Relationship between Monthly Load Factor and Passenger Revenue Miles for Southwest Airlines

The objective of the given paper is to highlight the relationship between monthly load factor and monthly passenger revenue miles for Southwest Airlines. The scatterplot between the monthly load factor (independent variable) and monthly passenger revenue miles (dependent variable) is highlighted. The requisite linear regression model with monthly load factor (independent variable) and monthly passenger revenue miles (dependent variable) has been obtained through the use of Excel and the output in this regards is indicated. Based on the above, it can be concluded that a positive and strong linear relationship exists between load factor and passenger revenue miles for Southwest airlines based on the data provided.

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Introduction
The objective of the given paper is to highlight the relationship between monthly load factor
and monthly passenger revenue miles for Southwest Airlines. In order to facilitate the same,
monthly data from the airlines has been obtained for the period starting from January 2006
and ending in December 2012.
Analysis
The scatterplot between the monthly load factor (independent variable) and monthly
passenger revenue miles (dependent variable) is highlighted below.
From the above graph, it is apparent that there is a positive relationship between the given
variables since the scatter points are arranged with in an upward slopping trend. This is on
expected lines as higher the load factor, higher would be the occupancy of the available seats
leading to higher revenue generation. Also, there is a broad linear trend being exhibited by
the scatter points as they seem to be concentrated in the form of an upward sloping straight
line. The presence of outliers in the given data also seems minimal (Hillier, 2016).
The requisite linear regression model with monthly load factor (independent variable) and
monthly passenger revenue miles (dependent variable) has been obtained through the use of
Excel and the output in this regards is indicated below.

The linear regression equation is indicated below.
Monthly passenger revenue miles = -2800556.63 + 120639.60*Monthly Load Factor
In the given regression equation, the intercept is -2800556.63 while the slope coefficient of
the line is 120639.60. The slope coefficient implies that an increase by 1 unit in the monthly
load factor would lead to a corresponding increase in the monthly passenger revenue miles by
120639.60 (Flick, 2015). The R2 value for the above regression model is 0.7753 which
implies that the the variation in the independent variable can offer explanation for 77.53% of
the variation in the dependent variable. Hence, the given model represents a good fit
(Eriksson & Kovalainen, 2015).
In order to ascertain if there is a significant relationship between monthly load factor and
monthly passenger revenue miles, it needs to be ascertained if the above regression slope is
significant or not through the means of hypothesis testing.
The relevant hypotheses are as stated below.
Null Hypothesis: βloadfactor = 0
Alternative Hypothesis: βloadfactor ≠ 0
The level of significance is assumed as 5%.

For the slope coefficient of load factor, the t statistic is 16.82 with the corresponding p value
of 0.0000. Since the p value is lower than the level of significance, hence the available
evidence warrants null hypothesis rejection in favour of acceptance of alternative hypothesis
(Flick, 2015). Hence, it may be concluded that the slope is significant which implies that
there is a significant relationship between load factor and passenger revenue miles.
Further, one of the key assumptions with regards to linear regression is that the underlying
variables should be normally distributed. In order to ascertain the same, histograms of the two
variables have been pasted below.
From the above histograms, it is apparent that while the revenue passenger miles tends to
approximate normal distribution closely, the same cannot be said about the monthly load
factor which has a significant negative skew. The presence of skew implies that the
underlying data distribution is non-normal as normal distribution requires the skew in the
data to be zero or thereabout (Hair, Wolfinbarger, Money, Samouel & Page, 2015).
Conclusion

Based on the above, it can be concluded that a positive and strong linear relationship exists
between load factor and passenger revenue miles for Southwest airlines based on the data
provided. The results obtained are in line with expected as higher load factor leads to higher
occupancy and hence improves the passenger revenue miles. The linear regression model
between the given variables presents a good fit and the relationship is significant. However,
the non-normality of the independent variable i.e. monthly load factor poses a concern with
regards to the validity of the linear regression model.

References
Eriksson, P. & Kovalainen, A. (2015). Quantitative methods in business research London:
Sage Publications.
Flick, U. (2015). Introducing research methodology: A beginner's guide to doing a research
project New York: Sage Publications.
Hair, J. F., Wolfinbarger, M., Money, A. H., Samouel, P., & Page, M. J. (2015). Essentials of
business research methods New York: Routledge.
Hillier, F. (2016). Introduction to Operations Research.New York: McGraw Hill
Publications.