The weight of a car (in pounds) can influence the mileage (in mpg) that the car can obtain. A random sample of 19 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) 2750 36.3 3000 31.5 3500 32.6 3500 31.3 2250 38.9 4500 17.2 5500 13.2 3000 32.2 3000 31.4 2750 46.9 2250 53.3 2250 41.1 3000 32.2 4000 23.6 4000 23.4 3500 28 4500 19.5 4000 23.1 3500 28 a) State the random variables. rv X = of rv Y = of b) Make a scatterplot of X versus Y in StatCrunch (optional). Why do we wish to sketch a scatterplot? 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: = + * X restricted domain: pounds <= X <= pounds
The weight of a car (in pounds) can influence the mileage (in mpg) that the car can obtain. A random sample of 19 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) |
|---|---|
| 2750 | 36.3 |
| 3000 | 31.5 |
| 3500 | 32.6 |
| 3500 | 31.3 |
| 2250 | 38.9 |
| 4500 | 17.2 |
| 5500 | 13.2 |
| 3000 | 32.2 |
| 3000 | 31.4 |
| 2750 | 46.9 |
| 2250 | 53.3 |
| 2250 | 41.1 |
| 3000 | 32.2 |
| 4000 | 23.6 |
| 4000 | 23.4 |
| 3500 | 28 |
| 4500 | 19.5 |
| 4000 | 23.1 |
| 3500 | 28 |
a) State the random variables.
rv X = of
rv Y = of
b) Make a scatterplot of X versus Y in StatCrunch (optional). Why do we wish to sketch a scatterplot?
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: = + * X
restricted domain: pounds <= X <= pounds
d) Interpret the slope from part c in the context of this problem. (Pay attention to the units)
- Every time we increase by we can expect to by on average.
e) Interpret the Y-intercept from part c in the context of this problem. Include units.
- When is , we expect to be
Does it make sense to interpret the Y-intercept on this problem?
Why or why not?
f) Should you use the regression equation to predict the mileage of a randomly selected car that has a weight of 5369 pounds?
Should you use the regression equation to predict the mileage of a randomly selected car that has a weight of 7400 pounds?
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 final answer to 3 decimal places.
- The predicted mileage for a randomly selected car that has a weight of pounds is
g) Compute the residual for the following ordered pair in the data: (3000, 32.2).
Make sure you use the stored equation and not the rounded equation from part c.
Round final answer to 3 decimal places.
The residual for the car with a weight of 3000 pounds is
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 what was predicted.
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