The quality of the orange juice produced by a manufacturer (e.g., Minute Maid, Tropicana) is constantly monitored.

Question:

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 on the next page. Suppose a manufacturer wants to use simple linear regression to predict the sweetness (v) from the amount of pectin (x).

a. Find the least squares line for the data.
b. Interpret 0 and 1, in the words of the problem.
c. Predict the sweetness index if amount of pectin in the orange juice is 300 ppm. [A measure of reliability of such a prediction is discussed in Section 11.6)