Problems for Chapters 47 Through 49

Fizzy Drugs wants to optimize the yield from an important chemical process. The company thinks that the number of pounds produced each time the process is run depends on the size of the container used, the pressure, and the temperature. The scientists involved believe the effect of changing one variable might depend on the values of other variables. The size of the process container must be between 1.3 and 1.5 cubic meters, pressure must be between 4 and 4.5 mm, and temperature must be between 22 and 30 degrees Celsius. The scientists patiently set up experiments at the lower and upper levels of the three control variables and obtain the data shown in the file Fizzy.xlsx.

1. Determine the relationship between yield, size, temperature, and pressure.

2. Discuss the interactions between pressure, size, and temperature.

3. What settings for temperature, size, and pressure would you recommend?

   Here are additional multiple regression problems:

4. For 12 straight weeks, you have observed the sales (in number of cases) of canned tomatoes at Mr. D’s Supermarket. (See the file Grocery.xlsx.) Each week, you keep track of the following:

   • Was a promotional notice for canned tomatoes placed in all shopping carts?

   • Was a coupon for canned tomatoes given to each customer?

   • Was a price reduction (none, 1, or 2 cents off) given?

   Use this data to determine how the above factors influence sales. Predict sales of canned tomatoes during a week in which we use a shopping cart notice, a coupon, and reduce price by 1 cent.

5. The file Countryregion.xlsx contains the following data for several underdeveloped countries:

   • Infant mortality rate

   • Adult literacy rate

   • Percentage of students finishing primary school

   • Per capita GNP

   Use this data to develop an equation that can be used to predict infant mortality. Are there any outliers in this set of data? Interpret the coefficients in your equation. Within what value should 95 percent of our predictions for infant mortality be accurate?

6. The file Baseball96.xlsx gives runs scored, singles, doubles, triples, home runs, and bases stolen for each major league baseball team during the 1996 season. Use this data to determine the effects of singles, doubles, and other activities on run production.

7. The file Cardata.xlsx provides the following information for 392 different car models:

   • Cylinders

   • Displacement

   • Horsepower

   • Weight

   • Acceleration

   • Miles per gallon (MPG)

Determine an equation that can be used to predict MPG. Why do you think all the independent variables are not significant?