Marital Status & Family Income: An Interpretation of the Model Coefficients

What is the relationship between Separated, Widowed, Divorced, and Married as they relate to Infrastructure Index?

Interpretation of the Coefficients for the Model

The coefficient of multiple determination for Model 1 in .385. Therefore, 14.82% of the variation in participants’ Family Income in Constant Dollars is explained by Separated, Widowed, Divorced, and Married statuses. The predictor variables statistically significantly predict the outcome variable, F(4, 2307) = 100.664, p < .05, R2 = .288

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Diagnostics for The Regression Model

Linearity Assumption

In multiple regression analysis, the linearity assumption is met when there is a linear relationship between the outcome variable and each of the independent variables. Additionally, there should be a linear relationship between the dependent variable and the predictors collectively. In SPSS, scatterplots are used to check whether the linearity assumption has been met. The independent variables in the regression did not have a straight-line relationship with the dependent variable. Therefore, the linearity assumption was not met. When this assumption has not been met, a researcher can either run a non-linear regression analysis or “transform” the data.

Scatterplot

Independence of Observation Assumption

Independence of observation assumption implies that the observations in the sample are not related to each other. This means that the measurements for each of the elements in the sample are not influenced by others or related to the measurements of other elements in the sample. This assumption is checked in SPSS using the Durbin-Watson statistic. Because the Durbin-Watson value is not below 1.0 and not above 3.0, the model does not suffer from autocorrelation. That is, the independence of observation assumption has been met.

Homoscedasticity Assumption

Another assumption of multiple regression analysis is that the variance of the residuals is homogeneous across levels of the predicted values. Homoscedasticity assumption is tested by determining whether data lied along the best line of fit. According to the results for this test, there is no discernable pattern to the scatter. There is no funnel or cone-shaped pattern. Therefore, the homoscedasticity assumption was met.

Multicollinearity Assumption

Another assumption of multiple regression analysis is that the predictor variables should not be highly correlated with each other. To check whether the assumption has been met, VIF values are used. As a general rule, values close to 10 and above 10 shows serious multicollinearity in the model (Laureate Education, 2016m). All the VIF values for all the independent variables less than 1.5. This means that the predictors do not show multicollinearity. Therefore, the assumption has been met.

Undue Influence Assumption

Cook’s distance is used to check for individual observations that cause undue influence on the coefficients. Noteworthy, a single observation that is significantly different from others can make a substantial difference in the results of regression analysis. As a general rule, Cook’s distance values of 1.0 or higher are considered problematic because it indicates that there is the presence of undue influence (Laureate Education, 2016m). Cook’s distance values range from 0.000 to 0.032. Therefore, there is no undue influence.

Residual Statistics

Normal Distribution of Errors Assumption

In multiple regression analysis, data should show a normal distribution of error (Laureate Education, 2016m). This assumption is checked in SPSS using a histogram. The distribution is fairly normal. Therefore, the assumption of a normal distribution of errors has been met.

References

Laureate Education (Producer). (2016m). Regression diagnostics and model evaluation [Video file]. Baltimore, MD: Author.