we use dummy variables in regression in analysis of covariance.
we use dummy variables in regression in analysis of covariance.
when do we use dummy variables in regression?
analysis of covariance
dummy variables are "proxy" variables or numeric stand-ins for qualitative facts in a regression model. in regression analysis, the dependent variables may be influenced not only by quantitative variables (income, output, prices, etc.), but also by qualitative variables (gender, religion, geographic region, etc.). a dummy independent variable (also called a dummy explanatory variable) which for some observation has a value of 0 will cause that variable's coefficient to have no role in influencing the dependent variable, while when the dummy takes on a value 1 its coefficient acts to alter the intercept. for example, suppose membership in a group is one of the qualitative variables relevant to a regression. if group membership is arbitrarily assigned the value of 1, then all others would get the value 0. then the intercept (the value of the dependent variable if all other explanatory variables hypothetically took on the value zero) would be the constant term for non-members but would be the constant term plus the coefficient of the membership dummy in the case of group members.
dummy variable (statistics)
in statistics and regression analysis, an independent variable that can take on only two possible values is called a dummy variable. for example, it may take on the value 0 if an observation is of a white subject or 1 if the observation is of a black subject. the two possible categories associated with the two possible values are mutually exclusive, so that no observation falls into more than one category, and the categories are exhaustive, so that every observation falls into some category. sometimes there are three or more possible categories, which are pairwise mutually exclusive and are collectively exhaustive — for example, under 18 years of age, 18 to 64 years of age, and age 65 or above. in this case a set of dummy variables is constructed, each dummy variable having two mutually exclusive and jointly exhaustive categories — in this example, one dummy variable (called d) would equal 1 if age is less than 18, and would equal 0 "otherwise"; a second dummy variable (called d) would equal 1 if age is in the range 18-64, and 0 otherwise. in this set-up, the dummy variable pairs (d, d) can have the values (1,0) (under 18), (0,1) (between 18 and 64), or (0,0) (65 or older) (but not (1,1), which would nonsensically imply that an observed subject is both under 18 and between 18 and 64). then the dummy variables can be included as independent (explanatory) variables in a regression. note that the number of dummy variables is always one less than the number of categories: with the two categories black and white there is a single dummy variable to distinguish them, while with the three age categories two dummy variables are needed to distinguish them.
mutual exclusivity