Question

Question 2

Dummy variables can be used to represent categorical data ___

	a) only when the categorical data is used as a response variable
	b) only when the categorical data is used as an explanatory variable
	c) when the categorical is used as either the response or explanatory variable
	d) Dummy variables can never be used to represent categorical data

Question 3

Consider the following OLS regression equation: predicted y = b₀ + b₁X₁ + b2d. The "X₁" refers to a

	a) categorical response variable, while the "d" refers to the numeric response variable
	b) categorical explanatory variable, while the "d" refers to the numeric explanatory variable
	c) numeric response variable, while the "d" refers to the categorical response variable
	d) numeric explanatory variable, while the "d" refers to the categorical explanatory variable

Answer 1

Question 2

Dummy variables can be used to represent categorical data

c)	when the categorical is used as either the response or explanatory variable

A dummy variable is a special type of variable which takes the value 0 or 1 to indicate the absence or presence of some categorical variable it denotes. It can both act as a response variable as well as an explanatory variable. For example
1. Suppose we want to estimate the amount the height of students belonging to a particular class. Here a dummy variable can be used as an explanatory variable which is gender where a male is denoted by 1 and female by 0 (or the other way round).
2. Suppose we want to estimate whether a family living in a particular society owns a car or not. For this purpose our response variable is categorical and 1 represents that the family owns a car while 0 represents the family doesn't. Here the explanatory variables may include Income, savings of the family etc.    

Question 3

Consider the following OLS regression equation: predicted y = b0 + b1X1 + b2d. The "X1" refers to a

d)	numeric explanatory variable, while the "d" refers to the categorical explanatory variable

An explanatory variable is a variable which is used to predict some other variable. Usually, the numerical variable is denoted by X and the categorical variable is denoted by d. A numerical variable is one which can take any numeric value in its range of variation. like while predicting the height of individuals, weight can be taken as a numerical explanatory variable ( as it can take many values within a certain range ) while gender can be considered as a categorical explanatory variable (as it takes only two values 0 or 1 depending on whether it is boy or girl as defined by the experimenter.) Here y is actually the response variable and not X or d.