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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