8 points each) Aeolus Air developed a regression model to predict revenue from f

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8 points each) Aeolus Air developed a regression model to predict revenue from flights that connect feeder cities to its hub airport in Athens. The response in the model is the revenue generated by flights operating to the feeder cities (in €1000 per month), and the two explanatory variables are the air distance between Athens and the feeder city (distance in km) and the population of the feeder city (in 1000). The regression equation based on data for 28 locations last month is Revenue = 87 + 0.3 Distance + 1.5 Population with an adjusted R2 = 0.74 and SE (of residuals) = 32.7. i. The airline plans to expand its operations to add an additional feeder city. One possible city has population of 100,000 and is 250km away from Athens. A second possible city has population 75,000 and it is 200km away from Athens. Which one would you recommend if the airline wants to increase total revenue? The table below gives further details of the multiple regression estimated above. ii. Fill in the tstatistics, the SE and pvalues missing. Also, calculate the accurate coefficient of population. iii. What is the interpretation of the coefficient of distance “0.3..”? iv. Do you think that the addition of Distance to a simple regression using only Population as an explanatory variable produces a statistically significant increase in the adjusted R2 ? v. Based on her past experience, the recently appointed director of operations, Mrs Zorba, believes that the additional revenue generated by every thousand extra people in the population of a new feeder city is €1800. Is her claim sensible based on your analysis?
8 points each) Aeolus Air developed a regression model to predict revenue from flights that connect feeder cities to its hub airport in Athens. The response in the model is the revenue generated by flights operating to the feeder cities (in €1000 per month), and the two explanatory variables are the air distance between Athens and the feeder city (distance in km) and the population of the feeder city (in 1000). The regression equation based on data for 28 locations last month is Revenue = 87 + 0.3 Distance + 1.5 Population with an adjusted R2 = 0.74 and SE (of residuals) = 32.7. i. The airline plans to expand its operations to add an additional feeder city. One possible city has population of 100,000 and is 250km away from Athens. A second possible city has population 75,000 and it is 200km away from Athens. Which one would you recommend if the airline wants to increase total revenue? The table below gives further details of the multiple regression estimated above. ii. Fill in the tstatistics, the SE and pvalues missing. Also, calculate the accurate coefficient of population. iii. What is the interpretation of the coefficient of distance “0.3..”? iv. Do you think that the addition of Distance to a simple regression using only Population as an explanatory variable produces a statistically significant increase in the adjusted R2 ? v. Based on her past experience, the recently appointed director of operations, Mrs Zorba, believes that the additional revenue generated by every thousand extra people in the population of a new feeder city is €1800. Is her claim sensible based on your analysis?
8 points each) Aeolus Air developed a regression model to predict revenue from flights that connect feeder cities to its hub airport in Athens. The response in the model is the revenue generated by flights operating to the feeder cities (in €1000 per month), and the two explanatory variables are the air distance between Athens and the feeder city (distance in km) and the population of the feeder city (in 1000). The regression equation based on data for 28 locations last month is Revenue = 87 + 0.3 Distance + 1.5 Population with an adjusted R2 = 0.74 and SE (of residuals) = 32.7. i. The airline plans to expand its operations to add an additional feeder city. One possible city has population of 100,000 and is 250km away from Athens. A second possible city has population 75,000 and it is 200km away from Athens. Which one would you recommend if the airline wants to increase total revenue? The table below gives further details of the multiple regression estimated above. ii. Fill in the tstatistics, the SE and pvalues missing. Also, calculate the accurate coefficient of population. iii. What is the interpretation of the coefficient of distance “0.3..”? iv. Do you think that the addition of Distance to a simple regression using only Population as an explanatory variable produces a statistically significant increase in the adjusted R2 ? v. Based on her past experience, the recently appointed director of operations, Mrs Zorba, believes that the additional revenue generated by every thousand extra people in the population of a new feeder city is €1800. Is her claim sensible based on your analysis?

Explanation / Answer

Given regression line

Revenue=87+0.3 Distance+1.5 population

(i) Option 1 population=100,000 distance=250 km

Revenue=87+0.3 *250+1.5*100000=150162

Option 2 population=75000 distance=200 km

Revenue=87+0.3*200+1.5*75000=112647

Hence option 1 is better in terms of revenue

iii)

The coefficient of distance 0.3 means that for every 1 unit increase in distance we get an increase of 0.3 times the value in revenue

iv) The R square value of 0.74 means that distance and population together explain 74% of variation in revenue

only population wil be able to explain less than 74% of revenue

v) For every 1000 extra people the revenue goes up by 1.5*1000=1500

Mrs Zorba claims an increase of 1800>1500 . Her claim is false and not sensible

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