Question

Define and describe the nature of dummy variables. Include an explanation of how the number of dummy variables included in the model depends on the number of characteristics of the variable.

Describe a regression model that includes an intercept-differential variable.

Describe a regression model that includes a slope-differential variable.

Describe how can a dummy variable can be used in the second assignment’s regression model to determine if the difference in math scores differs significantly between men and women?

Second assignment Data:

Table 1. Grade Point Average (Y) and Family Income (X) in Thousands of Dollars

n	Y	X
1	4.0	21.0
2	3.0	15.0
3	3.5	15.0
4	2.0	9.0
5	3.0	12.0
6	3.5	18.0
7	2.5	6.0
8	2.5	12.0

Answer 1

Multiple questions has been posted. As HOMEWORKLIB RULES's policy, answering the first question below:

It shall be noted that dummy variables are those variable that takes values 0 and 1 only and they are created for a categorical variable , one dummy variable per value the categorical variable takes.

The value of 1 taken by dummy variable shows the presence of the value of the categorical variable, whereas, the value 0 shows the absence of that value that categorical variable takes.

The dummy variables can act as an explanatory variable in regression analysis.

Categorical variable	D1	D2	D3	D4	D5
1	1	0	0	0	0
2	0	1	0	0	0
3	0	0	1	0	0
4	0	0	0	1	0
5	0	0	0	0	1

In regression model with intercept, Dummy Variables that could be included as explanatory variables is always 1 less than the number of dummy variables created per categorical variable to avoid the problem of dummy trap.

It would not make sense to pass the categorical variable as an explanatory variable in the regression model with intercept.

If there are 5 values (or characteristics) of a categorical variable and there are 5 dummy variables created, one each of the values taken by categorical variable, then in the regression model with intercept, instead of passing the categorical variable as independent explanatory variable, use any four dummy variables, while keeping one dummy variable as the constant.

For example:

Yi = b0 + b1*X1 + b2*X2 + b3*D1 + b4*D2 +b5*D3 + b6*D4

Thus, in the above regression model, b0 is the intercept, X1 and X2 are continuous explanatory variables and D1, D2, D3 and D4 are the dummy variables

The dummy variable D5 is observed as the base

It shall be noted that D1, D2, D3, D4 and D5 are the dummy variables corresponding to the given categorical variable.