Principal Component Analysis

According to Wikipedia, an online encyclopedia, Southwest Airlines is currently the third largest airline in the world, measured by the number of passengers carried. Total number of passengers that were carried in the year 2005 amounted to 77.7 million. They are behind American Airlines and Delta Air Lines. After the tragic September 11th incident, Southwest airlines remains as one of the only major airlines that are still profitable. After the September 11th attacks, Southwest Airline's 6 biggest competitors grounded 240 planes and laid off 70,000 people. Southwest kept every single person and plane flying. In fact, they have been so successful, even other airlines have started to copy their practices. One of the biggest reasons why Southwest has been able to remain profitable compared to their rivals would be the practice of fuel hedging that they participate in. What they do is purchase fuel options that allow them to smooth out the fluctuations in the price of fuel. Because of this, they are currently paying only about 50% the current market price for fuel. Their rivals are currently paying more for fuel and carrying fewer passengers. Fuel consumption is the 2nd largest expense for airlines after labor.

Method: Principal components analysis 1/3

A form of factor analysis

Assuming empirical mean zero (mean subtraction necessary)

Linear combination of variables so that maximum variance is

extracted from the variables

Then removes this variance and seeks second linear

combination which explains again maximum proportion of the

remaining variance

Risk aversion indicators

Method: PCA 19

| 26

Method: Principal components analysis 2/3

Repeat until no further significant components show up.

Values in the remaining dimensions tend to be highly

correlated and can be dropped without risking bigger loss

’Total variance’ expresses how much information is contained

in the components retained:

T =

p

j =1

Var (Xj...