Reference no: EM131723683

Question: Sweetness of orange juice. Refer to Exercise 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. Find a 90% confidence interval for the true slope of the line. Interpret the result

Exercise: 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 on p. 102. 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 β₀ and β₁ in the words of the problem.

(c) Predict the sweetness index if amount of pectin in the orange juice is 300 ppm.