MATH 110 Exam 8 Statistics Questions and Answers Portage Learning Actual Exam
2026/2027 – Complete 25 Questions with Detailed Rationales | 100% Verified | Pass
Guaranteed – A+ Graded
Section A: Correlation & Scatterplots
Q1: A scatterplot of weekly study hours (x) versus exam scores (y) shows points rising
steadily from the lower-left to the upper-right of the graph. Which description best
characterizes this association?
A. Negative linear association
B. Positive linear association [CORRECT]
C. No association
D. Curvilinear association
Correct Answer: B
Rationale: Points trending upward from left to right indicate that as x increases, y tends
to increase—a positive linear association. A negative association would trend
downward, and a curvilinear pattern would bend rather than follow a straight-line trend.
Q2: Which statement about the correlation coefficient r is NOT true?
A. r is always a value between −1 and +1
B. r measures both the strength and direction of a linear association
C. r remains unchanged if the roles of x and y are swapped
D. r changes value when the units of measurement of x are changed (e.g., from inches
to centimeters) [CORRECT]
Correct Answer: D
Rationale: r is a unitless measure, so converting units does not affect its value, making
statement D false. Options A, B, and C are all true properties of the correlation
coefficient.
Q3: A researcher computes a correlation of r = 0.92 between adult height and weight for
a sample of 50 adults. Which interpretation is correct?
A. There is a strong positive linear relationship between height and weight [CORRECT]
B. There is a weak negative linear relationship
C. There is no linear relationship between the variables
D. There is a perfect positive relationship, with every point exactly on a line
Correct Answer: A
, Rationale: A value of 0.92 is close to +1, indicating a strong positive linear association.
Options B and C contradict the sign and magnitude, and a perfect relationship would
require r = 1.00 exactly.
Q4: A study finds r = 0.85 between monthly ice cream sales and drowning deaths. What
is the most appropriate conclusion?
A. Ice cream consumption causes drowning, so sales should be restricted
B. Drowning deaths cause survivors to purchase more ice cream
C. The association is likely explained by a lurking (confounding) variable such as hot
summer weather; correlation does not imply causation [CORRECT]
D. Since r = 0.85, the causal relationship between the variables is proven
Correct Answer: C
Rationale: High correlation alone cannot establish causation, and a third
variable—summer heat—plausibly drives both ice cream sales and swimming (and thus
drownings). Options A, B, and D all commit the classic correlation-equals-causation
error.
Q5: A statistics student computes r = 0.03 between engine size and fuel efficiency... but
a scatterplot of the same data shows a strong, clear curved (U-shaped) pattern. What is
the best interpretation?
A. No relationship of any kind exists between the two variables
B. There is essentially no linear relationship, but a strong nonlinear (curved) relationship
can still exist, since r only measures linear association [CORRECT]
C. The variables must have a strong negative linear relationship
D. The correlation coefficient was definitely calculated incorrectly
Correct Answer: B
Rationale: r measures only linear association, so r near zero is compatible with a strong
curvilinear relationship. Option A overstates the conclusion, C contradicts the near-zero
value, and the calculation can be correct while r fails to capture curvature.
Section B: Simple Linear Regression & Least-Squares Line
Q6: The least-squares regression line is defined as the line that:
A. Minimizes the sum of the squared vertical distances (residuals) between the
observed data points and the line [CORRECT]
B. Minimizes the sum of the residuals themselves
C. Passes through every observed data point in the sample
2026/2027 – Complete 25 Questions with Detailed Rationales | 100% Verified | Pass
Guaranteed – A+ Graded
Section A: Correlation & Scatterplots
Q1: A scatterplot of weekly study hours (x) versus exam scores (y) shows points rising
steadily from the lower-left to the upper-right of the graph. Which description best
characterizes this association?
A. Negative linear association
B. Positive linear association [CORRECT]
C. No association
D. Curvilinear association
Correct Answer: B
Rationale: Points trending upward from left to right indicate that as x increases, y tends
to increase—a positive linear association. A negative association would trend
downward, and a curvilinear pattern would bend rather than follow a straight-line trend.
Q2: Which statement about the correlation coefficient r is NOT true?
A. r is always a value between −1 and +1
B. r measures both the strength and direction of a linear association
C. r remains unchanged if the roles of x and y are swapped
D. r changes value when the units of measurement of x are changed (e.g., from inches
to centimeters) [CORRECT]
Correct Answer: D
Rationale: r is a unitless measure, so converting units does not affect its value, making
statement D false. Options A, B, and C are all true properties of the correlation
coefficient.
Q3: A researcher computes a correlation of r = 0.92 between adult height and weight for
a sample of 50 adults. Which interpretation is correct?
A. There is a strong positive linear relationship between height and weight [CORRECT]
B. There is a weak negative linear relationship
C. There is no linear relationship between the variables
D. There is a perfect positive relationship, with every point exactly on a line
Correct Answer: A
, Rationale: A value of 0.92 is close to +1, indicating a strong positive linear association.
Options B and C contradict the sign and magnitude, and a perfect relationship would
require r = 1.00 exactly.
Q4: A study finds r = 0.85 between monthly ice cream sales and drowning deaths. What
is the most appropriate conclusion?
A. Ice cream consumption causes drowning, so sales should be restricted
B. Drowning deaths cause survivors to purchase more ice cream
C. The association is likely explained by a lurking (confounding) variable such as hot
summer weather; correlation does not imply causation [CORRECT]
D. Since r = 0.85, the causal relationship between the variables is proven
Correct Answer: C
Rationale: High correlation alone cannot establish causation, and a third
variable—summer heat—plausibly drives both ice cream sales and swimming (and thus
drownings). Options A, B, and D all commit the classic correlation-equals-causation
error.
Q5: A statistics student computes r = 0.03 between engine size and fuel efficiency... but
a scatterplot of the same data shows a strong, clear curved (U-shaped) pattern. What is
the best interpretation?
A. No relationship of any kind exists between the two variables
B. There is essentially no linear relationship, but a strong nonlinear (curved) relationship
can still exist, since r only measures linear association [CORRECT]
C. The variables must have a strong negative linear relationship
D. The correlation coefficient was definitely calculated incorrectly
Correct Answer: B
Rationale: r measures only linear association, so r near zero is compatible with a strong
curvilinear relationship. Option A overstates the conclusion, C contradicts the near-zero
value, and the calculation can be correct while r fails to capture curvature.
Section B: Simple Linear Regression & Least-Squares Line
Q6: The least-squares regression line is defined as the line that:
A. Minimizes the sum of the squared vertical distances (residuals) between the
observed data points and the line [CORRECT]
B. Minimizes the sum of the residuals themselves
C. Passes through every observed data point in the sample
