The U.S. Food and Drug Administration (FDA) requires nutrition labeling for most foods. Under FDA regulations, manufacturers

Question:

The U.S. Food and Drug Administration (FDA) requires nutrition labeling for most foods. Under FDA regulations, manufacturers are required to list the amounts of certain nutrients in their foods, such as calories, sugar, fat, and carbohydrates. This nutritional information is displayed in the “Nutrition Facts” panel on the food’s package.

The table shows the nutritional content below for one cup of each of 21 different breakfast cereals.

C = calories S = sugar in grams F = fat in grams R = carbohydrates in grams

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1. Use technology to draw a scatter plot of the \((x, y)\) pairs in each data set.

(a) (calories, sugar)

(b) (calories, fat)

(c) (calories, carbohydrates)

(d) (sugar, fat)

(e) (sugar, carbohydrates)

(f) (fat, carbohydrates)
2. From the scatter plots in Exercise 1, which pairs of variables appear to have a strong linear correlation?
3. Use technology to find the correlation coefficient for each pair of variables in Exercise 1. Which has the strongest linear correlation?
4. Use technology to find an equation of a regression line for each pair of variables.

(a) (calories, sugar)

(b) (calories, carbohydrates)
5. Use the results of Exercise 4 to predict each value.

(a) The sugar content of one cup of cereal that has 120 calories

(b) The carbohydrate content of one cup of cereal that has 120 calories 6. Use technology to find the multiple regression equations of each form.

(a) \(C=b+m_{1} S+m_{2} F+m_{3} R\)

(b) \(C=b+m_{1} S+m_{2} R\)
7. Use the equations from Exercise 6 to predict the calories in 1 cup of cereal that has 7 grams of sugar, 0.5 gram of fat, and 31 grams of carbohydrates.