Correlation and Regression Analysis: A Comprehensive Guide for Nursing Students

Question 1

What is the primary purpose of the Pearson correlation coefficient?

Accepted Answer

A. To measure the strength and direction of a linear relationship between two variables

Answer

B. To determine if a linear relationship exists between two variables

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C. To calculate the slope of the regression line between two variables

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D. To test the statistical significance of the relationship between two variables

Question 2

Which of the following are properties of the Pearson correlation coefficient?

Accepted Answer

It ranges from -1 to 1.

Accepted Answer

It measures the strength of the linear relationship between two variables.

Answer

It can predict the value of one variable based on the value of another.

Question 3

A researcher investigates the relationship between study time and exam scores, calculating a Pearson's correlation coefficient of 0.8. What does this finding suggest?

Accepted Answer

A strong positive linear relationship, indicating that increased study time generally leads to higher exam scores.

Answer

A strong negative linear relationship, indicating that increased study time generally leads to lower exam scores.

Answer

No linear relationship, indicating that study time has no impact on exam performance.

Answer

A curvilinear relationship, indicating that the relationship between study time and exam scores is not linear but follows a curved pattern.

Question 4

What does the coefficient of determination (R²) represent?

Accepted Answer

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

Answer

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

Answer

The probability of a statistically significant effect of the independent variable on the dependent variable.

Answer

The error in the estimated regression line.

Question 5

A researcher investigating the relationship between sleep duration and academic performance calculates a Pearson's correlation coefficient of 0.6. What does this value suggest?

Accepted Answer

A moderate positive relationship between sleep duration and academic performance

Answer

A strong positive relationship between sleep duration and academic performance

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A weak negative relationship between sleep duration and academic performance

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No relationship between sleep duration and academic performance

Question 6

In a study examining the relationship between age and hospital stay duration, Pearson's correlation coefficient was calculated as 0.42. What does this value indicate?

Accepted Answer

A moderate positive correlation between age and hospital stay duration

Answer

A strong positive correlation between age and hospital stay duration

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A weak negative correlation between age and hospital stay duration

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No significant relationship between age and hospital stay duration

Question 7

What is the main purpose of a correlation coefficient?

Accepted Answer

To measure the strength and direction of a linear relationship between two variables

Answer

To predict the value of one variable based on another

Answer

To test the significance of a relationship between two variables

Answer

To determine the causal relationship between two variables

Question 8

Which of the following values indicates a strong positive correlation?

Accepted Answer

0.7

Answer

-0.9

Answer

-0.2

Answer

0.1

Question 9

What measure precisely quantifies the strength and direction of a linear relationship between two numerical variables?

Accepted Answer

Pearson's correlation coefficient

Answer

Mean

Answer

Standard deviation

Answer

Regression coefficient

Question 10

Which of the following is NOT an assumption of Pearson's correlation coefficient?

Accepted Answer

No outliers

Answer

Linear relationship between variables

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Homoscedasticity

Answer

Interval or ratio scale measurement

Question 11

What does a correlation coefficient of -0.9 indicate?

Accepted Answer

A strong, negative relationship between the variables

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A moderate, positive relationship between the variables

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No relationship between the variables

Question 12

Calculate the Pearson correlation coefficient using the formula:

Accepted Answer

r = (Σ(x - x̄)(y - ȳ)) / √(Σ(x - x̄)²Σ(y - ȳ)²)

Answer

r = (Σxy) / n

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r = (Σx² + Σy²) / n

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r = (Σ(x - y)) / n

Question 13

A researcher is studying the relationship between study hours and test scores. What does a Pearson correlation coefficient of 0.60 indicate?

Accepted Answer

A moderately strong positive correlation

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A perfect positive correlation

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No correlation

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An increase of 0.6 points on the test score for each additional hour of study

Question 14

Which of the following formulas calculates Pearson's correlation coefficient?

Accepted Answer

r = (Σ(x - x̄)(y - ȳ)) / √(Σ(x - x̄)²Σ(y - ȳ)²)

Answer

r = (Σ(x + x̄)(y + ȳ)) / √(Σ(x + x̄)²Σ(y + ȳ)²)

Answer

r = (Σ(x - y)(x̄ - ȳ)) / √(Σ(x - y)²Σ(x̄ - ȳ)²)

Question 15

What does a Pearson correlation coefficient of r = 0.8 indicate?

Accepted Answer

A strong positive relationship, where one variable increases as the other increases.

Answer

A strong negative relationship, where one variable increases as the other decreases.

Answer

A weak positive relationship, where one variable slightly increases as the other increases.

Answer

No relationship between the variables.

Question 16

In a study on student motivation and academic performance, a Pearson's correlation coefficient of 0.76 was found. How would you describe the strength of this relationship?

Accepted Answer

Strong positive correlation

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Weak positive correlation

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Moderate negative correlation

Question 17

For the Pearson correlation coefficient to be valid, which assumption must be met?

Accepted Answer

A linear relationship between the two variables

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Normally distributed variables

Question 18

In a study examining the relationship between age and health status, the Pearson's correlation coefficient was calculated as -0.5. What does this indicate?

Accepted Answer

A strong negative correlation between age and health status

Answer

A strong positive correlation between age and health status

Answer

No correlation between age and health status

Answer

The relationship between age and health status cannot be determined from the given information

Question 19

What's the main purpose of using the Pearson correlation coefficient?

Accepted Answer

To measure the strength and direction of the linear relationship between two variables.

Answer

To find the slope of the regression line.

Answer

To calculate the y-intercept of the regression line.

Question 20

Which assumption is NOT required for simple linear regression?

Accepted Answer

Absence of multicollinearity

Answer

Linear relationship between variables

Answer

Normally distributed residuals

Answer

Constant variance of residuals

Question 21

In linear regression, what does a positive slope suggest about the relationship between the independent and dependent variables?

Accepted Answer

A positive association, where increases in the independent variable are linked to increases in the dependent variable.

Answer

A negative association, where increases in the independent variable are linked to decreases in the dependent variable.

Answer

No linear relationship between the variables.

Question 22

Which assumption must be met for linear regression analysis to be valid?

Accepted Answer

The residuals are normally distributed.

Answer

The relationship between the dependent and independent variables is non-linear.

Answer

The independent variables are independent of each other.

Answer

The sample is representative of the population.

Question 23

Which assumptions are crucial for valid regression analysis results?

Accepted Answer

Linear relationship between variables

Accepted Answer

Equal spread of residuals

Accepted Answer

Independent errors

Answer

Normal distribution of independent variables

Question 24

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

Accepted Answer

Absence of multicollinearity

Answer

Linearity

Answer

Independence of errors

Answer

Normally distributed errors

Question 25

Which of the following assumptions are essential for the validity of linear regression analysis?

Accepted Answer

The residuals are normally distributed.

Accepted Answer

There is no multicollinearity among the predictor variables.

Answer

The relationship between the variables is perfectly linear.

Answer

The sample size is large enough to ensure statistical significance.

Question 26

Which assumption is NOT required for linear regression analysis?

Accepted Answer

Multivariate normality

Answer

Linearity

Answer

Homoscedasticity

Answer

Independence of errors

Question 27

What is the range of values that the Pearson correlation coefficient can assume?

Accepted Answer

-1 to 1

Answer

0 to 1

Answer

-2 to 2

Question 28

When is multiple regression analysis appropriate?

Accepted Answer

Predicting a single dependent variable from multiple independent variables.

Answer

There is a single independent variable and a single dependent variable.

Answer

The independent variables are highly correlated.

Answer

There is a non-linear relationship between the independent variables and the dependent variable.

Question 29

Which statistical measure quantifies the linear relationship's strength and direction between two variables?

Accepted Answer

Pearson's correlation coefficient

Answer

Regression equation

Answer

Coefficient of determination (R2)

Answer

Standard error of the estimate

Question 30

A Pearson's correlation coefficient of -0.7 indicates:

Accepted Answer

A strong negative relationship

Answer

A weak positive relationship

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A strong positive relationship

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A weak negative relationship

Question 31

The equation of a regression line enables us to:

Accepted Answer

Forecast the value of one variable based on another

Answer

Establish the correlation between two variables

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Examine the significance of a relationship between variables

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Calculate the mean and variance of a variable

Question 32

A scatterplot exhibiting a strong positive correlation typically displays points:

Accepted Answer

Clustered along a diagonal line sloping upwards from left to right

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Clustered along a diagonal line sloping downwards from left to right

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Randomly dispersed across the plot

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Concentrated in a circular pattern

Question 33

In regression analysis, the dependent variable is:

Accepted Answer

The variable whose value is being predicted

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The variable used for prediction

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The variable with the strongest correlation

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The variable with the highest mean

Question 34

In a nursing research study examining the relationship between patient satisfaction and nurse-patient communication, the most appropriate statistical test would be:

Accepted Answer

Pearson's correlation coefficient

Answer

Regression analysis

Answer

Analysis of variance (ANOVA)

Answer

Chi-square test

Question 35

In a scatterplot, which pattern indicates a negative linear relationship between two variables?

Accepted Answer

Downward-sloping diagonal line from left to right

Answer

Upward-sloping diagonal line from left to right

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Randomly scattered points without a pattern

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Horizontal line

Question 36

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

Accepted Answer

Normality of the dependent variable

Answer

Linearity

Answer

Homoscedasticity

Answer

Independence of observations

Question 37

Which of the following is not a type of correlation?

Accepted Answer

Causal relationship

Answer

Positive correlation

Answer

Negative correlation

Answer

Spearman's rank correlation

Question 38

Which statistical measure quantifies the strength and direction of a linear relationship between two variables?

Accepted Answer

Pearson's correlation coefficient

Answer

Mean

Answer

Standard deviation

Answer

Regression coefficient

Question 39

In regression analysis, which assumption is essential for ensuring that the residuals are independent and have constant variance?

Accepted Answer

Homoscedasticity

Answer

Linearity

Answer

Normality

Answer

Multicollinearity

Question 40

Identify the assumptions of simple linear regression:

Accepted Answer

Linear relationship between variables

Accepted Answer

Normally distributed residuals

Accepted Answer

Constant variance of residuals

Question 41

In a scatterplot, what does a positive correlation indicate about the relationship between the variables?

Accepted Answer

The variables increase together.

Answer

The variables decrease together.

Answer

There is no relationship between the variables.

Question 42

In a scatterplot, what does a **negative** slope suggest about the direction of the correlation between two variables?

Accepted Answer

Negative correlation

Answer

Positive correlation

Answer

No correlation

Answer

Curvilinear relationship

Question 43

Which assumption is NOT required for simple linear regression analysis?

Accepted Answer

Normally distributed errors

Answer

Linearity

Answer

Independence of errors

Answer

Homoscedasticity

Question 44

In a research study, a Pearson's correlation coefficient of 0.65 is calculated between two variables. What is the strength of this relationship?

Accepted Answer

Moderate relationship

Answer

Weak relationship

Answer

Strong relationship

Question 45

What is the formula to calculate Pearson's correlation coefficient?

Accepted Answer

r = (∑(X - X̄)(Y - Ȳ)) / sqrt(∑(X - X̄)² * ∑(Y - Ȳ)²) / (n - 1)

Answer

Cov(X, Y) / (SD(X) * SD(Y))

Answer

r = 1 - (∑(X - X̄)² / ∑(Y - Ȳ)²) / (n - 1)

Answer

r² = (∑(X - X̄)² / ∑(Y - Ȳ)²) / (n - 1)

Question 46

A correlation coefficient value of -0.8 suggests:

Accepted Answer

A strong negative relationship

Answer

A moderate positive relationship

Answer

A weak negative relationship

Answer

A strong positive relationship

Question 47

The slope of a regression line represents:

Accepted Answer

Predicted change in the dependent variable with a one-unit change in the independent variable

Answer

Correlation coefficient between variables

Answer

Intercept of the regression line

Answer

Standard error of the estimate

Question 48

In a study predicting the length of stay for pneumonia patients, which variable could potentially be a confounding variable?

Accepted Answer

Severity of illness

Answer

Patient age

Answer

Smoking status

Answer

Length of time since diagnosis

Question 49

Which assumption is NOT required for simple linear regression?

Accepted Answer

Normality of residuals

Answer

Linearity

Answer

Independence of errors

Answer

Homoscedasticity

Question 50

What range of values does Pearson's correlation coefficient (r) typically fall within?

Accepted Answer

-1 to 1

Answer

-0.5 to 0.5

Answer

0 to 1

Answer

0 to 2

Question 51

In a positive correlation, as the value of one variable increases, what is the general trend for the value of the other variable?

Accepted Answer

Increases

Answer

Decreases

Answer

Stays the same

Answer

Varies randomly

Question 52

Which of the following best describes the slope of a regression line?

Accepted Answer

The change in the dependent variable for every one-unit change in the independent variable

Answer

The mean difference between the independent and dependent variables

Answer

The correlation coefficient between the variables

Answer

The y-intercept of the regression line

Question 53

In a nursing research study, a strong positive correlation was found between the number of hours of sleep patients get and their reported pain levels. What does this suggest?

Accepted Answer

Patients who sleep fewer hours typically experience higher pain levels.

Answer

Patients who sleep more hours typically experience higher pain levels.

Answer

There is no apparent relationship between sleep duration and pain levels.

Answer

The relationship between sleep duration and pain levels is negative.

Question 54

What is the primary purpose of using a scatterplot in correlation analysis?

Accepted Answer

To visually represent the relationship between two variables

Answer

To calculate the exact value of the Pearson's correlation coefficient

Answer

To determine the equation of the regression line

Answer

To identify potential outliers in the data

Question 55

In a correlation test, what is the null hypothesis typically used?

Accepted Answer

There is no significant correlation between the variables.

Answer

There is a significant correlation between the variables.

Answer

The slope of the regression line is equal to 0.

Answer

The y-intercept of the regression line is equal to 0.

Question 56

A study investigates the relationship between exercise frequency and cardiovascular health and finds a weak negative correlation. What does this generally imply?

Accepted Answer

Individuals who exercise less frequently tend to have poorer cardiovascular health.

Answer

Individuals who exercise more frequently tend to have poorer cardiovascular health.

Answer

There is no apparent relationship between exercise frequency and cardiovascular health.

Answer

The relationship between exercise frequency and cardiovascular health is positive.

Question 57

A p-value less than 0.05 in a Pearson's correlation analysis suggests:

Accepted Answer

A statistically significant correlation, rejecting the null hypothesis of no correlation.

Answer

No statistically significant correlation, failing to reject the null hypothesis of no correlation.

Answer

A moderate correlation, with no definitive conclusion about the null hypothesis.

Answer

A strong correlation, indicating a perfect relationship between the variables.

Question 58

Which of the following is the most precise formula for calculating Pearson's correlation coefficient?

Accepted Answer

r = (Σ(X - X̄)(Y - Ȳ)) / √(Σ(X - X̄)²Σ(Y - Ȳ)²)

Answer

r = (Σ(X + X̄)(Y + Ȳ)) / √(Σ(X + X̄)²Σ(Y + Ȳ)²)

Answer

r = (Σ(X - Y)² / Σ(X - X̄)²Σ(Y - Ȳ)²)

Answer

r = (Σ(X + Y)² / Σ(X + X̄)²Σ(Y + Ȳ)²)

Question 59

A correlation coefficient of -0.8 indicates which type of linear relationship between the variables?

Accepted Answer

Strong and negative

Answer

Weak and positive

Answer

Absent or non-linear

Answer

Strong and positive

Question 60

In the equation for a regression line, the slope represents:

Accepted Answer

The change in the dependent variable for each unit change in the independent variable.

Answer

The value of the dependent variable when the independent variable is zero.

Answer

The strength of the relationship between the variables.

Answer

The probability of the dependent variable occurring.

Question 61

To assess the goodness-of-fit of a regression model, which statistic is typically employed?

Accepted Answer

R-squared

Answer

F-statistic

Answer

P-value

Answer

AIC

Question 62

In multiple regression, the coefficient of determination (R-squared) represents:

Accepted Answer

The proportion of variance in the dependent variable explained by the independent variables.

Answer

The strength of the linear relationship between the variables.

Answer

The probability of the dependent variable occurring.

Answer

The change in the dependent variable for each unit change in the independent variables.

Question 63

Which statistical measure quantifies the strength and direction of a linear relationship between two variables?

Accepted Answer

Pearson's correlation coefficient

Answer

Coefficient of determination

Answer

Regression coefficient

Question 64

A correlation coefficient of -0.7 indicates:

Accepted Answer

A moderately strong negative linear relationship between the variables.

Answer

No linear relationship between the variables.

Answer

A strong positive linear relationship between the variables.