Price per square foot declines as homes get larger. What does this imply for a linear regression of price on area?
Correct Answer
C) A straight line may not describe it adequately
Why this is correct: If price per square foot declines as size increases, the relationship between total price and area is not linear (a straight line). A linear regression assumes a constant rate of change, which would misrepresent this curved relationship. Why the other choices are wrong: "The model will fit the relationship perfectly" is false; a straight line cannot perfectly fit a curved pattern. "Area should be removed from the model entirely" is wrong; area is relevant, but the model form needs adjustment. "The dependent variable has been misidentified" is incorrect; price is the correct dependent variable. Exam tip: A declining unit rate (price per SF) signals non-linearity. Consider transformations or segmented analysis.
Why This Is the Correct Answer
Why this is correct: If price per square foot declines as size increases, the relationship between total price and area is not linear (a straight line). A linear regression assumes a constant rate of change, which would misrepresent this curved relationship. Why the other choices are wrong: "The model will fit the relationship perfectly" is false; a straight line cannot perfectly fit a curved pattern. "Area should be removed from the model entirely" is wrong; area is relevant, but the model form needs adjustment. "The dependent variable has been misidentified" is incorrect; price is the correct dependent variable. Exam tip: A declining unit rate (price per SF) signals non-linearity. Consider transformations or segmented analysis.
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