A dummy variable is depicted as a dichotomous predictor variable which is coded to present a variable possessing higher level of measurement. In a regression model, a categorical variable is re-coded to a dichotomous variable indicating that it will take two mutually exclusive outcomes – presence or absence of the anticipated outcome (Kutner et al. 2008). For example, a dummy variable on smoking would be “Smokers” or “Otherwise” and it tells that the research could have different levels of measuring smoking and therefore, one can be a smoker or not but cannot fit in the two categories.
One of the potential studies that can use multivariate dummy regression model is assessing the impact of age, infrastructure index, country by region, on the current level of democracy based on the Afrobarometer survey data. Based on the three variables, the research question can be phrased as: Are age, country by region, and infrastructure index significant predictors of respondents’ level of democracy today? Notably, the level of democracy today is treated as the dependent variable and is measured on a ratio scale.
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On the other hand, age, infrastructure index, and country by region are the independent variables. Ideally, age and infrastructure index are measured on a ratio scale while the country by region is measured on a categorical scale, though it is treated as a dummy variable. It is recoded to 1 (West Africa) and 0 (Otherwise). In this case, “Otherwise” tells that the respondent comes from other regions but not west Africa (Warner, 2008). The model can be written as follows:
Level of democracy today = β + β 1 *Age + β 2 *infrastructure index + β 3 *Country by region
Model findings
The regression model hypothesized that there is no relationship between the dependent and predictor variables or that the beta coefficients were equal to zero. Country by region, infrastructure index, and age were good predictors of the level of democracy today for the respondents. The model was significant at 5% alpha level, F (3, 39,067) = 1,591.87, p < 0.05.
Table 1
ANOVA Findings for the Regression Model
The R-squared for the model is observed to be 0.109 and this tells that the three predictor variables included in the model explained 10.9% of the variation in the regression model. In other words, it tells that 10.9% of the model variation in the level of democracy today was explained by changes in age, infrastructure index, and country by origin (Warner, 2008).
Table 2
Model Summary
Model coefficients
The model constant was 2.419 which was significant at 5% alpha level, t = 37.287, p < 0.05. This shows the average score of democracy level that does not depend on age, infrastructure, and country by region. Age had a very weak positive correlation (shown by the positive sign of the coefficient) with the democracy level today, β = 0.005 and this tells that an increase in age by one year would increase the respondent’s democracy score by 0.005 units, t = 4.795, p < 0.05 (Kahane, 2001). Country by origin was negatively correlated with democracy level today, β = -0.103 (indicated by the negative sign of the coefficient). This tells that respondents from the West African region had less democracy score by 0.103 on average, t = -7.888, p < 0.05. Lastly, infrastructure index was positively correlated with democracy level and an increase in infrastructure index score by one unit, increased the democracy score by 0.274, ceteris paribus, t = 68.651, p < 0.05 (Fox, 2015). Therefore, the model can be written as:
Level of democracy today = 2.419 + 0.005*Age - 0.103*infrastructure index + 0.274*Country by region
Table 3
Model Coefficients
Regression Diagnostics and Model Implications
To test if the multi regression assumptions were met, the tests for normality, multicollinearity, multivariate normality, and homoscedasticity tests were considered. Through the partial correlation matrix, none of the predictor pairs were highly correlated – hence the no multicollinearity assumption was met (Kahane, 2001). Also, the predictors variables had a linear association with the dependent variable indicating that the linear relationship assumption was met. To test for the homoscedasticity, the variance inflator factor (VIF) approach was used and none of the variables had a VIF value greater than 10 – indicating that the variance error terms were homogeneous (Fox, 2015). Therefore, the model can be relied in making predictions. One implication with this model can be initiating social projects to the West Africa that are age oriented can increase people’s democracy level. Similarly, people from the West Africa appear to be sensitive to matters influencing democracy than people from other regions, and that implementing infrastructure – related projects may not increase the democracy of the people.
References
Fox, J. (2015). Applied regression analysis and generalized linear models . Sage Publications.
Kahane, L. H. (2001). Regression basics . Thousand Oaks [Calif.: Sage Publications.
Kutner, M. H., Nachtsheim, C., & Neter, J. (2008). Applied linear regression models . Boston: McGraw-Hill.
Warner, R. M. (2008). Applied statistics: From bivariate through multivariate techniques . Sage.
