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# QMBU

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Fall 2005 …

Fall 2005
Koç University QMBU 301 Quantitative Methods in Business
Final Project
Homework

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• 1. QMBU 301 FORECASTING YEARLY AREA SOWN IN TURKEY Ceren Sekban Özge Şahlanan Tutku Özmen Burcu Kurt Beste Yılmayan
• 2.
• 3. OBSERVED PATTERNS
• Increasing trend.
• Trend component increased significantly after 1980
• Not random
• Consequtive years have similar areas sown
• Decreasing trend after 1990
• 4. CANDIDATE METHODS
• Regression
• Single exponential smoothing
• Double exponential smoothing
• Moving average
• Trend analysis (linear trend)
• 5. REGRESSION
• 6. Potential Drivers
• Employed population in agriculture
• The percentage of area that is fallowed each year
• The amount of forest fires that is done to open new agricultural areas
• Number of equipment and machinery used for agricultural purposes
• The value of agricultural output in a year
• Observed technological development in agriculture; development of new machinery with the capability of cultivating a land which was hard to cultivate with previous methods
• 7.
• Regression Analysis: Area sown versus total agricu; Forest area ; ...
• The regression equation is
• Area sown = 20283 - 0,000683 total agricultural credits
• + 0,0289 Forest area burned(hectares)
• - 0,000049 Fertilizer used(tons)
• Predictor Coef SE Coef T P
• Constant 20282,9 108,0 187,80 0,003
• total agricultural credits -0,00068339 0,00001841 -37,12 0,017
• Forest area burned(hectares) 0,028945 0,001202 24,08 0,026
• Fertilizer used(tons) -0,00004892 0,00000833 -5,87 0,107
• S = 16,4593 R-Sq = 99,9% R-Sq(adj) = 99,7%
• Analysis of Variance
• Source DF SS MS F P
• Regression 3 421765 140588 518,95 0,032
• Residual Error 1 271 271
• Total 4 422036
• Residual Plots for Area sown
Regression Analysis
• 8.
• 9. OBSERVED PATTERNS AVAILABLE DATA
• Consequtive years have similar areas sown
• Trend component increased significantly after 1980 due to existence of free trade
• Lag 1
• Economic Policy (Free Trade)( Free trade years expressed in a duumy variable)
• 10. Correlations: Area sown; free trade; lag1 Area sown free trade free trade 0,834 0,000 lag1 0,987 0,828 0,000 0,000 Cell Contents: Pearson correlation P-Value
• 11.
• Regression Analysis: Area sown versus free trade; lag1
• The regression equation is
• Area sown = 2904 + 429 free trade + 0,821 lag1
• 48 cases used, 1 cases contain missing values
• Predictor Coef SE Coef T P
• Constant 2903,9 531,2 5,47 0,000
• free trade 429,2 124,8 3,44 0,001
• lag1 0,82052 0,03486 23,54 0,000
• S = 240,376 R-Sq = 98,0% R-Sq(adj) = 97,9%
• Analysis of Variance
• Source DF SS MS F P
• Regression 2 128717224 64358612 1113,84 0,000
• Residual Error 45 2600132 57781
• Total 47 131317356
• Durbin-Watson statistic = 2,19863
• 12.
• 13. SINGLE EXPONENTIAL SMOOTHING
• 14. Single Exponential Smoothing
• 15. Single Exponential Smoothing
• 16. DOUBLE EXPONENTIAL SMOOTHING
• 17. Double Exponentioal Smoothing
• 18. Double Exponentioal Smoothing
• 19. MOVING AVERAGE (k=3)
• 20. Moving Average, k=3
• 21. Moving Average, k=3
• 22. TREND ANALYSIS (LINEAR TREND MODEL)
• 23. Trend Analysis (Linear Trend Model)
• 24. Trend Analysis (Linear Trend Model)
• 25. 286367 404 3 x Linear Trend 188862 312 2 x Moving average (k=3) 73662.8 217.3 1.4 √ Double Exponential Smoothing 100983 227 1 √ Single Exponential Smoothing 57781 - - √ Regression MSD MAD MAPE Adequacy
• 26. 17692.4 17913.1 18133.9 Double Ex. Smoothing 18280,95 18280,95 18280,95 Regression Forecast 3 Forecast 2 Forecast 1