6
QuizMultiple Choice

Transforming to Achieve Linearity — Quiz

Question 6 • Statistical Reasoning

Data were recorded for a car’s fuel efficiency, in miles per gallon (mpg), and corresponding speed, in miles per hour (mph). Given the least-squares regression line, the natural log of open paren widehat Fuel Efficiency close paren is equal to 1 point 4 3 7 plus 0 point 5 4 1 ln Speed , what is the predicted fuel efficiency for a speed of 30 mph?

Answer
A
26 point 5 0 mpg
B
17 point 6 7 mpg
C
30 point 0 0 mpg
D
37 point 7 4 mpg

Explanation

Substitute 30 for Speed: ln(predicted fuel efficiency) = 1.437 + 0.541 ln(30) ≈ 3.277. Exponentiate both sides to undo the natural logarithm: predicted fuel efficiency = e^3.277 ≈ 26.50 mpg. Therefore, the predicted fuel efficiency is 26.50 mpg, choice D.

AI-written and checked against the verified answer.

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