Rebekah,
You presented great insights in this discussion! Considering the multiple regression presented earlier on assessing whether the respondent’s personal income was influenced by their hours of work in a week, hours of watching TV, and highest year of school completed was a normal regression since none of these predictors was a dummy variable. Recoding gender into a dummy variable now makes the model a dummy one – which technically means that one of the predictors takes the values 1 and 0 to indicate presence and absence of a categorical effect, respectively ( Weisberg, 2005). In this case, 1 translated to a male respondent while 0 indicated otherwise (which would take a female or any other biologically accepted gender).
Also, your interpretations of the coefficients were right. Despite the aspect that your model is statistically significant at 0.05 alpha level, not all the predictors were significant. Only the hours worked in a week affected the respondent’s income significantly as the p-value observed with its coefficient was less than 0.05 significance level ( Wagner, 2016). The dummy variable sex had no significant effect on the model, its beta was statistically insignificant – and there was no need to include it in the model in this case as you did. You could have only considered the model constant and the hours worked in a week and it could have looked like this:
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Income = 1513.045*HoursWorked – 32908.850
In running the model diagnostics to see if all the multiple regression assumptions were met, it seems you considered normality of the variable residuals and the distribution of the income and the hours worked. You could have assessed the homoscedasticity, linear relationship, and multicollinearity of the model variables too to see if all the assumptions were met before running the analysis. To evaluate the linear relationship between the predictors and the outcome variable, you could have scatter plots which would easily tell you if the variables had a curvilinear or linear relationship. To assess the multicollinearity of the independent variables, it was directly accessible from the correlation matrix while for homoscedasticity it would be simple to plot it using the SPSS ( Statistics Solutions , n.d). Homoscedasticity tries to show if the predicted and standardized values are equally distributed. For instance, if one of the assumptions is not met, it tells that the model linearity is not reliable for making predictions despite its significance ( Weisberg, 2005) . It simply tells that; the model can be significant but there is a high variability around the regression line. You can get more details of these assumptions on the source by Statistics Solutions which I have provided a web link below.
References
Statistics Solutions (n.d). Assumptions of Multiple Linear Regression . Advanced Through Clarity. February 1, 2019. Retrieved from https://www.statisticssolutions.com/wp- content/uploads/wp-post-to-pdf-enhanced-cache/1/assumptions-of-multiple-linear- regression.pdf
Wagner, W. E. (2016). Using IBM® SPSS® statistics for research methods and social science statistics (6th ed.). Thousand Oaks, CA: Sage Publications. https://gssdataexplorer.norc.org
Weisberg, S. (2005). Applied linear regression (Vol. 528). John Wiley & Sons.
