Number of Certified Organic Farms in the United States, 2001–2008 Year Farms 2001 6,231 2002 6,574 2003 7,237 2004 7,211 2005 7,701 2006 8,581 2007 10,302 2008 11,796 Click here for the Excel Data File (a) Fit three trends (linear, quadratic, exponential) to the time series. (A negative value should be indicated by a minus sign. Do not round the intermediate calculations. Round your final answers to 2 decimal places.) Linear yt = xt + Quadratic yt = xt2+ xt + Exponential yt = e x (b) Use each of the three fitted trend equations to make numerical forecasts for the next three years. (Round the intermediate calculations to 2 decimal places and round your final answers to 1 decimal place.) t Linear Exponential Quadratic 9 10
Inverse Normal Distribution
The method used for finding the corresponding z-critical value in a normal distribution using the known probability is said to be an inverse normal distribution. The inverse normal distribution is a continuous probability distribution with a family of two parameters.
Mean, Median, Mode
It is a descriptive summary of a data set. It can be defined by using some of the measures. The central tendencies do not provide information regarding individual data from the dataset. However, they give a summary of the data set. The central tendency or measure of central tendency is a central or typical value for a probability distribution.
Z-Scores
A z-score is a unit of measurement used in statistics to describe the position of a raw score in terms of its distance from the mean, measured with reference to standard deviation from the mean. Z-scores are useful in statistics because they allow comparison between two scores that belong to different normal distributions.
| Number of Certified Organic Farms in the United States, 2001–2008 |
|
| Year | Farms |
| 2001 | 6,231 |
| 2002 | 6,574 |
| 2003 | 7,237 |
| 2004 | 7,211 |
| 2005 | 7,701 |
| 2006 | 8,581 |
| 2007 | 10,302 |
| 2008 | 11,796 |
Click here for the Excel Data File
(a) Fit three trends (linear, quadratic, exponential) to the time series. (A negative value should be indicated by a minus sign. Do not round the intermediate calculations. Round your final answers to 2 decimal places.)
| Linear | yt = xt + |
| Quadratic | yt = xt2+ xt + |
| Exponential | yt = e x |
(b) Use each of the three fitted trend equations to make numerical forecasts for the next three years. (Round the intermediate calculations to 2 decimal places and round your final answers to 1 decimal place.)
| t | Linear | Exponential | Quadratic |
| 9 | |||
| 10 | |||
| 11 | |||
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