Sweetness of orange juice. Refer to Exercise,Sweetness of orange juice The quality of the...

Sweetness of orange juice. Refer to 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.

and the simple linear regression relating the sweetness index ( y ) of an orange juice sample to the amount ofwater-soluble pectin ( x ) in the juice. The data are saved in the OJUICE file. Find a 95% confidence interval for the true slope of the line. Interpret the result.