QuantitativeAnalysis for Management
Accordingto the case study of the amalgamation of the two airlines, Northern,and Southern Airline, which formed the largest U.S. carrier, theproblem statement depicts that the maintenance cost rises as theaircrafts ages. Mr. Stephen distress is the high maintenance cost ofthe aircraft, B737200, which previous information regarding theindustry shows that the maintenance cost increases as the aircraftages. Therefore, the main objectives of the study are outline asfollows:
Thestudy seeks to examine the correlation between the average fleet agesand direct airframe maintenance cost which was incurred in differentyears.
Secondly,it examines the relationship between the average fleet age and directengine maintenance cost.
Thecorrelation coefficient in statistics refers to the measure ofassociation between two variables (Mari 2001). From the study, weshall examine the Pearson correlation coefficient between the averagefleet ages and direct engine maintenance cost. Northern and Southernairline have the correlation coefficients of 0.8772 and 0.6249respectively. The Northern Airline shows a strong linear correlationbetween the average fleet age and the airframe maintenance cost ascompared to the Southern Airline which is moderately positive(Table1.1 and 2.1). This shows that there is a relatively positiverelationship among the two variables. This relationship depicts thedirection of the association between the two variables as delineatedby the positive figure that show the degree of association.
Additionally,the study focused on examining the relationship between the averagefleet age and the direct engine cost. To effectively show thisrelationship, statistical regression analysis is applied in order toportray and capture the association amongst the exogenous andendogenous variables. Regression analysis refers the statistical toolused for investigation of the relationship between two or morevariables. The main focus of regression is primarily for predictionand causal inference (Campbell et al. 2008). From the data provided,we shall be looking whether the average fleet age influences theengine maintenance cost over the period of time. The regressionanalysis shows that a one unit change in the average fleet age ofboth the Northern and the Southern airline will increase enginemaintenance cost by 231.70 and 113.13 respectively (Table 2.1 and2.2). This shows that there is a causal effect from the average fleetage which causes the maintenance cost to increase. However, we cannotcompletely term the increase in the maintenance cost to be purelydepend on the aging fleet. It is a combination of the aging fleet andother factors which are present in the airline industry. Thus, thisbrings us to the interpretation of the adjusted R^{2}.This shows the percentage variation caused by the explanatoryvariable. The adjusted R^{2}of Northern Airline shows that aging fleet accounts for 53.49% of thetotal variation of the maintenance cost leaving about 46.51% of thevariation explained by other factors. On the other hand, the adjustedR^{2}of the Southern Airline show that 35.19% of the variation arecontributed by the aging fleet and the remaining 64.81% of thevariation are contributed by other factors.
Conclusion
Fromthe study, there is a strong linear correlation relationship betweenthe direct airframe maintenance cost and the average fleet age inboth locations. On the other hand, the study confirms that averagefleet age contributes 53.49% and 35.19% of the variation in directengine costs while the rest of the variation is explained by otherfactors present in the industry in Northern and Southern Airline.
Northern Airline Pearson Correlation Coefficients 

  
Year 
Airframe Cost 
Engine Cost 
Average Age (hours) 
Year 
1.0000 
  
  

Airframe Cost 
0.8721 
1.0000 
  
  
Engine Cost 
0.7150 
0.6360 
1.0000 
  
Average Age (hours) 
0.9887 
0.8772 
0.7826 
1.0000 
Fig 1.1
Southern Airline Pearson Correlation Coefficients 

  
Year 
Airframe 
Engine Cost 
Average Age (hours) 
Year 
1.0000 
  
  

Airframe Cost 
0.7673 
1.0000 
  
  
Engine Cost 
0.3398 
0.6826 
1.0000 
  
Average Age (hours) 
0.6110 
0.6249 
0.6782 
1.0000 
Fig1.2
Fig2.1 Northern Airline
Regression Statistics 

Multiple R 
0.782592494 

R Square 
0.612451011 

Adjusted R Square 
0.534941213 

Standard Error 
2738.098181 

Observations 
7 

ANOVA 

  
df 
SS 
MS 
F 

Regression 
1 
59239691.18 
59239691 
7.901595 

Residual 
5 
37485908.25 
7497182 

Total 
6 
96725599.43 
  
  

  
Coefficients 
Standard Error 
t Stat 
Pvalue 

Intercept 
82.98818591 
4450.483976 
0.01865 
0.985844 

Engine (X) 
231.694552 
82.4249032 
2.810978 
0.037505 
Fig2.2 Southern Airline
Regression Statistics 

Multiple R 
0.678175096 

R Square 
0.459921461 

Adjusted R Square 
0.351905754 

Standard Error 
1187.740833 

Observations 
7 

ANOVA 

  
df 
SS 
MS 
F 

Regression 
1 
6006757.991 
6006757.99 
4.257913 

Residual 
5 
7053641.437 
1410728.29 

Total 
6 
13060399.43 
  
  

  
Coefficients 
Standard Error 
t Stat 
Pvalue 

Intercept 
4022.943093 
1654.223222 
2.43192275 
0.05924 

Engine (X) 
113.131633 
54.82588816 
2.06347105 
0.094017 
Reference
Schroeder,L., & Sjoquist, D. (1986). Understanding regression analysis anintroductory guide. Beverly Hills, Calif.: Sage Publications.
Introductionto Regression and Data Analysis – StatLab. (n.d.). Retrieved August15, 2015. 
Campbell,D., & Kenny, D. (1999). A primer on regression artifacts.New York: Guilford Press. 
Mari,D., & Kotz, S. (2001). Correlation and dependence. London:Imperial College Press