28 Sweetness of orange juice The quality of the orange juice produced by a manufacturer 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 is 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 during 24 production runs at a juice-manufacturing plant are shown in the table and saved in the OJUICE file. Suppose a manufacturer wants to use simple linear regression to predict the sweetness ( y ) from the amount of pectin ( x ).

a. Find the least squares line for the data.

b. Interpret b n

0 and b n

1 in the words of the problem.

c. Predict the sweetness index if the amount of pectin in the orange juice is 300 ppm. [ Note: A measure of reliability of such a prediction is discussed in Section 6 .]

Transcribed Image Text:

Run Sweetness Index Pectin (ppm) 1234567 567890122882 5.2 5.5 220 227 6.0 259 5.9 210 5.8 224 6.0 215 5.8 231 5.6 268 5.6 239 5.9 212 11 5.4 410 5.6 256 13 5.8 306 14 5.5 259 5.3 5.3 284 383 5.7 271 5.5 264 5.7 227 5.3 263 5.9 232 5.8 220 23 24 5.8 246 5.9 241 Note: The data in the table are authentic. For reasons of confidentiality, the name of the manufacturer cannot be disclosed.