Run SweetIndex Pectin 1 5.2 220 2 5.5 227 3 6.0 259 4 5.9 210 5 5.8 224 6 6.0 215 7 5.8 231 8 5.6 268 9 5.6 239 10 5.9 212 11 5.4 410 12 5.6 256 13 5.8 306 14 5.5 259 15 5.3 284 16 5.3 383 17 5.7 271 18 5.5 264 19 5.7 227 20 5.3 263 21 5.9 232 22 5.8 220 23 5.8 246 24 5.9 241 The quality of the orange juice produced by a manufacturer (e.g Minute Maid, Tropicana) is constantly monitored. There are numerous sensory and chemical components that combine to make the best tasting orange juice. The higher the index, the sweeter the juice. Is there a relationship between the sweetness index and a chemical measure such as the amount of water-soluble pectin (parts per million) in the orange juice? Data collected on these two variables for 24 production runs at a juice manufacturing plant are in the file OJUICE.txt (on blackboard). Suppose a manufacturer wants to use simple linear regression to predict the sweetness (y) from the amount of pectin (x). Based on the scatterplot, would a simple linear regression be appropriate to use? If yes, find the least squares line for the data. Compute 4th and 20th residuals and interpret. Interpret the slope and intercept in the words of the problem. Predict the sweetness index if the amount of pectin in the orange juice is 300 pp
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.
|
Run
|
SweetIndex
|
Pectin
|
|
|---|---|---|---|
| 1 | 5.2 | 220 | |
| 2 | 5.5 | 227 | |
| 3 | 6.0 | 259 | |
| 4 | 5.9 | 210 | |
| 5 | 5.8 | 224 | |
| 6 | 6.0 | 215 | |
| 7 | 5.8 | 231 | |
| 8 | 5.6 | 268 | |
| 9 | 5.6 | 239 | |
| 10 | 5.9 | 212 | |
| 11 | 5.4 | 410 | |
| 12 | 5.6 | 256 | |
| 13 | 5.8 | 306 | |
| 14 | 5.5 | 259 | |
| 15 | 5.3 | 284 | |
| 16 | 5.3 | 383 | |
| 17 | 5.7 | 271 | |
| 18 | 5.5 | 264 | |
| 19 | 5.7 | 227 | |
| 20 | 5.3 | 263 | |
| 21 | 5.9 | 232 | |
| 22 | 5.8 | 220 | |
| 23 | 5.8 | 246 | |
| 24 | 5.9 | 241 |
The quality of the orange juice produced by a manufacturer (e.g Minute Maid, Tropicana) is constantly monitored. There are numerous sensory and chemical components that combine to make the best tasting orange juice.
The higher the index, the sweeter the juice.
Is there a relationship between the sweetness index and a chemical measure such as the amount of water-soluble pectin (parts per million) in the orange juice? Data collected on these two variables for 24 production runs at a juice manufacturing plant are in the file OJUICE.txt (on blackboard). Suppose a manufacturer wants to use simple linear regression to predict the sweetness (y) from the amount of pectin (x).
- Based on the
scatterplot , would a simple linear regression be appropriate to use? - If yes, find the least squares line for the data.
- Compute 4th and 20th residuals and interpret.
- Interpret the slope and intercept in the words of the problem.
- Predict the sweetness index if the amount of pectin in the orange juice is 300 ppm.
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