5. An analyst wants to determine whether the cost of a flight depends on the dis

Question

5. An analyst wants to determine whether the cost of a flight depends on the distance. She collects a set of data of the round-trip fare for flights between Boston and some other cities on major airlines and the distance between cities. The following table gives the descriptive statistics of the distance (in miles) and the cost (in dollars). Standard Deviation 1074.4 110.71 Mean Miles Costs r 0.7563 1648.4 284 (a) Find the regression line of the cost of a flight in terms of the miles traveled. Hint: Treat the Miles as x-variable and the Cost as y-variable.] (6 points) (b) Suppose someone flies 500 miles, what will be the estimated cost for him/her? 2 points (c) Find the Coefficient Determination (2) and interpret it. (2 points)

Explanation / Answer

a) here slope b1 =r*Sy/Sx =0.7563*(110.71/1074.4)=0.0779

and intercept bo=Ybar-b1*Xbar =284-0.0779*1648.4 =152.7316

hence line equation :Yhat=152.7316+0.0779*x

b)

foc x=500 ; estimated cost =152.7316+0.0779*500=191.6816

c)

coefficient of determination =r2 =(0.7563)2 =0.5720

for above tells that 57.20% of variaiton in predicted values of cost can be explained by this regression model.

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