Question

In addition to state-of-the-art technologies, the production of quality wine is strongly influenced by the natural endowments of the grape-growing region—called the ‘‘terroir.’’ The Economic Journal (May 2008) published an empirical study of the factors that yield a quality Bordeaux wine. A quantitative measure of wine quality (y) was modeled as a function of several qualitative independent variables, including grape-picking method (manual or automated), soil type (clay, gravel, or sand), and slope orientation (east, south, west, southeast, or southwest).

a. Create the appropriate dummy variables for each of the qualitative independent variables.

b. Write a model for wine quality (y) as a function of grape-picking method. Interpret the β’s in the model.

c. Write a model for wine quality (y) as a function of soil type. Interpret the β’s in the model.

d. Write a model for wine quality (y) as a function of slope orientation. Interpret the β’s in the model.

e. Write an interaction model relating wine quality to the two qualitative independent variables; grape-picking method (manual or automated) and soil type (clay, gravel, or sand). Let ‘‘automated’’ and ‘‘sand’’ represent the base levels for the two variables, respectively.

f. Interpret the value of ?0 in the model.

g. In terms of the β’s, what is the mean quality of wine produced from grapes picked manually from clay soil?

h. In terms of the β’s, what is the difference between the mean quality of wine produced from grap

Answer 1

a.

The qualitative independent variables are grape-picking method (manual or automated), soil type (clay, gravel, or sand), and slope orientation (east, south, west, southeast, or southwest).

Dummy variable for grape-picking method is,

grape-picking-manual = 0 for automated grape-picking method

grape-picking-manual = 1 for manual grape-picking method

Dummy variable for soil type is,

soil-type-clay = 0, soil-type-gravel = 0 for sand

soil-type-clay = 1, soil-type-gravel = 0 for clay

soil-type-clay = 0, soil-type-gravel = 1 for gravel

Dummy variable for slope orientation is,

slope-south = 1 for south else = 0

slope-west = 1 for west else = 0

slope-southeast = 1 for southeast   else = 0

slope-southwest = 1 for southwest else = 0

b.

Model for wine quality (y) as a function of grape-picking method is,

y = + grape-picking-manual

is the wine quality for automated grape-picking method

is the difference between wine quality for manual and automated grape-picking method.

c.

The model for wine quality (y) as a function of soil type

Model for wine quality (y) as a function of grape-picking method is,

y = + soil-type-clay + soil-type-gravel

is the wine quality for sand soil

is the difference between wine quality for sand and clay soil.

is the difference between wine quality for sand and gravel soil.

d.

The model for wine quality (y) as a function of slope orientation.

y = + slope-south + slope-west + slope-southeast + slope-southwest

is the wine quality for east slope orientation

is the difference between wine quality for east slope orientation and south slope orientation.

is the difference between wine quality for east slope orientation and west slope orientation

is the difference between wine quality for east slope orientation and southeast slope orientation

is the difference between wine quality for east slope orientation and southwest slope orientation