Question

An engineer wants to determine how the weight of a gas-powered car, x, affects gas mileage, y. The accompanying data represent the weights of various domestic cars and their miles per gallon in the city for the most recent model year. Complete parts (a) through (d) below.

Click here to view the weight and gas mileage data.

Weight (pounds), x	Miles per Gallon, y
3711	16
3828	17
2625	24
3648	19
3313	21
2914	24
3786	17
2694	23
3405	19
3768	18
3284	17

(a) Find the least-squares regression line treating weight as the explanatory variable and miles per gallon as the response variable.

^y=  __________x +____________(Round the x coefficient to five decimal places as needed. Round the constant to two decimal places as needed.)

(b) Interpret the slope and y-intercept, if appropriate. Choose the correct answer below and fill in any answer boxes in your choice.

(Use the answer from part a to find this answer.)

A. A weightless car will get __________ miles per gallon, on average. It is not appropriate to interpret the slope.

B. For every pound added to the weight of the car, gas mileage in the city will decrease by________mile(s) per gallon, on average. It is not appropriate to interpret the y-intercept.

C. For every pound added to the weight of the car, gas mileage in the city will decrease by_________mile(s) per gallon, on average. A weightless car will get                                  

_____________ miles per gallon, on average.

D. It is not appropriate to interpret the slope or the y-intercept.

(c) A certain gas-powered car weighs 3700 pounds and gets 17 miles per gallon. Is the miles per gallon of this car above average or below average for cars of this weight?

A.    Above

B.    Below

(d) Would it be reasonable to use the least-squares regression line to predict the miles per gallon of a hybrid gas and electric car? Why or why not?

A. Yes, because the absolute value of the correlation coefficient is greater than the critical value for a sample size of n = 11.

B. No, because the hybrid is a different type of car.

C. Yes, because the hybrid is partially powered by gas.

D. No, because the absolute value of the correlation coefficient is less than the critical value for a sample size of n = 11.

Answer 1

Answer a) y = -0.006*x + 39.67

Answer b)

B. For every pound added to the weight of the car, gas mileage in the city will decrease by 0.006 mile(s) per gallon, on average. It is not appropriate to interpret the y-intercept.

Answer c)

For a car weighted 3700 pounds, average miles per gallon can be obtained using regression equaiton:

y = -0.006*x + 39.67

y = -0.006*3700 + 39.67

y = 17.47

Since gas-powered car weighs 3700 pounds and gets 17 miles per gallon which is lower than average 17.47. Thus, miles per gallon of this car is below average (Option B is correct)

Answer d) Option B is correct

No, it would not be not reasonable to use the least-squares regression line to predict the miles per gallon of a hybrid gas and electric car. This is because the hybrid is a different type of car. The data used for deriving regression equation belongs to gas-powered car.