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, , what is the fuel efficiency for a speed of 60 mph?

3.65 mpg
33.90 mpg
36.52 mpg
38.55 mpg

The least-squares regression line equation gives the line that approximate the relationship between the variables in the fuel efficiency data

The fuel efficiency when the speed is 60 mph is approximately 38.55 mpg.

Reason:

The given least-squares regression line equation is presented as follows;

ln(Fuel Efficiency) = 1.437 + 0.541 × ln(speed)

Required:

The value of the fuel efficiency for a speed of 60 mph.

Solution:

The general form of the least-squares regression line equation is [tex]\hat y[/tex] = a + b·x

Where, in the current question, we have;

[tex]\hat y[/tex] = The predicted value = ln(Fuel Efficiency)

a = The y-intercept = 1.437

b = The slope = 0.541

x = The input value = ln(speed)

When the speed = 60 mph, we have;

ln(Fuel Efficiency) = 1.437 + 0.541 × ln(60) = 3.65204040816

Therefore;

[tex]Fuel \ Efficiency = e^{(1.437 + 0.541 \times ln(60))} \approx 38.55[/tex]

The fuel efficiency when the speed is 60 mph ≈ 38.55 miles per gallon

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Answer:

the person above me is correct.

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