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In statistics and econometrics, particularly in regression analysis, a dummy variable (also known as an indicator variable, design variable, Boolean indicator, categorical variable, binary variable, or qualitative variable〔〔) is one that takes the value 0 or 1 to indicate the absence or presence of some categorical effect that may be expected to shift the outcome.〔Draper, N.R.; Smith, H. (1998) ''Applied Regression Analysis'', Wiley. ISBN 0-471-17082-8 (Chapter 14)〕 Dummy variables are used as devices to sort data into mutually exclusive categories (such as smoker/non-smoker, etc.). For example, in econometric time series analysis, dummy variables may be used to indicate the occurrence of wars or major strikes. A dummy variable can thus be thought of as a truth value represented as a numerical value 0 or 1 (as is sometimes done in computer programming). 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 Gender is one of the qualitative variables relevant to a regression. Then, female and male would be the categories included under the Gender variable. If female is arbitrarily assigned the value of 1, then male would get the value 0.〔(【引用サイトリンク】first=Susan Garavaglia )〕 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 males but would be the constant term plus the coefficient of the gender dummy in the case of females. Dummy variables are used frequently in time series analysis with regime switching, seasonal analysis and qualitative data applications. Dummy variables are involved in studies for economic forecasting, bio-medical studies, credit scoring, response modelling, etc. Dummy variables may be incorporated in traditional regression methods or newly developed modeling paradigms.〔 ==Incorporating a dummy independent== Dummy variables are incorporated in the same way as quantitative variables are included (as explanatory variables) in regression models. For example, if we consider a regression model of wage determination, wherein wages are dependent on gender (qualitative) and years of education (quantitative): :Wage = α0 + δ0female + α1education + U In the model, ''female'' = 1 when the person is a female and ''female'' = 0 when the person is male. δ0 can be interpreted as: the difference in wages between females and males, keeping education and the error term 'U' constant. Thus, δ0 helps to determine whether there is a discrimination in wages between males and females. On the other hand, if δ0>0 (positive coefficient), then women earn a higher wage than men (keeping other factors constant). Note that the coefficients attached to the dummy variables are called differential intercept coefficients. The model can be depicted graphically as an intercept shift between females and males. In the figure, the case δ0<0 is shown (wherein, men earn a higher wage than women). Dummy variables may be extended to more complex cases. For example, seasonal effects may be captured by creating dummy variables for each of the seasons: D1=1 if the observation is for summer, and equals zero otherwise; D2=1 if and only if autumn, otherwise equals zero; D3=1 if and only if winter, otherwise equals zero; and D4=1 if and only if spring, otherwise equals zero. In the panel data fixed effects estimator dummies are created for each of the units in cross-sectional data (e.g. firms or countries) or periods in a pooled time-series. However in such regressions either the constant term has to be removed or one of the dummies has to be removed, with its associated category becoming the base category against which the others are assessed in order to avoid the dummy variable trap: The constant term in all regression equations is a coefficient multiplied by a regressor equal to one. When the regression is expressed as a matrix equation, the matrix of regressors then consists of a column of ones (the constant term), vectors of zeros and ones (the dummies), and possibly other regressors. If one includes both male and female dummies, say, the sum of these vectors is a vector of ones, since every observation is categorized as either male or female. This sum is thus equal to the constant term's regressor, the first vector of ones. As result, the regression equation will be unsolvable, even by the typical pseudoinverse method. In other words: if both the vector-of-ones (constant term) regressor and an exhaustive set of dummies are present, perfect multicollinearity occurs, and the system of equations formed by the regression does not have a unique solution. This is referred to as the dummy variable trap. The trap can be avoided by removing either the constant term or one of the offending dummies. The removed dummy then becomes the base category against which the other categories are compared. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Dummy variable (statistics)」の詳細全文を読む スポンサード リンク
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