We expect a car\'s highway gas mileage to be related to its city gas mileage. Da

Question

We expect a car's highway gas mileage to be related to its city gas mileage. Data for all 1198 vehicles in the government's 2008 Fuel Economy Guide gives the following regression line: highway mpg = 4.62 + (1.109 X city mpg) for predicting highway mileage from city mileage.

What is the slope of this line? Give your answer to 3 decimal places.

Say in words what the numerical value of the slope tells us.

On the average, highway mileage increases by 4.62 mpg for each additional mpg in city mileage.

On the average, highway mileage increases by 1.109 mpg for each additional mpg in city mileage.

On the average, highway mileage decreases by 1.109 mpg for each additional mpg in city mileage.

What is the intercept? Give your answer in mpg's to 2 decimal places.

Explain why the value of the intercept is not statistically meaningful.

Because this is the highway mileage for slope 0.

Because this is the highway mileage for zero city mpg.

Because this is an average value, calculated from a sample.

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Explanation / Answer

Here the equation is mpg = 4.62 + (1.109 X city mpg)

As we know the equation for regression is y=intercept+slope*x

Hence here slope is positive value 1.109 so the answer is as below:

On the average, highway mileage increases by 1.109 mpg for each additional mpg in city mileage.

Here the intercept is 4.62

Because this is the highway mileage for slope 0.

Now for x=16 we get mpg = 4.62 + (1.109 X 16) =22.36

Now for x=28, we get mpg = 4.62 + (1.109 X 28) =35.67

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