91影视

The qualitative independent variables here are the grape-picking method, soil type, and slope orientation.

Let ${\mathbf{x}}_{\mathbf{1}}$be a grape-picking method, where ${\mathbf{x}}_{\mathbf{1}}\mathbf{=}\mathbf{1}$when it is manual and ${\mathbf{x}}_{\mathbf{1}}\mathbf{=}\mathbf{0}$when it is automated.

Since the soil type is categorized into three types, (k-1) = 2 no of dummy variables will be used

${\mathbf{x}}_{\mathbf{2}}$= soil type where value of ${\mathbf{x}}_{\mathbf{2}}$= 1 if soil type is clay; role="math" localid="1649840223066" ${\mathbf{x}}_{\mathbf{2}}$= 0 if soil type is gravel

role="math" localid="1649840195626" ${\mathbf{x}}_{\mathbf{3}}$= soil where value of role="math" localid="1649840208029" ${\mathbf{x}}_{\mathbf{3}}$= 1 if soil type is sand; role="math" localid="1649840215484" ${\mathbf{x}}_{\mathbf{3}}$= 0 if soil type is gravel

Similarly, slope orientation has 4 types hence (k-1) = 3dummy variables will be introduced in the model

${\mathbf{x}}_{\mathbf{4}}$= slope orientation where ${\mathbf{x}}_{\mathbf{4}}$= 1 if slope orientation is east; 0 otherwise

${\mathbf{x}}_{\mathbf{5}}$= slope orientation where ${\mathbf{x}}_{\mathbf{5}}$= 1 if slope orientation is west; 0 otherwise

${\mathbf{x}}_{\mathbf{6}}$= slope orientation where ${\mathbf{x}}_{\mathbf{6}}$= 1 if slope orientation is southeast; 0 otherwise

Therefore, to represent the 3 qualitative independent, 7 dummy variables will be created.

A model for wine quality (y) as a function of the grape-picking method can be written as $\mathbf{y}\mathbf{=}{\mathbf{尾}}_{\mathbf{0}}\mathbf{+}{\mathbf{尾}}_{\mathbf{1}}{\mathbf{x}}_{\mathbf{1}}$where ${\mathbf{x}}_{\mathbf{1}}$represents the grape-picking method.

${\mathbf{尾}}_{\mathbf{0}}$represents the wine quality (y) at a base level (here base level means the level when ${\mathbf{x}}_{\mathbf{1}}$= 0, meaning the wine quality when the grapes are picked automatically)

${\mathbf{尾}}_{\mathbf{1}}$ represents the changes in wine quality (y) when the grape-picking is manual.

A model for wine quality (y) as a function of soil type can be written as $\mathbf{y}\mathbf{=}{\mathbf{尾}}_{\mathbf{0}}\mathbf{+}{\mathbf{尾}}_{\mathbf{1}}{\mathbf{x}}_{\mathbf{2}}\mathbf{+}{\mathbf{尾}}_{\mathbf{2}}{\mathbf{x}}_{\mathbf{3}}$where ${\mathbf{x}}_{\mathbf{2}}$and ${\mathbf{x}}_{\mathbf{3}}$both represent soil type.

${\mathbf{尾}}_{\mathbf{0}}$represents the wine quality (y) at a base level (here base level means the level when ${\mathbf{x}}_{\mathbf{2}}$= 0 and ${\mathbf{x}}_{\mathbf{3}}$= 0, meaning the wine quality when the soil type is gravel)

${\mathbf{尾}}_{\mathbf{1}}$represents the changes in wine quality (y) when the soil type is clay.

${\mathbf{尾}}_{\mathbf{2}}$represents the changes in wine quality (y) when the soil type is sand.

A model for wine quality (y) as a function of the grape-picking method can be written as $\mathbf{y}\mathbf{=}{\mathbf{尾}}_{\mathbf{0}}\mathbf{+}{\mathbf{尾}}_{\mathbf{1}}{\mathbf{x}}_{\mathbf{4}}\mathbf{+}{\mathbf{尾}}_{\mathbf{2}}{\mathbf{x}}_{\mathbf{5}}\mathbf{+}{\mathbf{尾}}_{\mathbf{3}}{\mathbf{x}}_{\mathbf{6}}$where ${\mathbf{x}}_{\mathbf{4}}\mathbf{,}\mathbf{}{\mathbf{x}}_{\mathbf{5}}$and ${\mathbf{x}}_{\mathbf{6}}$represents slope orientation.

${\mathbf{尾}}_{\mathbf{0}}$represents the wine quality (y) at a base level (here base level means the level when ${\mathbf{x}}_{\mathbf{4}}$= 0, ${\mathbf{x}}_{\mathbf{5}}$= 0, and ${\mathbf{x}}_{\mathbf{6}}$= 0 meaning the wine quality when the slope orientation is southwest)

${\mathbf{尾}}_{\mathbf{1}}$represents the changes in wine quality (y) when the slope orientation is east.

${\mathbf{尾}}_{\mathbf{2}}$represents the changes in wine quality (y) when the slope orientation is west.

${\mathbf{尾}}_{\mathbf{3}}$represents the changes in wine quality (y) when the slope orientation is southeast.