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.

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

a. Find the le_ast squ_ares line for the data.

b. Interpret P,, and PI in the words of the problem.

c. Predict the sweetness index if amount of pectin in the orangc juice is 300 ppm. [Note: A measure of reliability of such a prediction is discussed in Section 9.81