Sweetness of orange juice. Refer to Exercise 11.28 (p. 565) and the simple linear regression relating the sweetness index ( y ) of an orange juice sample to the amount of water-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.

Exercise 11.28

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 ₀ and 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 11.6.]