Statistics project

1. Factors Influencing the Price of Florida Bell Peppers Presented by: BikramAulakh and Catherine Klasne

2. Introduction Imagine you are a typical South Florida farmer with a decision to make about what to plant on your 195 acres.

4. Should you grow bell peppers and, if so, how many should you aim to produce? Beyond pure judgment, is there a way to make these choices, and what model-based formulas or equations would aid in decision-making? What factors influence the price of Floridabell peppers? Considerations

5. Statistics can help! Depending on how much data can be gathered by farms’ marketing and research personnel, and how much time they have to work with it – and on how well they recognize trends and use them to forecast – our models can provide insight.

6. Our data We found 37 complete observations we could manipulate with ordinary-least-squares software to arrive at useful models that should hold for any year under consideration.

7. The unit of observation The state of Florida in one year.

8. The time period covered: 1960 to 2006.

9. Variables in the following classifications were tested:1. Supply U.S. annual production of bell peppers, U.S. annual imports and U.S. total annual supply, all in millions of pounds U.S. annual exports in millions of pounds U.S. acreage planted in bell peppers and U.S.acreage on which bell peppers were harvested annually Independent variables:

10. More supply-related variables: Total annual U.S. yield in hundredweights Florida acreage planted annually in bell peppers and acreage within the state on which bell peppers were harvested annually Florida’s total production in thousands of hundredweights (or yield in hundredweights) Independent variables:

11. 2. Demand U.S. domestic consumption of bell peppers in millions of pounds annually Average U.S. population in millions U.S. annual per capita use in pounds Independent variables:

12. 3. Related pricing Average U.S. price of bell peppers per hundredweight U.S. farm value per unit in dollars per hundredweight Average price of bell peppers in dollars per hundredweight in a competing state, such as California Independent variables:

13. Data sources: Lucier & Toland, U.S. Bell and Chile Pepper Statistics, Stock #2007-001, 2008. This data set contains 67 tables concerning bell peppers, “also known as green, sweet or nonpungent,” in the U.S. and various states, covering acreage, yield, production, price, crop value and per capita use.

14. Regression estimations A brief trip through our model iterations

15. MINITAB eliminated three of the possible independent variables for which data existed, leaving us with an equation that contained a constant and 19 other X’s: FL farm value per unit ($/cwt) = 25.8 - 21.9 US production (Mlbs) - 21.9 US imports (Mlbs) + 21.9 US exports (Mlbs) +21.9US domestic use (Mlbs) + 2.17 US price ($/cwt)- 0.136 US population (Millions) - 11.4 US per capita use (lbs)+ 0.000121 US planted acreage + 0.000290 US harvested acreage+ 0.109 US yield (cwt) + 0.000596 FL planted acreage - 0.00137 FL harvested acreage + 0.00452 FL production (1000 cwt) - 0.0683 FL yield (cwt) - 0.00255 Cal planted acreage +0.00253 Cal harvested acreage + 0.00195 Cal production(1000 cwt) - 0.0135 Cal yield (cwt) - 1.09 Cal farm valueper unit ($/cwt) Initial model

16. Comment The model passes the F-test with a p-value of 0.000, less than the tolerated maximum value of .05, probably meaning at least one of the independent variables affects the dependent variable. The adjusted R2is 99.4% -- variations in the independent variables probably explain 99.4% of the variation in the dependent variable, Florida farm value in units of dollars perhundredweight. Only about 0.6% of the variation in Y is left to be explained. Coefficient signs indicate a (+) positive or direct relationship between an X and the dependent variable or a (-) negative or inverse relationship between the particular X and the Y, or dependent variable.

17. In reviewing the analysis based on p-values and rho, we decided to weed out 13 more variables. Refining the model

18. We plotted the 19 IV’s individually against the DV; most plots were nonlinear, with the exception of that for US price against FL farm value per unit. Correct functional form? Omitted variables?

19. Nonlinear v. Linear We successfully converted the other 18 relationships into linear or straight-line graphs.

20. Our correlation matrix helped us to decide to keep one of the variables. Multicollinearity

21. We realized that even 19 variables could be an unwieldy model for practical purposes and wanted to drop some of them. However, the variance inflation factor is greater than 10 for all of the independent variables, meaning they all could be considered for our final model. Multicollinearity

22. With a constant and 6 independent variables, the equation looks like this: FL farm value per unit ($/cwt) = 3.70+ 0.00366 US imports (Mlbs)+ 2.27 US price ($/cwt)+ 0.633 US per capita use (lbs)+ 0.000344 FL planted acreage- 0.000835 FL harvested acreage - 1.21 Cal farm value per unit ($/cwt) Final model

23. The adjusted R2 of 97.3% means the variation in the independent variables for the final model probably explains 97.3% of the variation in the dependent variable; about 2.7% remains to be explained. Based on the equation and individual T-test p-values, we can say:+ 0.00366 US imports (Mlbs): For every increase of 1 million pounds of imported bell peppers, we can be 55.9% confident the price of purchasing a hundredweight (100 pounds) of bell peppers from a Florida farmer rises by about 4 cents on averagefor that year. Final model evaluation

24. Interpretation of coefficients continued:+ 0.633US per capita use (lbs): For every increase of 1 pound in per capita consumption of bell peppers in the United States, Florida farmers will be paid an average of 63 cents more for a hundredweight of bell peppers (75.3% confidence).+ 0.000344 FL planted acreage: For every additional Florida acre planted in bell peppers, Florida farmers will be paid about 1/3 cent more for a hundredweight of bell peppers (64.5% confidence). Final model evaluation

25. Interpretation of coefficients continued: - 0.000835 FL harvested acreage: For every 1-acre increase in Florida land on which bell peppers are harvested, the Florida farmers’ price falls by less than a tenth of a cent per hundredweight (93.4% confidence).- 1.21 Cal farm value per unit ($/cwt): For each additional dollar California farmers are paid for a hundredweight of bell peppers, Florida farmers’are paid $1.21 less (nearly 100% confidence). Final model evaluation

26. Additional analysis shows that we could further refine our model, but we believe the VIF values favor keeping all six remaining X’s. Final model evaluation

27. Summary A useful and highly relevant model

28. All of our models, generally, are highly relevant. By plugging the required values into our equations, Florida bell-pepper farmers can achieve results that will be of use in determining, for example: How many bell peppers to aim at growing and reasonable asking prices. How many laborers to hire to harvest this quantity. How much fertilizer, pesticide and other supplies to purchase. The factors that influence the price of bell peppers produced on Florida farms. We have shown, in a quantifiable way, the direction and strength of these influences – instructive information for the state’s major bell pepper growers.

29. Our study answered our major questions well and provided some additional insights.