# 28 Sweetness of orange juice The quality of the orange juice produced by a manufacturer is constantly

## Question:

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 .]

## Step by Step Answer:

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