Statistical Models Used in the
Forecasting of Automobile Sales
Ben Nelson, Ling-Chih Chen, Hsiu-Jung Hu,
Yuliy Nesterenko, Bin Shi, Kimberly Williams
Introduction
F Objective
F Models Used
F Variables Used
F Multiple Regression
F Time Series
F Multiple Regression vs Time Series
F Managerial Explanation
Objective
The objective of this project was to
select the most viable statistical
model to forecast Auto-sales for the
USA.
Our exercise included model
building, model validating and
model selection.
Models Used
F Multiple Regression Models
F Time Series Decomposition
F ARIMA Box Jenkins
Multiple Regression Variables
F Dependent Variable (Y)
- Auto Sales
F Independent Variables (X’s)
-
Number of unemployed persons (thousands)
Bank credit
Real personal income (billions of chanied)
Federal funds rate
Japan (yen per US)
Germany (Deutsche mark per US)
Manufacturing of autos & light trucks
Manufacturing of rubber & plastic products
Petroleum products consumption
Truck tonnage index
Multiple Regression Variables
F Independent Variables (X’s) -- continued
-
Central & South America nuclear electric
Texas marketed production of natural gas (unit 10,000)
Imports on machinery (transportation equipment)
Exports on manufactured goods
S&P stock price index on transportation
Producer price index in finished consumer goods
Real wages & salaries in mining manufacturing
Expenditures on furniture & household equipment
S&P’s stock prices (500 common stocks)
Index of help wanted advertising
Passenger fares
Independent Variable Assessment
F Scatterplots: indicate a majority of the
dependent variables have a linear
relationship with the independent variable.
X2
X3
X4
X5
X6
X23
X1
X8
X13
X14
X9
X10
X11
X12
X23
X7
X23
X16
X23
X20
X21
X22
X17
X18
X19
We transformed
2 variables:
(Producer price
index of finished
consumer goods
& S&P's stock
prices of 500
common stocks )
by using their
squared value.
Independent Variable Assessment
F Using the Pearson Correlation report for all
variables, the variables with a coefficient of
.75 or higher were picked. (There were 4 of
the 21 variables which were > .75).
F All Possible Regression Report
Model 1 : “Auto-sales” with variable 14: “Exports of
manufactured goods” only.
Model 2 : “Auto-sales” with variables 13 and 14: “Exports
of manufactured goods ” and “Imports of machinery &
transportation equity”.
Model 3 : “Auto-sales” with variables 14, 2, and 19:
“Exports of manufactured goods”, “Bank credit” and
“Expenditures on furniture & household equity”.
Multiple Regression Analysis
F Model Evaluation Section
Model 1
Model 2
Model 3
Probability
0.000000
0.000000
0.000000
Adj R-Squared
0.6517
0.6529
0.6479
Significance
component variables
1 of 1
1 of 2
1 of 3
Linearity
OK
OK
OK
Independence
OK
OK
OK
Normality
Rejected
Rejected
Rejected
Equal variance
OK
OK
OK
Model 1: Auto sales = 58,13.639 + 1.100639 (Exports of manufactured goods)
Time-Series Decomposition
F Time-Series Decomposition Analysis
Cycle Ratio Chart
1.3
1.3
1.1
1.1
C ycle
T rend
Trend Ratio Chart
1.0
0.9
0.9
0.8
1992.9
1.0
1994.1
1995.3
Time
1996.6
1997.8
0.8
1992.9
1994.1
1995.3
Time
1996.6
1997.8
Time-Series Decomposition
F Time-Series Decomposition Analysis – cont.
Error Ratio Chart
1.3
1.3
1.1
1.1
Error
Season
Season Ratio Chart
1.0
0.9
0.9
0.8
1992.9
1.0
1994.1
1995.3
Time
1996.6
1997.8
0.8
1992.9
1994.1
1995.3
Time
1996.6
1997.8
Time-Series Decomposition
X23 Chart
55000.0
X23
50000.0
45000.0
40000.0
35000.0
1992.9
1994.1
1995.3
Time
1996.6
1997.8
Time-Series ARIMA
X23-TREND Chart
60000.0
X23-T R EN D
53750.0
47500.0
41250.0
35000.0
1992.9
2004.9
2016.9
Time
2028.9
2040.9
Regression vs. Time-Series
F Comparison of Forecast vs. Actual
Year/
Month
Sep-96
Oct-96
Nov-96
Dec-96
Regression
Actual
Value
49,673.38
52,510.95
46,584.91
44,653.54
Total Variation
Actual
Value
51,475.00
51,684.00
51,024.00
51,091.00
Decomposition
51,699.42
52,965.07
53,679.86
53,808.89
ARIMA
MRA
50,632.00
50,965.90
51,299.90
51,633.90
49,206.32
53,625.39
52,258.40
51,395.50
ABS value ABS value ABS value
of Residule of Residule of Residule
for Decom. for ARIMA
for MRA
224.42
843.00
467.06
1,281.07
718.10
1,114.44
2,655.86
275.90
5,673.49
2,717.89
542.90
6,741.96
6,879.24
2,379.90
13,996.95
Managerial Summary
F ARIMA presents the best forecasting model
Jan. 1997 . . . . . . . 51,412.70
Feb. 1997 . . . . . . . 51,734.50
Mar. 1997 . . . . . . . 52,056.20
Apr. 1997 . . . . . . . 52,377.90