Sweetness of orange juice. Refer to the study of the quality of orange juice produced at a...

Sweetness of orange juice. Refer to the study of the quality of orange juice produced at a juice manufacturing plant, Exercise.

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.

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b. Interpret  in the words of the problem.

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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 9.6 .]

Note: The data in the table are authentic. For reasons of confidentiality, the name of the manufacturer cannot be disclosed.

The data are saved in the OJUICE file. Recall that simple linear regression was used to predict the sweetness index ( y ) from the amount of pectin ( x ) in orange juice manufactured during a production run.

a. Give the values of SSE, s2 , and s for this regression.

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b. Explain why it is difficult to give a practical interpretation to s2 .

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c. Use the value of s to derive a range within which most (about 95%) of the errors of prediction of sweetness index fall.