Concept explainers
Sweetness of orange juice. 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. For example, one manufacturer has developed a quantitative index of the “sweetness” of 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 shown in the table below. Suppose a manufacturer wants to use simple linear regression to predict the sweetness (y) from the amount of pectin (x).
Run | Sweetness Index | Pectin (ppm) |
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 |
Note: The data in the table are authentic. For confidentiality reasons, the manufacturer cannot be disclosed. |
a. Find the least squares line for the data.
b. Interpret
c. Predict the sweetness index if amount of pectin in the orange juice is 300 ppm. [Note: A measure of reliability of such a prediction is discussed in Section 11.6]
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Statistics for Business and Economics, Student Value Edition (13th Edition)
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