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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.

Weight and gas mileage data:

WieghtMiles per Gallon

379918
387715
271024
358218
333720
298423
374216
256624
337320
369616
339219

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. LOADING... Click here to view the weight and gas mileage data.

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

b) Interpret the slope and y-intercept, if appropriate. Choose the correct answer below and fill in any answer boxes in your choice:
For every pound added to the weight of the car, gas mileage in the city will decrease by _________ mile(s) per gallon, on average.

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?

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?

Respuesta :

Answer:

A. For every pound added to the weight of the​ car, gas mileage in the city will decrease by

0.005920.00592 ​mile(s) per​ gallon, on average. It is not appropriate to interpret the​ y-intercept

​(c) ABOVE

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

Step-by-step explanation:

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  • The least square regression equation for the relationship between Weight and miles per gallon is Ŷ = 42.7911 - 0.006954X

  • The negative slope value means that ; gas mileage will decrease by 0.006954 on average per increase in weight in pounds of car.

  • Miles per gallon of the car is within the average value for cars weighing 3700

  • Weight__Miles per Gallon

  • 3799___18
  • 3877___15
  • 2710___24
  • 3582___18
  • 3337___20
  • 2984___23
  • 3742___16
  • 2566___24
  • 3373___20
  • 3696___16
  • 3392___19

Using excel or a linear regression calculator ; the least - square regression equation obtained from the data is :

  • Ŷ = 42.7911 - 0.006954X

Recall the least square regression equation formula :

  • Ŷ = c + bx
  • c = intercept = 42.7911
  • b = slope = rate of change  - 0.006954

  • For every pound added in weight, miles per gallon decreases by 0.006954 (slope value)

C.)

  • Weight(x) = 3700 ; miles per gallon(y) = 17
  • Using the regression equation, let's predict the miles per gallon for a car with weight x = 3700

  • Ŷ = 42.7911-0.006954(3700)
  • Ŷ = 17.0613

  • We can conclude that, the miles per gallon of this vehicle is within range for cars of its weight since the predicted value of miles per gallon is also approximately 17.

D.)

  • The hybrid gas and electric vehicle are different type of vehicle and hence, will require it's own specific data in other to make prediction.

Learn more :https://brainly.com/question/18405415

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