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Modeling Functions

Modeling Functions. -Regression Project. Data Subject Chosen for the Project. The price of:. How it’s set up for the problems. Number of Years since 1959 (x-axis). Dollars converted to cents (y-axis). 1 (1960) 2 (1961) 3 (1962) 4 (1963) 5 (1964) 6 (1965) 7 (1966) 8 (1967) 9 (1968)

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Modeling Functions

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  1. Modeling Functions -Regression Project

  2. Data Subject Chosen for the Project The price of:

  3. How it’s set up for the problems Number of Years since 1959 (x-axis) Dollars converted to cents (y-axis) • 1 (1960) • 2 (1961) • 3 (1962) • 4 (1963) • 5 (1964) • 6 (1965) • 7 (1966) • 8 (1967) • 9 (1968) • 10 (1969) • 11 (1970) • 12 (1971) • 13 (1972) • 14 (1973) • 15 (1974) • 16 (1975) • 17 (1976) • 18 (1977) • 19 (1978) • 20 (1979) • 21 (1980) • 22 (1981) • 23 (1982) • 24 (1983) • 25 (1984) • 45 cents • 45 cents • 49 cents • 45 cents • 39 cents • 43 cents • 43 cents • 49 cents • 45 cents • 51 cents • 48 cents • 59 cents • 49 cents • 52 cents • 59 cents • 95 cents • 83 cents • 95 cents • 84 cents • 112 cents • 106 cents • 142 cents • 139 cents • 156 cents • 143 cents

  4. Table

  5. Scatter Plot of Data

  6. Linear Regression • Equation: • y=4.58769x+15.4 • r=.89232

  7. Linear Regression Plot

  8. Exponential Regression • Equation: • y=31.8206×1.05935ˆx • r=.92078

  9. Exponential Regression Plot

  10. Power Regression • Equation: • y=25.98941×xˆ.41028 • r=.74278

  11. Power Regression Plot

  12. Best Equation • EXPONENTIAL!

  13. Inside Predicted Data • 1965: 45 cents • 1968: 53 cents • 1976: 85 cents • 1982: 120 cents

  14. Outside Predicted Data Before 1960 After 1984 • 1922: 4cents • 1932: 7 cents • 1948: 17 cents • 1955: 25 cents • 1993: 226 cents • 1995: 301 cents • 2004: 426 cents • 2008: 602 cents

  15. Inside Comparison Between Predicted and Actual Predicted Actual • 1965: 45 cents • 1968: 53 cents • 1976: 85 cents • 1982: 120 cents • 1965: 43 cents – 2 cent diff. • 1968: 45 cents – 8 cent diff. • 1976: 43 cents – 42 cent diff. • 1982: 139 cents – 19 cent diff.

  16. Outside Comparison Between Predicted and Actual Before 1960 Predicted Before 1960 Actual • 1922: 4 cents • 1932: 7 cents • 1948: 17 cents • 1955: 25 cents • 1922: 32 cents – 28 cent diff. • 1932: 25 cents – 16 cent diff. • 1948: 53 cents – 36 cent diff. • 1955: 53 cents – 28 cent diff.

  17. Outside Comparison Between Predicted and Actual Cont. After 1984 Predicted After 1894 Actual • 1993: 226 cents • 1995: 254 cents • 2004: 426 cents • 2008: 537 cents • 1993: 328 cents – 102 cent diff. • 1995: 363 cents – 109 cent diff. • 2004: 299 cents – 127 cent diff. • 2008: 381 cents – 256 cent diff.

  18. Write up/Analysis I chose the price of Nabisco’s Oreo cookies because they are one of the most delicious treats ever and they are milk’s favorite cookie.  The first step was choosing the years. I chose 1960-1984 because every year was presented at “The Food Timeline” site. The only problem that was faced while collecting the data was that all the prices were not consistent with the weight of the snack so I had to convert some of the prices to per pound instead of their original weight. Then, I put all the data into my calculator into the STAT edit area and onto the computer in Microsoft Excel for graphing purposes. Then, I made a scatter plot of the collected data using Microsoft Excel. After completing this, I was then ready to find the appropriate equation that best represents the data. To do this, I pressed STAT, CALC, then scrolled down to the “LinReg(ax+b)” and pressed ENTER. I was then given the equation which was presented in slide 5. Then, I used Microsoft Excel to create the graph with the linear regression line on it. Next, I repeated those steps except after the STAT CALC, I pressed ENTER on “ExpReg” instead of the last one. Then I found the exponential equation. I then used Microsoft Excel again to create the graph for the exponential equation using the “trendline” function of the program. Finally, I repeated these steps one last time for the power regression equation. I pressed “PwrReg” and was given the final equation. I then made the last graph using Microsoft Excel and the “trendline” function and added it to this PowerPoint as I did with all three of the other graphs. Then, I moved on to begin the analysis. I first found out that the exponential function was the equation that best represented the data because the correlation coefficient was closest to the value 1.

  19. Write up/Analysis Cont. (This makes sense with the collected data because the cost of the Oreo’s seem to increase at an exponential rate rather than a linear or power rate.) With this equation, I was able to predict the values of specific data points inside the years I chose to work with. I chose the years 1965, 1968, 1976, and 1983. I noticed that there was up to a 42 cent difference between the actual and the predicted data. I then chose four points before 1960 and four points after 1984 to predict data outside the years that I chose to work with. With this predicted data, there was up to a 256 cent difference between the actual and the predicted! These large differences is most likely due to the fact that it’s a man made product that is in the market. The price, like gasoline, increases or decreases with demand. If more people want Oreo’s, the price increases and vise versa. It’s also a situational problem. If the economy is bad, then the prices could go down in order to keep the product in the market. This explains why some of the prices didn’t stay consistent with the pattern.

  20. Resources • http://www.foodtimeline.org/foodfaq5.html#oreoprices • http://logos.wikia.com/wiki/File:Oreo_logo.png • http://www.yenra.com/oreo/

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