Transport Economics: Regression Analysis of Air Passenger Travel

This report presents a comprehensive regression analysis of the factors influencing air passenger travel in Australia. The analysis uses data from 1970 to 2015 and examines the relationship between air passenger numbers (dependent variable Y) and independent variables such as GDP per capita ...Read More

Running Head: TRANSPORT ECONOMICS
Transport Economics
Name of the Student
Name of the University
Author note

1TRANSPORT ECONOMICS
Table of Contents
Task 1.........................................................................................................................................2
Task 2.........................................................................................................................................3
Bivariate regression................................................................................................................3
Residual plot...........................................................................................................................7
Task 3.........................................................................................................................................9
Model 1..................................................................................................................................9
Model 2................................................................................................................................11
Model 3....................................................................................................................................12
Task 4.......................................................................................................................................14
Forecast................................................................................................................................14
References................................................................................................................................16

2TRANSPORT ECONOMICS
Task 1
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f(x) = 922.330951872083 x + 2851837.16103047
R² = 0.977320752162377 f(x) = 5.87873434629525 x − 74877468.3237875
R² = 0.945320839513967
R² = 0R² = 0
Scatter Plot
International tourism, number of departures (X2)
Linear (International tourism, number of departures (X2))
International tourism, number of arrivals (X3)
Linear (International tourism, number of arrivals (X3))
Population (X4)
Linear (Population (X4))
GDP per capita (X1)
Linear (GDP per capita (X1))
Scatter plot is useful in understanding the association between two or more variables.
The scatter plot above shows the number of air passengers travelled with three independent
variables such as per capita GDP, number of departures, number of arrival and population.
The scatter plot of per capita GDP indicates a positive relation between number of passengers
travelled and GDP per capita. The corresponding correlation coefficient is 0.9773. For
number of arrivals, the scatter plot reveals an uphill pattern indicating a positive association
between the two variables. All the scatter points are around fitted linear trend. The
corresponding correlation co-efficient is 0.9693. The scatter plot between number of arrivals
and passengers travelled again shows an upward trend indicating positive between the two.

3TRANSPORT ECONOMICS
Population also has a positive relation with passengers travelled. Therefore, all the variables
have a linear relationship with the dependent variables. Scatter plot however shows only
degree of association (Fox, 2015). It does not indicate any cause and effect relation. For the
later, a regression needs to be done.
Task 2
Bivariate regression
Y on X1
Regression Statistics
Multiple R 0.99
R Square 0.98
Adjusted R Square 0.98
Standard Error 2924283.82
Observations 46
ANOVA
df SS MS F Significance F
Regression 1 1.62144E+16 1.62E+16 1896.1 8.06008E-38
Residual 44 3.76263E+14 8.55E+12
Total 45 1.65906E+16
Coefficients
Standard
Error
t
Stat
P-
value Lower 95% Upper 95%
Intercept 2851837.16 742741.64 3.84 0.00 1354939.73 4348734.59
GDP per capita (X1) 922.33 21.18 43.54 0.00 879.64 965.02
Estimated regression equation
Y =2851837.16+922.33 X1
The estimated value of adjusted R square is 0.98. This implies the variable GDP per capita
(X1) can explain 98 percent variation in number of passengers travelled by air mode. The co-

4TRANSPORT ECONOMICS
efficient of X1 is 934.64. The positive value of the coefficient implies that GDP per capita has
a positive impact on passengers travelled. The corresponding p value for the co-efficient is
0.00. The p value less than significance level (0.05) means the variable is statistically
significant at the corresponding level of significance. The high value of R square along with a
significant p value implies the model is best fitted for the given variables.
Y on X2
Regression Statistics
Multiple R 0.98
R Square 0.97
Adjusted R
Square 0.97
Standard Error
2600676.02
9
Observations 21
ANOVA
df SS MS F Significance F
Regression 1 4.058E+15 4.058E+15 599.98417 7.76555E-16
Residual
1
9 1.28507E+14 6.764E+12
Total
2
0 4.18651E+15
Coefficients
Standard
Error
t
Stat
P-
value Lower 95% Upper 95%
Intercept
14178876.5
1 1439058.67 9.85 0.00
11166892.
10
17190860.9
3
International tourism,
number of departures
(X2) 6.16 0.25
24.4
9 0.00 5.64 6.69
Estimated regression equation
Y =14178876.51+6.16 X2

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The estimated value of adjusted R square is 0.97. This implies the variable; number of
departure (X2) can explain 97 percent variation in number of passengers travelled by air
mode. The co-efficient of X1 is 6.16. As most of the variation in the dependent variable is
explained by the independent variable, the model is good fit model. The positive value of the
coefficient implies that number of departure has a positive impact on passengers travelled.
The corresponding p value for the co-efficient is 0.00. The p value less than significance level
(0.05) means the variable is statistically significant at the corresponding level of significance.
Y on X3
Regression Statistics
Multiple R 0.93
R Square 0.87
Adjusted R Square 0.86
Standard Error 5373940.94
Observations 21
ANOVA
df SS MS F Significance F
Regression 1 3.6378E+15 3.64E+15 125.966 7.95091E-10
Residual
1
9 5.48706E+14 2.89E+13
Total
2
0 4.18651E+15
Coefficients
Standard
Error
t
Stat
P-
value Lower 95% Upper 95%
Intercept -30773593.76 6990416.4 -4.4 0.0 -45404703.4
-
16142484.1
International
tourism,
number of
arrivals (X3) 14.57 1.3 11.2 0.0 11.9 17.3
Estimated regression equation
Y =−30773593.76+14.57 X3

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The estimated value of adjusted R square is 0.87. This implies the variable; number of
arrival (X3) can explain 87 percent variation in number of passengers travelled by air mode.
The co-efficient of X3 is 14.57. The positive value of the coefficient implies that number of
arrival has a positive impact on passengers travelled. The corresponding p value for the co-
efficient is 0.00. The p value less than significance level (0.05) means the variable is
statistically significant at the corresponding level of significance. The regression output
shows the number of arrivals is a positive significant determinant of number of passengers
travel and accounts 87 percent to total variation in passengers travelled.
Y on X4
Regression Statistics
Multiple R 0.97
R Square 0.95
Adjusted R Square 0.94
Standard Error 4540630.02
Observations 46
ANOVA
df SS MS F Significance F
Regression 1 1.56835E+16 1.57E+16 760.6941 2.09649E-29
Residual 44 9.07162E+14 2.06E+13
Total 45 1.65906E+16
Coefficients
Standard
Error t Stat
P-
value Lower 95% Upper 95%
Intercept
-
74877468.32 3832016.43
-
19.54 0.00
-
82600389.99
-
67154546.66
Population
(X4) 5.88 0.21 27.58 0.00 5.45 6.31
Estimated regression equation
Y =−74877468.32+5.88 X 4

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The estimated value of adjusted R square is 0.95. This implies the variable; population (X4)
can explain 95 percent variation in number of passengers travelled by air mode. The co-
efficient of X4 is 14.6. The positive value of the coefficient implies that population has a
positive impact on passengers travelled. The corresponding p value for the co-efficient is
0.00. The p value less than significance level (0.05) means the variable is statistically
significant at the corresponding level of significance. Like the previous three independent
variables, population is also a positive significant determinant of passengers travelled.
Residual plot
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GDP per capita (X1) Residual Plot
GDP per capita (X1)
Residuals
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International tourism, number of departures
(X2) Residual Plot
International tourism, number of departures (X2)
Residuals

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-10000000
-5000000
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International tourism, number of
arrivals (X3) Residual Plot
International tourism, number of arrivals (X3)
Residuals
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Population (X4) Residual Plot
Population (X4)
Residuals
The residual plot provides a test of linearity. In the residual plot, the residual values
are plotted against each of the independent variables. If the residual plot does not exhibit a
pattern, then this implies the error term does not relate with independent variables. Hence, the
error follows a normal distribution and suggest a linear model can be fitted model the
variables. A non-linear model is appropriate if there is a steady pattern observed for the
residual plot. As shown from the residual plot for four independent variables, residuals are
dispersed around the horizontal axis for all the variables. Therefore, linear model is best fitted
for all models.

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Task 3
Model 1
Regression Statistics
Multiple R 0.99
R Square 0.98
Adjusted R Square 0.98
Standard Error 2089216.11
Observations 21
ANOVA
df SS MS F Significance F
Regression 2 4.10794E+15 2.054E+15 470.57366 2.8873E-16
Residual
1
8 7.85668E+13 4.3648E+12
Total
2
0 4.18651E+15
Coefficient
s
Standard
Error
t
Stat
P-
value Lower 95% Upper 95%
Intercept
5885699.6
1 2710651.87 2.17 0.04 190831.35 11580567.86
GDP per capita (X1) 532.09 157.31 3.38 0.00 201.60 862.57
International tourism,
number of departures
(X2) 2.96 0.97 3.06 0.01 0.92 4.99
Estimated regression equation
Y =588569961+532.09 X1 +2.96 X2
The value of adjusted R square is 0.98. Adjusted R square shows the overall
explanatory power of the model (Darlington & Hayes, 2016). The two variable X1 and X2
together accounts for 98 percent variation in Y. GDP per capita has a positive influence on
number of passengers travelled. Number of departures also positively influence number of
passengers travelled. For both the variables probability value or p value is less than the

10TRANSPORT ECONOMICS
significance value of 0.05. As p value is defined as probability of accepting the null
hypothesis of insignificance of the regression coefficient, a low p value indicates statistical
significance of the concerned co-efficient. The p value for X1 is 0.00 and for X2 is 0.01,
therefore both the variables are statistically significant.
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GDP per capita (X1) Residual Plot
GDP per capita (X1)
Residuals
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International tourism, number of
departures (X2) Residual Plot
International tourism, number of departures (X2)
Residuals
The residual plot for both the explanatory variables scattered around the horizontal
axis. There is no observed pattern in the residual plot indicating normality of the error terms
and hence, appropriateness of a linear model.

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Model 2
Regression Statistics
Multiple R 0.99
R Square 0.98
Adjusted R Square 0.98
Standard Error 2807864.19
Observations 46
ANOVA
df SS MS F Significance F
Regression 2 1.62516E+16 8.13E+15 1030.658 4.70639E-37
Residual 43 3.39016E+14 7.88E+12
Total 45 1.65906E+16
Coefficients
Standard
Error
t
Stat
P-
value Lower 95% Upper 95%
Intercept
30201311.4
9 12603086.68 2.40 0.02
4784764.8
9
55617858.0
9
GDP per capita
(X1) 1235.59 145.55 8.49 0.00 942.06 1529.13
Population (X4) -2.05 0.94 -2.17 0.04 -3.95 -0.15
Estimated regression equation
Y =30201311.4 9+1235.59 X1−2.05 X 4
The value of adjusted R square is 0.98. The two variable X1 and X4 together account for 98
percent variation in Y. The variable GDP per capita has a positive association with Y as
shown by the positive sign of the co-efficient. However, in model 2, population shows an
inverse relation with number of air passengers travelled. The p value for X1 is 0.00. The
corresponding p value for X2 is 0.04. Both the p values are less than significant value of 0.05.
Therefore, both the variables are statistically significant.

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GDP per capita (X1) Residual Plot
GDP per capita (X1)
Residuals
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Population (X4) Residual Plot
Population (X4)
Residuals
Like model 1, here also both the variables follow normality assumption. The residuals
are randomly distributed around the horizontal axis.
Model 3
Regression Statistics
Multiple R 0.99
R Square 0.98
Adjusted R Square 0.98
Standard Error 2089126.37
Observations 21

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ANOVA
df SS MS F Significance F
Regression 3 4.11231E+15 1.37E+15 314.0766 4.41172E-15
Residual
1
7 7.41956E+13 4.36E+12
Total
2
0 4.18651E+15
Coefficients
Standard
Error
t
Stat
P-
val
ue Lower 95% Upper 95%
Intercept
-
34430892.18
40376539.4
7 -0.85
0.4
1
-
119617944.13
50756159.7
8
GDP per capita (X1) 331.23 255.00 1.30
0.2
1 -206.77 869.23
International
tourism,
number of
departures (X2) 2.18 1.24 1.76
0.1
0 -0.44 4.80
Population (X4) 2.61 2.61 1.00
0.3
3 -2.90 8.12
Estimated regression equation
Y =−34430892.18+ 331.23 X1+ 2.18 X2+ 2.61 X 4
The value of adjusted R square is 0.98. The two variable X1, X2 and X4 together account for 98
percent variation in Y. All the three variables have positive association with Y as shown by
the positive sign of the co-efficient. However, no variable in the model is statistically
significant as all the p values are greater than the significant level.

14TRANSPORT ECONOMICS
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GDP per capita (X1) Residual Plot
GDP per capita (X1)
Residuals
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-6000000
-4000000
-2000000
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International tourism, number of
departures (X2) Residual Plot
International tourism, number of departures (X2)
Residuals
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-6000000
-5000000
-4000000
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Population (X4) Residual Plot
Population (X4)
Residuals

15TRANSPORT ECONOMICS
As observed from the above three residuals plot, the error term does not have any
steady relation with any of the three independent variables. Henceforth, the residual satisfies
the normality assumption implying that a linear model can be set to model the variables.
Task 4
Forecast
Forecast
Model 1 X1 X2 Y
2016 68,589.26 10,345,000 72986075
2017 69,957.18 10,987,000 75613233
2018 71,123.67 11,453,000 77612531
2019 71,956.89 12,013,000 79712591
2020 73,267.90 12,857,000 82907067
Forecast
Model 2 X1 X4 Y
2016 68,589.26 24,127,159 65481971
2017 69,957.18 24,879,231 65630194
2018 71,123.67 25,346,967 66112505
2019 71,956.89 25,967,568 65869611
2020 73,267.90 26,456,902 66486208
Forecast
Model 3 X1 X2 X4 Y
2016 68,589.26 10,345,000 24,127,159 73894647
2017 69,957.18 10,987,000 24,879,231 77713093
2018 71,123.67 11,453,000 25,346,967 80337997
2019 71,956.89 12,013,000 25,967,568 83456960
2020 73,267.90 12,857,000 26,456,902 87010568
The forecasted value of dependent variable depends on the explanatory variables
considered and their corresponding coefficient. Different models consist of different
independent variable. For example, in model 1, per capita GDP and number of departures are
taken as independent variables while in model 2, per capita GDP and population is taken as
explanatory variables. Both the model though has two explanatory variables, the forecasted

16TRANSPORT ECONOMICS
value differs because of underlying difference in independent variables and their coefficients.
The forecasted value in model 3, is greater as compared to two other models because it
includes three independent variables as against two independent variables in the two former
model. The forecasted value of the explained variables also depends on the relative sign the
co-efficient. In model 2 for example the coefficient of population has a negative sign. For
this, the forecasted values of model 2 are less than the two other models. In model 3, the
intercept is negative. Because of the negative intercept despite having three independent
variables in the model, it has forecasted value of Y close of that are predicted from model 1.
References
Darlington, R. B., & Hayes, A. F. (2016). Regression analysis and linear models: Concepts,
applications, and implementation. Guilford Publications.
Fox, J. (2015). Applied regression analysis and generalized linear models. Sage Publications.