Refer to Exercise 11.4. Predict the firmness for a can of sweet potatoes treated with a 1% concentration of pectin (by weight) after 30 days of storage at 25°C.
Exercise 11.4
A food processor conducted an experiment to examine the effect of different concentrations of pectin on the firmness of canned sweet potatoes, using three concentrations: 0, 1.5, and 3% pectin by weight. The processor packed six number 303 × 406 cans with sweet potatoes in a 25% (by weight) sugar solution. Two cans were randomly assigned to each of the pectin concentrations with the appropriate percentage of pectin added to the sugar syrup. The cans were then sealed and placed in a 25°C environment for 30 days. At the end of the storage time, the cans were opened and a firmness determination made for the contents of each can. These data appear here:
Pectin concentration | 0%, 0% | 1.5%, 1.5% | 3.0%, 3.0% |
Firmness reading | 50.5, 46.8 | 62.3, 67.7 | 80.1, 79.2 |
a. Let x denote the pectin concentration of a can and y denote the firmness reading following the 30 days of storage at 25°C. Plot the sample data in a scatterplot.
b. Obtain least-squares estimates for the parameters in the model y = β0 + β1x + ε.
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