I am wondering if I performed the multiple regression with dummy variables correctly. Then I am wondering if what I wrote about the tables are correctly? Here is the assignment description.

Estimate a multiple regression model that answers your research question. Post your response to the following:

1. What is your research question?
2. Interpret the coefficients for the model, specifically commenting on the dummy variable.
3. Run diagnostics for the regression model. Does the model meet all of the assumptions? Be sure and comment on what assumptions were not met and the possible implications. Is there any possible remedy for one the assumption violations?

Thank you in advance!!!

Week 9: Discussion

Multiple regression gives researchers the ability to interpret and or predict the relationship between a dependent variable and two or more independent variables (Frankfort-Nachmias et. al., 2021). For this study, I assessed 3 variables in a multiple regression analysis. The dependent variable is the respondents' socioeconomic status. The independent variables are the parents' highest level of education completed, and respondents' school geographical location. Because the respondents' school geographical location is a categorical variable, dummy variables were created, those being: Northeast, Midwest, and South (West was used as the reference variable).

Research question: Is there a relationship between the respondents' geographical location, highest level of parents' education completed, and the respondents' socio economic status?

Null Hypothesis: There is no relationship between the schools' geographical location, highest level of parents' education and the respondents' socio economic status.

Hypothesis: A relationship between the respondents' schools' geographical location, parents' highest level of parents' education completed and the respondents' socio economic status does exist.

According to the model summary, the R square value is .792 and the adjusted R square value is .627. The Durbin Watson value is 2.014. This value indicates there is no correlation between the residuals. The Durbin Watson statistics provides information pertaining to independence of errors, and the values range between 0 - 4.0. The data shows a significance level of p< .000; therefore there the information is statistically significant, and the null hypothesis is rejected. In the ANOVA model,statistical significance is found at .000 (Wagner, 2020). The coefficient table reveals that for every one unit increase of the highest year of education completed there is a .017 unit of increase in the Northeast socio-economic index. In contrast, there is a - 0.36 unit decrease in the Midwest respondents' socio-economic status index and a - 0.18 decrease in the South respondents' socio-economic status. The Collinearity Diagnostic table reveals there is no correlation between the independent variables, meaning there is no multicollinearity. The assumption of independence of variables is satisfied. Because the Cook's distance values are lower than 1.0 the residuals are considered non problematic or normal in the Residual Statistics table; therefore the assumption of normality of residuals is also satisfied.

Table 1.

Model Summaryb
Model	R	R Square	Adjusted R Square	Std. Error of the Estimate	Durbin-Watson
1	.792a	.627	.627	.51739	2.014
a. Predictors: (Constant), T1 Parent 1: highest level of education, Midwest, Northeast, South
b. Dependent Variable: T1 Socio-economic status composite

Table 2.

ANOVAa
Model	Sum of Squares	df	Mean Square	F	Sig.
1	Regression	1844.739	4	461.185	1722.833	.000b
Residual	1096.725	4097	.268
Total	2941.464	4101
a. Dependent Variable: T1 Socio-economic status composite
b. Predictors: (Constant), T1 Parent 1: highest level of education, Midwest, Northeast, South

Table 3.

Coefficients
Model	Unstandardized Coefficients	Standardized Coefficients	t	Sig.	Collinearity Statistics
B	Std. Error	Beta	Tolerance	VIF
1	(Constant)	-1.325	.026		-51.357	.000
Northeast	.017	.029	.007	.602	.548	.616	1.624
Midwest	-.036	.025	-.019	-1.436	.151	.524	1.907
South	-.018	.023	-.010	-.752	.452	.495	2.022
T1 Parent 1: highest level of education	.478	.006	.791	82.638	.000	.993	1.007
Table 3. Collinearity Diagnostics
Model	Dimension	Eigenvalue	Condition Index	Variance Proportions
(Constant)	Northeast	Midwest	South	T1 Parent 1: highest level of education
1	1	2.770	1.000	.01	.01	.01	.02	.02
2	1.001	1.664	.00	.35	.00	.10	.00
3	1.000	1.664	.00	.07	.25	.06	.00
4	.165	4.096	.00	.32	.37	.40	.55
5	.065	6.532	.99	.24	.36	.43	.43
a. Dependent Variable: T1 Socio-economic status composite

Table 4.

Residuals Statistics

	Minimum	Maximum	Mean	Std. Deviation	N
Predicted Value	-.8828	2.0391	.1055	.67069	4102
Std. Predicted Value	-1.474	2.883	.000	1.000	4102
Standard Error of Predicted Value	.013	.031	.018	.004	4102
Adjusted Predicted Value	-.8841	2.0465	.1056	.67075	4102
Residual	-2.19931	1.77147	.00000	.51714	4102
Std. Residual	-4.251	3.424	.000	1.000	4102
Stud. Residual	-4.258	3.425	.000	1.000	4102
Deleted Residual	-2.20669	1.77274	-.00003	.51779	4102
Stud. Deleted Residual	-4.267	3.430	.000	1.000	4102
Mahal. Distance	1.477	13.586	3.999	2.228	4102
Cook's Distance	.000	.012	.000	.000	4102
Centered Leverage Value	.000	.003	.001	.001	4102
a. Dependent Variable: T1 Socio-economic status composite