Predictive Demand Analysis: Regression Models and Forecasts

This assignment focuses on predictive demand analysis using a dataset of Australian air passenger data from 1970 to 2015. The student analyzes the relationship between the number of air passengers (dependent variable) and several independent variables: GDP per capita, international tourism departures and arrivals, and population. The analysis involves bivariate and multiple regression models using Microsoft Excel. The student generates scatter plots, calculates regression equations, and interprets adjusted R-squared values and p-values to assess the statistical significance of each independent variable. Three different regression models are developed, and their forecasted values for the dependent variable are calculated for the years 2016-2020. Finally, the models are compared based on forecasting error, and the model that best fits the actual data is identified. The assignment demonstrates the application of regression analysis for predicting demand in the aviation industry, considering various economic and demographic factors.

Running head: PREDICTIVE DEMAND ANALYSIS
Predictive Demand Analysis
Name of the Student
Name of the University
Course ID

1PREDICTIVE DEMAND ANALYSIS
Table of Contents
Task 1...............................................................................................................................................2
Task 2...............................................................................................................................................2
Bivariate regression between Y and X1.......................................................................................2
Bivariate regression between Y and X2.......................................................................................4
Bivariate regression between Y and X3.......................................................................................5
Bivariate regression between Y and X4.......................................................................................6
Task 3...............................................................................................................................................7
Model 1........................................................................................................................................7
Model 2........................................................................................................................................8
Model 3........................................................................................................................................9
Task 4.............................................................................................................................................10
References......................................................................................................................................12

2PREDICTIVE DEMAND ANALYSIS
Task 1
- 10,000.00 20,000.00 30,000.00 40,000.00 50,000.00 60,000.00 70,000.00 80,000.00
10,000,000.00
30,000,000.00
50,000,000.00
70,000,000.00
90,000,000.00
f(x) = 5950.47497984865 x − 76037256.6584857
R² = 0.949241846083587
f(x) = 14572.1480553828 x − 30773593.7648714
R² = 0.868934820312903
f(x) = 6161.52834379035 x + 14178876.5144755
R² = 0.969304546178949
f(x) = 934.647088519814 x + 2627643.52401026
R² = 0.977527593520566
Scatter Plot
GDP per capita (X1)
Linear (GDP per capita (X1))
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))
Figure 1: Scatter plot between dependent and different independent variables
From the above scatter plot, it has been observed that all the independent variables has a
positive linear relationship with the dependent variable. The R square value are almost close to 1
meaning a strong association between dependent and all the independent variables (Chatterjee
and Hadi 2015).
Task 2
Bivariate regression between Y and X1
Table 1: Result of regression of Y on X1

3PREDICTIVE DEMAND ANALYSIS
The obtained regression equation from the above regression result is obtained as
Y =2627643.524+934.647 X1
The value of adjusted R square for the regression is estimated to be 0.98. From the
adjusted R square value, it can be said that GDP per capita (X1) can explain 98 percent variation
in number of passengers carried by air. The coefficient of per capita GDP is 934.647. Positive
coefficient implies a positive correlation between GDP per capita and number of passengers
carried out by air mode. That means as per capita GDP increases, number of passengers carried
in air mode and vice-versa. The value of adjusted R square close to 1 implies that there is a
strong correlation between per capita GDP and number of passenger carried by air mode (Fox
2015). The P value for the coefficient is 0.000. The p value is less than 5% significance level,
implying rejection of null hypothesis of no significant relation between Y and X1.

4PREDICTIVE DEMAND ANALYSIS
Bivariate regression between Y and X2
Table 2: Result of regression of Y on X2
The obtained regression equation from the above regression result is obtained as
Y =14178876.51+6.162 X2
The adjusted R square value from the above regression is obtained as 0.97. The
implication of adjusted R square value is that international tourism, number of departures
explains 97 percent variation in number of passengers carried by air travel. The coefficient of X2
is 6.162. The positive coefficient and high value of R square implies that the number of
departures in international tourism positively affects the number of passengers travelled by air.
Finally, the p value of the coefficient is 0.000. The p value less than significant value implies that
the variable is statistically significant.

5PREDICTIVE DEMAND ANALYSIS
Bivariate regression between Y and X3
Table 3: Result of regression of Y on X3
The regression equation between Y and X3 is obtained as
Y =−30773593.76+14.572 X2
The adjusted R square value for the above regression is 0.86. The obtained value of
adjusted R square value implies that international tourism, number of arrivals explains 86 percent
variation in number of passengers carried by air travel. The coefficient of X3 is 14.572. The
positive coefficient and high value of R square implies that the number of arrivals in
international tourism positively affects the number of passengers travelled by air. Finally, the p
value of the coefficient is 0.000. The p value less than significant value implies that the variable
is statistically significant.

6PREDICTIVE DEMAND ANALYSIS
Bivariate regression between Y and X4
Table 4: Result of regression of Y on X4
The estimated regression equation from the above regression equation is obtained as
Y =−76037256.658+ 5.950 X4
The estimated value of adjusted R square from the regression is 0.95. The implication of
adjusted R square value is that population accounts 95 percent variation in number of passengers
carried by air travel. The coefficient of X4 is 5.950. The positive coefficient along with high
value of R square implies that population has a strong positive influence on the number of
passengers travelled by air. The associated p value of the coefficient is 0.000 (Carroll 2017). The
p value less than significant value implying population has a statistically significant relation with
number of passengers travelled by air.

7PREDICTIVE DEMAND ANALYSIS
Task 3
Model 1
Table 5: Regression result of Y on X1 and X2
Using the regression result, the estimated regression equation is obtained as
Y =5885699.608+532.089 X1 +2.598 X2
The adjusted R square value for the regression model is 0.98. That means per capita GDP and
number of departures in international tourism account 98 percent variation in number of
passengers carried by air. Values of coefficient associated with GDP per capita and number of
departures in international tourism are 532.089 and 2.958 respectively. Both the coefficients are
positive meaning that both per capita GDP and number of departures in international tourism
positively influence passengers travelled by air (Darlington and Hayes 2016). The p value
associated with GDP per capita and number of departures in international tourism is 0.003 and

8PREDICTIVE DEMAND ANALYSIS
0.007 respectively. Both the p values are less than 5% significance level indicating that both are
statistically significant.
Model 2
Table 6: Regression result of Y on X1 and X4
Using the regression result, the estimated regression equation is obtained as
Y =2700834.078+ 1215.113 X 1−1.829 X4
In the above regression model, the value of adjusted R square is obtained as 0.98. GDP
per capita (X1) and population (X4) thus accounts for 98% percent variation in the passengers
carried by air travel. The associated coefficient of GDP per capita and population are 1215.115
and -1.829 respectively. GDP per capita thus has a positive association with number of
passengers carried by air mode. Population on the other hand has an adverse influence on
number of passengers carried by air mode. Associated p value for GDP per capita is 0.000
meaning the variable is statistically significant. P value associated with population is 0.071. For

9PREDICTIVE DEMAND ANALYSIS
population, P value exceeds the significance value and therefore implies the variable is not
statistically significant.
Model 3
Table 7: Regression result of Y on X1, X 2 and X4
Using the regression result, the estimated regression equation is obtained as
Y =−34430892.176+331.230 X1+2.181 X 2+2.613 X 4
For the third model, the adjusted R square value is 0.98. The independent variables in the
model that is GDP per capita, number of departures in international tourism and population
together account for 98 percent variation in number of passengers carried by air mode. The
respective regression coefficients of GDP per capita, number of departures in international
tourism and population are 331.230, 2.181 and 2.613. Positive regression coefficient implies all
the independent variables have a positive effect on number of passengers’ coefficient. P values

10PREDICTIVE DEMAND ANALYSIS
of all the three regression coefficients are greater than 0.05. Neither of the variables therefore are
statistically significant (Brook 2018).
Task 4
Table 8: Forecasted value of dependent variable
Year Model 1 Model 2 Model 3
2016
729860
75
662247
80
738946
47
2017
756132
33
665116
93
777130
93
2018
776125
31
670737
92
803379
97
2019
797125
91
669513
96
834569
60
2020
829070
67
676569
23
870001
16
The forecasted values of the dependent variable are derived from three different models
having different independent variables With differences in number of predictor variables and
associated valued of the coefficient predicted values also differ. In model 3 number of predictor
variables is 3 and all are positive. Therefore, predicted values obtained from model 3 are larger
compared to those obtained from model 1 and model 2 . In order to determine which model fits
the best forecasted values needs to be compared with the actual values (Hox, Moerbeek and Van
de Schoot 2017). The actual number of passengers in 2016 is 72597701. The predicated values
of number of passengers in 2016 from model 1, model 2 and model 3 are obtained as 72986075,
66224780 and 73894647 respectively. The forecasting error from the three model is given below
Model Forecasting Error
Model 1 - 388,374
Model 2 6,372,920
Model 3 - 1,296,946

11PREDICTIVE DEMAND ANALYSIS
As shown from the above table, forecasting error is minimum for model 1 while it is
highest for model 2. Model 1 therefore fits the best.