DNP 816 NKU QUIZ 3 EXAMS QUESTIONS AND
CORRECT ANSWERS |2026|2027|UPDATES |WITH
COMPLETE SOLUTIONS.
Questions 1–50: Correlation and Pearson's r
1. What is the primary purpose of Pearson's correlation coefficient?
A) To predict one variable from another
B) To measure the strength and direction of a linear relationship between two
continuous variables
C) To compare means between two groups
D) To assess categorical data association
Correct Answer: B
Rationale: Pearson's r quantifies both the strength (magnitude) and direction
(positive/negative) of a linear relationship between two continuous variables.
2. A Pearson r of -0.85 indicates:
A) A weak negative relationship
B) A strong negative relationship
C) No relationship
D) A moderate positive relationship
Correct Answer: B
,Rationale: The absolute value of 0.85 is close to 1.0, indicating a strong
relationship; the negative sign indicates an inverse direction.
3. The coefficient of determination (r²) for r = 0.60 is:
A) 0.36
B) 0.60
C) 0.77
D) 0.40
Correct Answer: A
Rationale: r² = 0.60² = 0.36, meaning 36% of the variance in one variable is
explained by the other.
4. Which r value represents the weakest linear relationship?
A) -0.90
B) 0.10
C) -0.50
D) 0.75
Correct Answer: B
Rationale: 0.10 has the smallest absolute value, indicating the weakest linear
relationship.
5. A scatter plot with points forming a perfect straight line ascending from left to
right has r =:
A) -1.0
,B) 0
C) +1.0
D) +0.5
Correct Answer: C
Rationale: A perfect positive linear slope yields r = +1.0.
6. Which assumption is NOT required for Pearson's r?
A) Linear relationship
B) Normal distribution of both variables
C) Homoscedasticity
D) Categorical variables
Correct Answer: D
Rationale: Pearson's r requires continuous variables, not categorical.
7. If r = 0.0, the best conclusion is:
A) There is no relationship between the variables
B) There is no linear relationship between the variables
C) The variables are independent
D) The correlation is perfect
Correct Answer: B
Rationale: r = 0 means no linear relationship, but a nonlinear relationship may
exist.
, 8. A positive correlation means:
A) As X increases, Y decreases
B) As X increases, Y increases
C) X causes Y
D) There is no relationship
Correct Answer: B
Rationale: Positive direction means both variables move in the same direction.
9. The range of Pearson's r is:
A) 0 to +1
B) -1 to +1
C) -∞ to +∞
D) 0 to 100
Correct Answer: B
Rationale: Pearson's r is bounded between -1.0 and +1.0 inclusive.
10. An r² of 0.81 means that _____% of the variance is explained.
A) 81
B) 9
C) 90
D) 18
Correct Answer: A
Rationale: r² is the proportion of explained variance, expressed as a percentage.
CORRECT ANSWERS |2026|2027|UPDATES |WITH
COMPLETE SOLUTIONS.
Questions 1–50: Correlation and Pearson's r
1. What is the primary purpose of Pearson's correlation coefficient?
A) To predict one variable from another
B) To measure the strength and direction of a linear relationship between two
continuous variables
C) To compare means between two groups
D) To assess categorical data association
Correct Answer: B
Rationale: Pearson's r quantifies both the strength (magnitude) and direction
(positive/negative) of a linear relationship between two continuous variables.
2. A Pearson r of -0.85 indicates:
A) A weak negative relationship
B) A strong negative relationship
C) No relationship
D) A moderate positive relationship
Correct Answer: B
,Rationale: The absolute value of 0.85 is close to 1.0, indicating a strong
relationship; the negative sign indicates an inverse direction.
3. The coefficient of determination (r²) for r = 0.60 is:
A) 0.36
B) 0.60
C) 0.77
D) 0.40
Correct Answer: A
Rationale: r² = 0.60² = 0.36, meaning 36% of the variance in one variable is
explained by the other.
4. Which r value represents the weakest linear relationship?
A) -0.90
B) 0.10
C) -0.50
D) 0.75
Correct Answer: B
Rationale: 0.10 has the smallest absolute value, indicating the weakest linear
relationship.
5. A scatter plot with points forming a perfect straight line ascending from left to
right has r =:
A) -1.0
,B) 0
C) +1.0
D) +0.5
Correct Answer: C
Rationale: A perfect positive linear slope yields r = +1.0.
6. Which assumption is NOT required for Pearson's r?
A) Linear relationship
B) Normal distribution of both variables
C) Homoscedasticity
D) Categorical variables
Correct Answer: D
Rationale: Pearson's r requires continuous variables, not categorical.
7. If r = 0.0, the best conclusion is:
A) There is no relationship between the variables
B) There is no linear relationship between the variables
C) The variables are independent
D) The correlation is perfect
Correct Answer: B
Rationale: r = 0 means no linear relationship, but a nonlinear relationship may
exist.
, 8. A positive correlation means:
A) As X increases, Y decreases
B) As X increases, Y increases
C) X causes Y
D) There is no relationship
Correct Answer: B
Rationale: Positive direction means both variables move in the same direction.
9. The range of Pearson's r is:
A) 0 to +1
B) -1 to +1
C) -∞ to +∞
D) 0 to 100
Correct Answer: B
Rationale: Pearson's r is bounded between -1.0 and +1.0 inclusive.
10. An r² of 0.81 means that _____% of the variance is explained.
A) 81
B) 9
C) 90
D) 18
Correct Answer: A
Rationale: r² is the proportion of explained variance, expressed as a percentage.
