Question

The computer output below predicts are fare for a discount airlines flight from Philadelphia to 13 different cities from the flights length in miles. A scatter plot of the data suggests that the relationship is roughly linear. One flight - Philadelphia to West Palm Beach, FL - is 953 miles long and costs $110. Which of the following expressions correctly represents the residual for this data point?

Answer 1

The answer is (d) 110 - (101.24 + 0.02977 * 953).

Residual: A residual is the difference between the actual observed value (in this case, the actual air fare of $110) and the predicted value from the regression model.

Predicted Value: The expression 101.24 + 0.02977 * 953 calculates the predicted air fare for a flight of 953 miles using the model's coefficients.

Calculating Residual: To find the residual, we subtract the predicted value from the actual value:

Residual = Actual Value - Predicted Value

= $110 - (101.24 + 0.02977 * 953)

Option (d) correctly represents this calculation.

Complete Question:

The computer output below predicts air fare for a discount airline’s flights from Philadelphia to 13 different cities from the flight’s length in miles. A scatterplot of the data suggests that the relationship is roughly linear.

`\begin{array}{lcccc}\text { Predictor } & \text { Coef } & \text { SE Coef } & T & P \\\text { Constant } & 101.24 & 13.49 & 7.50 & 0.000 \\\text { Distance } & 0.02977 & 0.01107 & 2.69 & 0.021 \\& & & & \\\mathrm{~S}=20.7237 & \mathrm{R}-\mathrm{Sq}=39.7 \% & \mathrm{R}-\mathrm{Sq}(\mathrm{adj})=34.2 \%\end{array}`

One flight—Philadelphia to West Palm Beach, FL—is 953 miles long and costs $110. Which of the following expressions correctly represents the residual for this data point?

a.101.24+0.02977⋅953

b.953-(101.24+0.02977⋅110)

c.(101.24+0.02977⋅110)-953

d.110-(101.24+0.02977⋅953)

e.(101.24+0.02977⋅953)-110