The following table reports the distance (in miles) as well as the airfare cost for seven destinations from Orlando, Florida. A linear function fit to the data is modeled by the equation y = 0.45x + 48.65 with the corresponding residual plots shown.

Question

City Distance (miles) Airfare Cost ($)
Atlanta, GA 438 229
Miami, FL 235 185
New Orleans, LA 640 339
Louisville, KY 859 441
Charleston, SC 378 200
Jackson, MS 689 374
Birmingham, AL 517 265
What is the residual value of Miami, FL, rounded to the nearest tenth?

Answer 1

To calculate the residual value for Miami, FL, we first need to find the predicted airfare using the given linear function \( y = 0.45x + 48.65 \), where \( x \) is the distance in miles.

The distance to Miami, FL is given as 235 miles.

Now, substituting \( x = 235 \) into the equation:

\[ y = 0.45(235) + 48.65 \]

Calculating \( 0.45 \times 235 \):

\[ 0.45 \times 235 = 105.75 \]

Now adding \( 48.65 \):

\[ y = 105.75 + 48.65 = 154.40 \]

So, the predicted airfare cost for Miami, FL is $154.40.

Next, we need to find the residual, which is the difference between the actual airfare cost and the predicted airfare cost. The actual airfare cost for Miami, FL is $185.

Calculating the residual:

\[ \text{Residual} = \text{Actual} - \text{Predicted} = 185 - 154.40 = 30.60 \]

Rounding to the nearest tenth, the residual value for Miami, FL is:

\[ \boxed{30.6} \]