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Logarithmic Transformation:

Speed vs. Miles per Gallon

APSTAT-EMJBL0

A consumer report gave the following regression equation on the relationship between the speed ($S$) in miles per hour and the average miles per gallon at that speed ($a$) for a particular car:

$$\widehat {\log (a)} =0.971+0.363\cdot\log (s)$$

Which of the following is closest to the predicted average miles per gallon when the speed of the car is $45$ miles per hour?

A

$1.571$

B

$1.879$

C

$4.811$

D

$28.642$

E

$37.239$