Refer to the simple linear regression of sweetness index y and amount of pectin x for n = 24 orange juice samples, Exercise 10.12. The SPSS printout of the analysis is shown below. A 90% confidence interval for the mean sweetness index, E(y), for each value of x is shown below on the SPSS spreadsheet. Select an observation and interpret this interval.    

Data from Exercise 10.12

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 next table. Suppose a manufacturer wants to use simple linear regression to predict the sweetness (y) from the amount of pectin (x).

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run sweet pectin lower90m upper90m 1 1 5.2 220 5.64898 5.83848 2 5.5 227 5.63898 5.81613 5.72904 259 210 3 6.0 5.57819 4 5.9 5.66194 5.87173 5 5.8 224 5.64337 5.82560 6 6.0 215 5.65564 5.85493 7 7 5.8 231 5.63284 5.80379 81 8 5.6 268 5.55553 5.71011 9 5.6 239 5.61947 5.78019 10 10 5.9 212 5.65946 5.86497 11 11 5.4 410 5.05526 5.55416 12 12 5.6 256 5.58517 5.73592 13 13 5.8 306 5.43785 5.65219 14 14 5.5 259 5.57819 5.72904 15 15 5.3 284 5.50957 5.68213 16 5.3 383 5.15725 5.57694 17 17 5.7 271 5.54743 5.70434 18 18 5.5 264 5.56591 5.71821 19 19 5.7 227 5.63898 5.81613 20 20 5.3 263 5.56843 5.72031 21 21 5.9 232 5.63125 5.80075 22 22 5.8 220 5.64898 5.83848 23 23 5.8 246 5.60640 5.76091 24 24 5.9 241 5.61587 5.77454 co co co LO lCO 555 555 n555 555 55 LO CO