Example of multiple Linear regression with dummies-3

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An Example of Multiple Linear Regression with Recoded Dummy Variables Dataset used: GSS2018.sav Research Question: How do race and family income explain respondent's occupational prestige? Null Hypothesis: Race and family income are not significant predictors of respondent's occupational prestige. Variable description Dependent variable (Continuous): Prestg10 - Occupational Prestige Independent variable 1 (Continuous): Realrinc- R's income in constent $ Independent variable2 (Nominal): Race - 3 categories Categories/Values: 1 = White 2 = Black 3 = Other Dummy recoding through " Transform "  " Recode into different variables " in SPSS A multiple linear regression will be performed to test the null hypothesis. However, the nominal variable (Race) should be first recoded into 3 dummy variables, each consisting of two values (1/0). The three dummies are: DWhite, DBlack, DOther. The recode process is as follows: Old Name New Name Recode Process Value Specification Race Dwhite 1 = 1 All others = 0 1 = White 0 = all others Race Dblack 2 = 1 All others = 0 1 = Black 0 = all others Race Dother 3 = 1 All others = 0 1 = Other 0 = all others Analysis In multiple linear regression, the dummy variable Dother is left out of the model as the reference for dummy variables . Table 1 Variable entry

Table 2 shows that the effect size of the model (adj. R 2 ) is .116, indicating that the model explains more than 11% of variances in occupational prestige score. Table 2 Table 3 suggests that the model is significant, F(3, 1352) = 60.274, P < .001. I reject the null hypothesis. Table 3 Table 4 of coefficients shows that the continuous variable Respondent's income is a significant positive predictor of variances in occupational prestige score (  = .311, P < .001).

In comparison with Other races, the occupational prestige score is 3.174 higher for white group; the difference is significant (P < .01). Blacks are not significantly different (P = .877). The dummy variables (White and Black) are moderately correlated (VIF white = 1.986, VIF Black = 1.968) Table 4 Linear regression diagnosis. Note : I will not pay much attention to your diagnosis writing. However, you should know the process by saving the video and this handout for the future use. If your dissertation will take a quantitative approach and use multiple linear regression for analysis, you should definitely go through diagnosis and show the committee and URR that you know the data and issues well. If assumptions are violated, you know how to fix the problem as the video demonstrates. Assumptions to be diagnosed : 1. Normality of the dependent variable. 2. Absence of outliers of all the variables 3. Linear relationship between independent variables and the dependent variable 4. Absence of collinearity between independent variables and the dependent variable. Normality test of the dependent variable The Sig. value under the Shapiro-Wilk column is greater than 0.05, I conclude that Occupational Prestige is normally distributed (see Table 1). Table 1 Normality tests of Occupational Tests

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In the Normal Q-Q Plot below, the data of Occupational Prestige appears to be normally distributed as it follows the diagonal line closely and does not appear to have a non-linear pattern. Figure 1 Normal Q-Q Plot of Occupational Prestige Absence of outliers of all variables Table 2 Table 2 shows the minimum Std residual is outside -3 and raises the concern of some outliers. However, the minimum and maximum of Cook's distance are both within the limit of concerns (1).

The outliers are also shown in the scatter plot (Figure 2) that some prestige scores are beyond 3 and 4. The video illustrates how to identify individual outliner cases. Figure 2 Collinearity between Independent Variables : Note : If the correlation is .7 or +, there is a collinearity concern) Table 2 shows Black and White dummies are correlated (r=-.701) Table 2

Linear relationship diagnosis: The normal P-P plot (Figure 2) below indicates the independent variables fall on or closely to the regression line of occupational prestige. Figure 2

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