Do heavier cars use more gasoline? To answer this question,a researcher randomly selected 15 cars.He collected their weight (in hundreds of pounds) and the mileage (MPG) for each car.From a scatter plot made with the data,a linear model seemed appropriate.The following output was obtained from SPSS: Which of the following descriptions of the value of the slope is the correct description?

A) We cannot interpret the slope because we cannot have a negative weight of a car.
B) We estimate the mileage to decrease by 0.521 miles per gallon when the weight of a car increases by 1 pound.
C) We estimate the mileage to decrease by 0.521 miles per gallon when the weight of a car increases by 100 pounds.
D) We estimate the mileage to decrease by 52.1 miles per gallon when the weight of a car increases by 100 pounds.

Question

Do heavier cars use more gasoline? To answer this question,a researcher randomly selected 15 cars.He collected their weight (in hundreds of pounds) and the mileage (MPG) for each car.From a scatter plot made with the data,a linear model seemed appropriate.The following output was obtained from SPSS:

Which of the following descriptions of the value of the slope is the correct description?

A) We cannot interpret the slope because we cannot have a negative weight of a car.
B) We estimate the mileage to decrease by 0.521 miles per gallon when the weight of a car increases by 1 pound.
C) We estimate the mileage to decrease by 0.521 miles per gallon when the weight of a car increases by 100 pounds.
D) We estimate the mileage to decrease by 52.1 miles per gallon when the weight of a car increases by 100 pounds.

Puneeta sharma · Accepted Answer

Final Answer : C, Explanation :  The slope coefficient in the SPSS output is -0.521. This means that for every 100 pounds increase in weight, we estimate the mileage to decrease by -0.521 miles per gallon. Therefore, option C is the correct description of the value of the slope. Option A is incorrect because negative weight does not exist. Option B and D are incorrect because they do not account for the weight being measured in hundreds of pounds.

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