potential consequence of multicollinearity in a regression model?

Accepted Answer

Inflated standard errors of the regression coefficients.

Answer

Improved predictive accuracy.

Answer

Increased goodness of fit.