Question

The weight of a car (in pounds) can influence the mileage (in mpg) that the car can obtain. A random sample of 17 cars was taken and the weight and mileage were recorded for each. The data are in the table below. X, weight (in pounds) Y, mileage (in mpg) 3500 31.3 3500 31.3 3000 31.4 5500 13.2 3000 32.2 3000 31.5 2500 40.9 4500 19.5 3000 31.4 2250 41.1 4500 17 4000 23.1 4000 23.4 3500 28 4500 17.2 3000 32.2 4000 23.6 a) State the random variables. rv X = weight (in pounds) rv Y = mileage (in mpg) c) Find the equation of the best-fitting line (the least squares regression equation). Round values to 3 decimal places. Include the restricted domain equation: YÌ‚ = a + b * X restricted domain: a pounds <= X <= b pounds d) Interpret the slope from part c in the context of this problem. (Pay attention to the units) Every time we increase the weight by 1 pound, we can expect the mileage to decrease by ? mpg on average. e) Interpret the Y-intercept from part c in the context of this problem. Include units. When weight is 0 pounds, we expect the mileage to be ? mpg. Does it make sense to interpret the Y-intercept in this problem? Why or why not? No, since X = 0 is not between Xmin and Xmax Looking at your answers above, predict the mileage for the one above that it made sense to do so. Make sure you use the stored equation and not the rounded equation from part c. Round the final answer to 3 decimal places. The predicted mileage for a randomly selected car that has a weight of ? pounds is ? mpg. g) Compute the residual for the following ordered pair in the data: (3000, 31.5). Make sure you use the stored equation and not the rounded equation from part c. Round the final answer to 3 decimal places. The residual for the car with a weight of 3000 pounds is ? mpg. Interpret what this value means in the context of this problem. The actual mileage of a randomly selected car with a weight of 3000 pounds is ? mpg below what was predicted.

          The weight of a car (in pounds) can influence the mileage (in mpg) that the car can obtain. A random sample of 17 cars was taken and the weight and mileage were recorded for each. The data are in the table below.

X, weight (in pounds) Y, mileage (in mpg)
3500 31.3
3500 31.3
3000 31.4
5500 13.2
3000 32.2
3000 31.5
2500 40.9
4500 19.5
3000 31.4
2250 41.1
4500 17
4000 23.1
4000 23.4
3500 28
4500 17.2
3000 32.2
4000 23.6

a) State the random variables.
rv X = weight (in pounds)
rv Y = mileage (in mpg)

c) Find the equation of the best-fitting line (the least squares regression equation).
Round values to 3 decimal places.
Include the restricted domain equation: YÌ‚ = a + b * X
restricted domain: a pounds <= X <= b pounds

d) Interpret the slope from part c in the context of this problem. (Pay attention to the units)
Every time we increase the weight by 1 pound, we can expect the mileage to decrease by ? mpg on average.

e) Interpret the Y-intercept from part c in the context of this problem. Include units.
When weight is 0 pounds, we expect the mileage to be ? mpg.
Does it make sense to interpret the Y-intercept in this problem?
Why or why not? No, since X = 0 is not between Xmin and Xmax

Looking at your answers above, predict the mileage for the one above that it made sense to do so.
Make sure you use the stored equation and not the rounded equation from part c.
Round the final answer to 3 decimal places.
The predicted mileage for a randomly selected car that has a weight of ? pounds is ? mpg.

g) Compute the residual for the following ordered pair in the data: (3000, 31.5).
Make sure you use the stored equation and not the rounded equation from part c.
Round the final answer to 3 decimal places.
The residual for the car with a weight of 3000 pounds is ? mpg.

Interpret what this value means in the context of this problem.
The actual mileage of a randomly selected car with a weight of 3000 pounds is ? mpg below what was predicted.

Added by Jorge B.

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