Question

Use the following linear regression equation regarding airline tickets to answer the question. (The dataset collected for Distance was from 500 miles to 5,687 miles) Note: that Distance is the number of miles between the departure and arrival cities, and Price is the cost in dollars of an airline ticket.

(a) Find the slope using the linear regression equation given to you above. Inter- pret the value that you got for the slope in the context of the problem. Predicted Price= 49 + 0.22 (Distance) (b) Find the y-intercept using the linear regression equation given to you. If ap- propriate interpret the value you got for the y-intercept in the context of the problem.

(c) If appropriate predict the Price of an airline ticket if the distance between the departure and arrival cities is 1,752 miles.

Answer 1

Ans (a): Here the regression equation is Price= 49 + 0.22 (Distance).

Then the slope of given regression line is, slope = 0.22

Interpretation: The slope is 0.22, it can be written write this as 0.22/1 and say that as you move along the line, as the Distance increases by 1 mile, the price of airline ticket also increases by 0.22 dollars.

Ans (b):  

Here the regression equation is Price= 49 + 0.22 (Distance).

Then the intercept of given regression line is, intercept = 49.

Interpretation:

The intercept (often labeled the constant) is the expected mean value of Price when all Distance = 0.

If Distance never equals 0, then the intercept has no intrinsic meaning. In scientific research, the purpose of a regression model is to understand the relationship between predictors and the response. If so, and if Distance never = 0, there is no interest in the intercept. It doesn’t tell you anything about the relationship between Distance and Price of airline ticket.

Ans (c):

Here the regression equation is Price= 49 + 0.22 (Distance).

We want to predict the Price of an airline ticket if the distance between the departure and arrival cities is 1,752 miles.

Therefore,

Predicted Price = 49 + 0.22(1752) = 434.44

Hence, the predicted price of an airline ticket = $434.44