Sweetness of orange juice. Refer to the simple linear regression of sweetness index y and amount of pectin  for  = 24 orange juice samples, Exercise 11.26 (p. 656). A 90% confidence interval for the mean sweetness index, E(y), for each of the first 5 runs is shown on the SPSS spreadsheet below. Select an observation and interpret this interval.

Exercise 11.26

Sweetness of orange juice. 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 below. 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 amount of pectin in the orange juice is 300 ppm.

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