A price-versus-living-area scatter plot shows a tight, approximately straight upward pattern. What does it suggest in this sample?
Correct Answer
A) A strong positive relationship between the two
A tight upward approximately straight pattern supports a strong positive linear association in the observed sample. It does not prove that area causes all price differences, eliminate confounding or verify the recorded facts. A negative association would slope downward. Association in this sample also does not establish applicability to another market.
Why This Is the Correct Answer
Option A is correct because a tight, approximately straight upward pattern shows that price tends to rise as living area rises, with little scatter around the line. That indicates a strong positive linear relationship between the two variables in this sample.
Why the Other Options Are Wrong
Option B: That living area does not influence sale price
Option B says living area does not influence sale price, but the plot shows the opposite pattern: a strong positive association in which price rises consistently with area. A plot alone does not prove causation, but a lack of relationship would appear as scattered points with no clear trend.
Option C: That the sample contains a recording error
Option C says the sample contains a recording error, but a tight, consistent pattern gives no sign of an error. A recording error would more likely appear as an isolated point far from the pattern.
Option D: A negative relationship between the variables
Option D describes a negative relationship, which would slope downward as area increases. The plot slopes upward, indicating a positive relationship.
Uphill Means Positive
Read the plot left to right: uphill is positive, downhill is negative, and a tight band means a strong relationship.
How to use: Use this left-to-right reading whenever a question describes a scatter plot pattern.
Exam Tip
Separate what a scatter plot shows (direction and strength of association) from what it does not prove (causation or data accuracy).
Common Mistakes to Avoid
- -Treating a strong association as proof of causation
- -Misreading the slope direction
- -Assuming the pattern applies to a different market
Concept Deep Dive
Analysis
This question tests reading a scatter plot. A tight, roughly straight upward pattern indicates a strong positive linear association between the plotted variables in the sample. It describes association, not causation or data accuracy.
Background Knowledge
A scatter plot places one variable on each axis to show their relationship. The direction of the pattern shows whether the association is positive or negative, and how tightly points cluster around a line indicates its strength, which the correlation coefficient measures numerically.
Real-World Application
An appraiser plots 40 recent neighborhood sales by price and living area and sees a tight upward band. This supports using living area as a key variable in further analysis, though the appraiser still considers other features that may move with size.
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Previous Question
The arithmetic mean is $480,000 and sample standard deviation is $36,000. Compute the coefficient of variation s/mean × 100, expressed as a percentage. Report three decimals.
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