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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