Statistical Models Used in the Forecasting of Automobile Sales

1. Statistical Models Used in the Forecasting of Automobile Sales Ben Nelson, Ling-Chih Chen, Hsiu-Jung Hu, Yuliy Nesterenko, Bin Shi, Kimberly Williams

2. F Objective F Models Used F Variables Used F Multiple Regression F Time Series F Multiple Regression vs Time Series F Managerial Explanation Introduction

3. 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.

4. F Multiple Regression Models F Time Series Decomposition F ARIMA Box Jenkins Models Used

5. F Dependent Variable (Y) F Independent Variables (X’s) Multiple Regression Variables - Auto Sales • - 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

6. F Independent Variables (X’s) -- continued Multiple Regression Variables • - 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

7. F Scatterplots:indicate a majority of the dependent variables have a linear relationship with the independent variable. Independent Variable Assessment 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.

8. F 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). All Possible Regression Report Independent Variable Assessment • 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”.

9. F Model Evaluation Section Multiple Regression Analysis 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)

10. F Time-Series Decomposition Analysis Time-Series Decomposition

11. Time-Series Decomposition F Time-Series Decomposition Analysis – cont.

12. Time-Series Decomposition

13. Time-Series ARIMA

14. F Comparison of Forecast vs. Actual Regression vs. Time-Series

15. F ARIMA presents the best forecasting model Managerial Summary Jan. 1997 . . . . . . . 51,412.70 Feb. 1997 . . . . . . . 51,734.50 Mar. 1997 . . . . . . . 52,056.20 Apr. 1997 . . . . . . . 52,377.90