MATH 110 Module 10 Exam Correlation Regression & Chi-Square Tests Actual
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Section A: Correlation & Scatterplots (Q1–Q5)
Q1: Which of the following statements correctly describes the correlation coefficient r?
A. r measures only the strength, but never the direction, of a relationship
B. r is a value that always ranges from −1 to +1 and measures the strength and direction
of a linear relationship [CORRECT]
C. r can take any value between 0 and 100
D. r equals the slope of the regression line
Correct Answer: B
Rationale: The correlation coefficient r always lies between −1 and +1, describing both
the direction and strength of a linear association. Values outside this range, restriction
to strength only, or equating r with slope are all incorrect.
Q2: A researcher collects data on weekly study hours (x) and exam scores (y) for 40
students and computes r = 0.85. Which interpretation is correct?
A. There is a strong positive linear association; students who study more hours tend to
earn higher exam scores [CORRECT]
B. Studying more hours causes higher exam scores
C. There is a weak negative linear association between the variables
D. 85% of the variation in exam scores is explained by study hours
Correct Answer: A
Rationale: An r of 0.85 indicates a strong positive linear relationship, meaning the
variables increase together. The statement commits a causation error, and 85%
confuses r with r², which would be about 72%.
Q3: A study finds r = 0.87 between ice cream sales and drowning deaths per month.
Which is the best analysis of this result?
A. Ice cream consumption directly causes drowning
B. The correlation must be a calculation error
C. A third variable, such as hot summer weather, likely drives both ice cream sales and
swimming (and thus drownings), so correlation does not establish causation
[CORRECT]
, D. The variables are unrelated because no cause is stated
Correct Answer: C
Rationale: A strong correlation without experimentation suggests a possible
lurking/confounding variable—here, hot weather increases both swimming and ice
cream purchases. Direct causation cannot be inferred, a high r is not an error, and a
strong correlation does indicate a real association.
Q4: A retailer records product price (x) in dollars and weekly units demanded (y) and
obtains r = −0.92. Which interpretation is correct?
A. There is a weak negative linear association
B. Price and demand are unrelated
C. There is a strong positive linear association
D. There is a strong negative linear association; as price increases, weekly demand
tends to decrease [CORRECT]
Correct Answer: D
Rationale: The negative sign indicates an inverse direction and the magnitude 0.92
indicates a very strong linear relationship. Calling the association weak or positive
misreads the sign and magnitude.
Q5: Which of the following correlation coefficients indicates the strongest linear
relationship between two variables?
A. r = 0.70
B. r = −0.85 [CORRECT]
C. r = 0.10
D. r = 0.65
Correct Answer: B
Rationale: Strength is judged by the absolute value of r, and |−0.85| = 0.85 exceeds all
the other magnitudes. The negative sign describes direction only, not weaker strength.
Section B: Simple Linear Regression & Least-Squares Line (Q6–Q10)
Q6: The least-squares regression line is defined as the line that minimizes which
quantity?
A. The sum of the residuals
B. The correlation coefficient between x and y
C. The sum of the squared vertical distances (residuals) between observed values and
the line [CORRECT]
Exam 2026/2027 – Complete Test Bank with Detailed Rationales | 100% Verified |
Pass Guaranteed – A+ Graded
Section A: Correlation & Scatterplots (Q1–Q5)
Q1: Which of the following statements correctly describes the correlation coefficient r?
A. r measures only the strength, but never the direction, of a relationship
B. r is a value that always ranges from −1 to +1 and measures the strength and direction
of a linear relationship [CORRECT]
C. r can take any value between 0 and 100
D. r equals the slope of the regression line
Correct Answer: B
Rationale: The correlation coefficient r always lies between −1 and +1, describing both
the direction and strength of a linear association. Values outside this range, restriction
to strength only, or equating r with slope are all incorrect.
Q2: A researcher collects data on weekly study hours (x) and exam scores (y) for 40
students and computes r = 0.85. Which interpretation is correct?
A. There is a strong positive linear association; students who study more hours tend to
earn higher exam scores [CORRECT]
B. Studying more hours causes higher exam scores
C. There is a weak negative linear association between the variables
D. 85% of the variation in exam scores is explained by study hours
Correct Answer: A
Rationale: An r of 0.85 indicates a strong positive linear relationship, meaning the
variables increase together. The statement commits a causation error, and 85%
confuses r with r², which would be about 72%.
Q3: A study finds r = 0.87 between ice cream sales and drowning deaths per month.
Which is the best analysis of this result?
A. Ice cream consumption directly causes drowning
B. The correlation must be a calculation error
C. A third variable, such as hot summer weather, likely drives both ice cream sales and
swimming (and thus drownings), so correlation does not establish causation
[CORRECT]
, D. The variables are unrelated because no cause is stated
Correct Answer: C
Rationale: A strong correlation without experimentation suggests a possible
lurking/confounding variable—here, hot weather increases both swimming and ice
cream purchases. Direct causation cannot be inferred, a high r is not an error, and a
strong correlation does indicate a real association.
Q4: A retailer records product price (x) in dollars and weekly units demanded (y) and
obtains r = −0.92. Which interpretation is correct?
A. There is a weak negative linear association
B. Price and demand are unrelated
C. There is a strong positive linear association
D. There is a strong negative linear association; as price increases, weekly demand
tends to decrease [CORRECT]
Correct Answer: D
Rationale: The negative sign indicates an inverse direction and the magnitude 0.92
indicates a very strong linear relationship. Calling the association weak or positive
misreads the sign and magnitude.
Q5: Which of the following correlation coefficients indicates the strongest linear
relationship between two variables?
A. r = 0.70
B. r = −0.85 [CORRECT]
C. r = 0.10
D. r = 0.65
Correct Answer: B
Rationale: Strength is judged by the absolute value of r, and |−0.85| = 0.85 exceeds all
the other magnitudes. The negative sign describes direction only, not weaker strength.
Section B: Simple Linear Regression & Least-Squares Line (Q6–Q10)
Q6: The least-squares regression line is defined as the line that minimizes which
quantity?
A. The sum of the residuals
B. The correlation coefficient between x and y
C. The sum of the squared vertical distances (residuals) between observed values and
the line [CORRECT]
