Question

3. Production technologies, terroir, and quality of Bordeaux wine. 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. Write a model for wine quality (y) as a function of soil type. b. Interpret the B1 in the model in part (a) c. Write a 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. Interpret the value of B3 in the model in part ( c). 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. Write an interaction model relating wine quality to the three qualitative independent variables; grape-picking method (manual or automated), soil type (clay, gravel, or sand) and slope orientation (east, south, west, southeast, or southwest) d. e. f.

Answer 1

We have three independent qualitative variables.

First of all creating a dummy variable,

x1= 1, if grape picking method is manual, otherwise 0.

x2=1,if soil type is clay,otherwise 0

x3=1,if soil type is gravel,otherwise 0

x4=if slope orientation is east, otherwise 0

x5=if slope orientation is south, otherwise 0

x6=1,if slope orientation is west,otherwise 0

x7=if slope orientation is southeast, otherwise 0

a.Model of y as a function of soil type

y=$\beta_{0}+\beta_{1}x_{2}+\beta_{3}x_{3}$

b.Here, is the difference between soil type clay and sand.

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c.$y=\beta_{0}+\beta_{1}x_{1}+\beta_{2}x_{2}+\beta_{3}x_{3}$

d.Here the $\beta_{3}$ is the difference between soil type gravel and sand.

Note: Please ask rest part separately.

Thank you.