## Contents

- Question 12
- Question 23
- Question 34
- Question 47
- Question 58
- Question 18
- Question 29
- Question 311
- Question 413
- Appendix 113
- Appendix 219

### Question 1

There are several possible factors that seem more relevant to be as a cost diver to estimate Delta’s salaries:

- Available Ton Miles
- Number of Departures(thousand)
- Revenue Passenger Miles
- Revenue Ton Miles
- Revenue Miles scheduled Salary cost for Delta consists of the payment to flight attendants and pilots so it can be determined by the hours flown.

The miles and the time flown are correlated so between these cost drivers, available ton miles seems to be the most reasonable cost driver since it indicate the time that the pilots and the flight attendant work for the Delta.

### Question 2

We first apply simple regression using each of the cost drivers mention above and other factor to estimate the salary by the cost drivers individually to see which one is best cost driver based on statistical reason and comparing R square. The scatter plots are shown in appendix 1. Results are as follows: X| Y| Y=AX+B| R square|

Available Seat Miles| Salary Cost| Y=38. 099X+262. 71| 0. 0997| Available Ton Miles| Salary Cost| Y=0. 5517X-682. 64| 0. 5577| Number of Departures| Salary Cost| Y=-8. 5728X+3184. 7| 0. 3229| Revenue Air Hours| Salary Cost| Y=3. 2063X+112. 59| 0. 1239| Revenue Miles flown| Salary Cost| Y=8. 0355X+21. 593| 0. 149| Revenue Miles Scheduled| Salary Cost| Y=8. 0801X-7. 3518| 0. 2023| Revenue Passengers Emplaned| Salary Cost| Y=16. 906X+890. 46| 0. 0408| Revenue Passengers Miles| Salary Cost| Y=38. 238X+577. 26| 0. 1764| Revenue Passengers Ton Miles| Salary Cost| Y=0. 821X+577. 91| 0. 1765| Revenue Ton Miles| Salary Cost| Y=0. 3301X+614. 33| 0. 1378| We can conclude from the above table that “Available Ton Mile” is better than the other factors since it has the most R square (0. 5577) and also the standard deviations are much smaller than coefficients so it’s statistically valid. On the other hand the Salary-Available Ton Miles plot shows a more linear relationship between the two variable (Salary and Available Ton Miles). Salary = 0. 5517* Available Ton Miles – 682. 64 | Coefficients| Standard Error| Intercept| -682. 433471| 282. 6032585| Available Ton Miles| 0. 551692525| 0. 079698325|

Advantage and Disadvantage Since this technique (single regression) uses the statistical rules to fit a function for all the historical data, it can be reliable. But we should consider that this method only use one cost driver to estimate salary cost at a time so it can not explain the whole variation for salary cost.

### Question 3

In this part we choose three cost drivers and use multiple regressions to estimate the salary cost.

- 1) Available Ton Miles
- 2) Number of Departure
- 3) Revenue Passenger Miles We choose this cost drivers because they had the best R square in the previous part (single regression).

Now we use multiple regressions to estimate the salary cost with each two of them.

1) Variable 1= Available Ton Miles, Variable 2= Number of Departure | Coefficients| Standard Error| R square| Intercept| 1120. 1809| 332. 9901692| 0. 798497104| Available Ton Miles| 0. 512423052| 0. 05483575| | Number of Departure| -7. 445802094| 1. 119799435| | Salary Cost = 1120. 1809 + 0. 512423052 * Available Ton Miles – 7. 45802094 * Number of Departure

2) Variable 1= Available Ton Miles, Variable 2= Revenue Passenger Miles | Coefficients| Standard Error| R square| Intercept| -1144. 549119| 243. 2101043| 0. 729846407| Available Ton Miles| 1. 05193654| 0. 12082857| | Revenue Passenger Miles| -72. 29550232| 14. 88974415| | Salary Cost = -1144. 549119 + 1. 05193654* Available Ton Miles -72. 29550232 * Revenue Passenger Miles

3) Variable 1= Revenue Passenger Miles, Variable 2= Number of Departure | Coefficients| Standard Error| R square| Intercept| 2554. 211| 398. 2843373| 0. 52871| Revenue Passenger Miles| 43. 87463| 10. 0582819| | Number of Departure| -9. 30278| 1. 666796821| | Salary Cost = 2554. 211 + 43. 87463 * Revenue Passenger Miles -9. 30278 * Number of Departure 4) Variable 1= Available Ton Miles, Variable 2= Revenue Passenger Miles, Variable 1= Number of Departure | Coefficients| Standard Error| R square| Intercept| 451. 6903684| 324. 8994338| 0. 861549482| Available Ton Miles| 0. 846337925| 0. 094468376| | Revenue Passenger Miles| -47. 10046906| 11. 63243252| | Number of Departure| -5. 927754287| 1. 01295063| |

Between these 4 alternatives for estimating the salary cost the 4th one has the biggest R square and the standard deviations are much smaller than coefficients so it is statistically more valid than the others. When we use multiple regressions to estimate the salary cost which one of the variable is the one that has the best R square in the single regression part, we definitely have a bigger R square. In this case also the R square for multiple regressions is bigger than the R square for single regression so it’s an improvement compare to the model estimated in question 2.

#### Advantage and Disadvantage

This technique (multiple regressions) takes more than one cost drivers into consideration so the estimation would be more close to the salary cost that we have already. In this problem the multiple regressions (0. 861549482) has the bigger R square than single regression (0. 5577). It shows that this technique can fit much variation by the cost drivers. Since this method uses the data from more than one cost driver, it would be harder to collect the data needed for variables and take more time than single regression method. It is also more complicated and hard to understand than single regression.

### Question 4

In question 1-3 we assume that the wage per hour for pilots and flight attendant remain the same through 1993 to 2002 and we estimate the salary cost based on this wage so if the wage does not change in 2003 and 2004 for Delta Airlines we can use the cost functions estimated in question 1-3. Another factor that is important to consider estimating the cost based on the data from previous years is that the number of employee and labor does not change through these year and the year we want to estimate the salary cost based on our cost function estimated in questions 1-3.

In summation we can say that the cost function estimated in question 1-3 are useful based on the following conditions:

1) The rate of wage for employee, labor, pilots and flight attendant will not change in year 2003 and 2004. So there should be no concerning about lowering staff’s salaries.

2) The number of employee, labor, pilots and flight attendant will not change in year 2003 and 2004. So there should be no regulation about reducing the number of Delta’s staff.

3) The fixed cost we estimate in our previous question should not change in 2003 and 2004.

The new security rules caused by the September 11 terrorist attack may cause an increase in Delta’s fixed cost but this problem can be removed easily by an overall shift upward. If these conditions are not in the years we want to estimate the salary cost, the cost function may not be useful for us.

### Question 5

The aircraft fuel can be another dependent variable other than the salary cost because it seems to vary based on the factor mile and it is the second biggest share of the total operating expenses. Question 1 There are two possible factors that seem to me to be more as a cost diver to estimate Delta’s aircraft fuel expenses.

1) Available Ton Miles

2) Revenue Air Hours The aircraft fuel is a kind of cost that is very related to the time that an aircraft is flown and since and mile flown and time are correlated, the available ton mile can also be a cost driver for fuel expenses. Question 2 We first apply simple regression using all of the cost drivers to estimate the aircraft fuel expenses by the cost drivers individually to see which one is most reasonable cost driver based on statistical reason and comparing R square. The scatter plots are shown in appendix 2. Results are as follows:

X| Y| Y=AX+B| R square| Available Seat Miles| Aircraft Fuel| Y= 17. 218X-52. 628| 0. 19| Available Ton Miles| Aircraft Fuel| Y= 0. 1619X-177. 59| 0. 4481| Number of Departures| Aircraft Fuel| Y= -1. 0606X+632. 1| 0. 0461| Revenue Air Hours| Aircraft Fuel| Y= 1. 2182X-44. 213| 0. 1668| Revenue Miles flown| Aircraft Fuel| Y= 3. 0296X-75. 169| 0. 1977| Revenue Miles Scheduled| Aircraft Fuel| Y= 2. 862X-56. 949| 0. 2368| Revenue Passengers Emplaned| Aircraft Fuel| Y=8. 5609X+203. 46| 0. 0976| Revenue Passengers Miles| Aircraft Fuel| Y= 13424X+152. 3| 0. 029| Revenue Passengers Ton Miles| Aircraft Fuel| Y= 0. 134X+152. 67| 0. 2027| Revenue Ton Miles| Aircraft Fuel| Y= 0. 1272X+142. 81| 0. 1911| We can conclude from the above table that “Available Ton Mile” is better than the other factors since it has the most R square (0. 4481) and also the standard deviations are much smaller than coefficients so it’s statistically valid. On the other hand the Aircraft Fuel-Available Ton Miles plot shows a more linear relationship between the two variables so we also choose this factor as the cost driver visually.

Aircraft Fuel = 0. 1619* Available Ton Miles -177. 59 | Coefficients| Standard Error| Intercept| -177. 5874543| 103. 3421877| Available Ton Miles| 0. 161896167| 0. 029144035| Advantage and Disadvantage: Since this technique (single regression) uses the statistical rules to fit a function for all the historical data, it can be reliable. But we should consider that this method only use one cost driver to estimate the aircraft fuel expenses at a time so it can not explain the whole variation for aircraft fuel expenses. Question 3 In this part we choose three cost drivers and use multiple regressions to estimate the salary cost.

- 1) Available Ton Miles
- 2) Revenue Passengers Miles
- 3) Revenue Miles Scheduled

We choose this cost drivers because they had the best R square in the previous part (single regression). Now we use multiple regressions to estimate the salary cost with each two of them.

1) Variable 1= Available Ton Miles, Variable 2= Revenue Passengers Miles | Coefficients| Standard Error| R square| Intercept| -261. 5797223| 108. 1820809| 0. 501250269| Available Ton Miles| 0. 252859805| 0. 53745654| | Revenue Passengers Miles| -13. 14610808| 6. 623094509| |

2) Variable 1= Available Ton Miles, Variable 2= Revenue Miles Scheduled | Coefficients| Standard Error| R square| Intercept| -88. 61131562| 107. 6948385| 0. 506861407| Available Ton Miles| 0. 276997702| 0. 061535907| | Revenue Miles Scheduled| -3. 141079013| 1. 496496135| |

3) Variable 1= Revenue Passengers Miles, Variable 2= Revenue Miles Scheduled | Coefficients| Standard Error| R square| Intercept| -22. 88712355| 147. 8036525| 0. 242581541| Revenue Passengers Miles| 4. 189516357| 7. 83381014| | Revenue Miles Scheduled| 2. 166566929| 1. 555757517| |

4) All of them | Coefficients| Standard Error| R square| Intercept| -170. 5035836| 121. 9438271| 0. 531481269| Available Ton Miles| 0. 315735826| 0. 067013535| | Revenue Passengers Miles| -9. 527820484| 6. 927283907| | Revenue Miles Scheduled| -2. 399100854| 1. 574107817| | Between these 4 alternatives for estimating the salary cost the 4th one has the biggest R square and the standard deviations are smaller than coefficients so it is statistically more valid than the others. The R square (0. 31481269) does not change much compare to single regression (0. 4481) even though we consider 3 variables to estimate the Aircraft Fuel but we can say it’s an improvement compare to the model estimated in question

#### 2. Advantage and Disadvantage

This technique (multiple regressions) takes more than one cost drivers into consideration so the estimation would be more close to the Aircraft Fuel Cost that we have already. In this problem the multiple regressions (0. 531481269) has the bigger R square than single regression (0. 4481). It shows this technique can fit much variation by the cost drivers.

Since this method the data for more than one cost driver, it would be harder to collect the data need for variables and take more time than single regression. It is also more complicated and hard to understand than single regression. Question 4 In question 1-3 we assume that the price for fuel did not change through 1993 to 2002 and we estimate the Aircraft Fuel Cost based on this constant price so if the price does not change in 2003 and 2004 for Delta Airlines we can use the cost functions estimated in question 1-3. Conclusion Appendix 1 Appendix 2