The table shows the advertised horsepower ratings and expected gas mileage for several 2012 vehicles as reported by Kelley Blue Book.

Question

Vehicle Horsepower Gas Mileage (MPG)
Acura MDX 300 21
Chevy Sonic 138 35
Porsche Panamera 500 26
Lincoln MKS 263 27
Subaru Impreza 265 36
Mazda 5 157 28
Honda Civic 140 41
Ford Flex 262 24
Toyota FJ Cruiser 260 20
Nissan 370Z 350 26
Fiat 500 101 38
GMC Acadia 288 24
Chevy Silverado 1500 403 22
Toyota Tacoma 236 25
Ford Expedition 310 20
The linear function f(x) = -0.0308x + 37.701 can be fit to the scatter plot below. The residual plot is also shown.
Complete the statement.

Using the model, the predicted gas mileage for the Toyota Tacoma is (25, 30.4322, or 44.9698)
so the residual value for this vehicle is (0, 5.4322, -5.4322, 19.9698 or -19.9698)

Answer 1

To find the predicted gas mileage for the Toyota Tacoma using the given model \( f(x) = -0.0308x + 37.701 \), we need to plug the horsepower of the Toyota Tacoma into this function.

The horsepower of the Toyota Tacoma is 236.

Now, substituting \( x = 236 \) into the function:

\[ f(236) = -0.0308(236) + 37.701 \]

Calculating the first part:

\[ -0.0308 \times 236 = -7.2608 \]

Now, adding this to 37.701:

\[ f(236) = -7.2608 + 37.701 = 30.4402 \text{ (approximately)} \]

Thus, the predicted gas mileage for the Toyota Tacoma is about 30.4402 MPG.

Next, we can find the residual value. The residual is calculated as:

\[ \text{Residual} = \text{Actual Mileage} - \text{Predicted Mileage} \]

From the data, the actual gas mileage for the Toyota Tacoma is 25 MPG.

Calculating the residual:

\[ \text{Residual} = 25 - 30.4402 = -5.4402 \]

So, rounding to four decimal places, the residual value is approximately -5.4402.

Based on the options given, we choose the closest rounded value for the predicted gas mileage and the residual value:

Predicted gas mileage for the Toyota Tacoma is approximately 30.4322, so the residual value for this vehicle is approximately -5.4322.