Brilliant Answer Peers

Respond to one of your colleagues’ posts and provide a constructive comment on their assessment of diagnostics.

1. Were all assumptions tested for?

2. Are there some violations that the model might be robust against? Why or why not?

3. Explain and provide any additional resources (i.e., web links, articles, etc.) to provide your colleague with addressing diagnostic issues.

Colleague

1. What is your research question?

The research question is whether R's socioeconomic index depends on Age of Respondent, RS Highest Degree, and Respondents Income.

1. Interpret the coefficients for the model, specifically commenting on the dummy variable.

Once a categorical variable has been labeled as a dummy variable, the dummy variable can be used in regression analysis as any other quantitative variable.

For instance, to determine whether the R's socioeconomic index depends on AGE OF RESPONDENT, RS HIGHEST DEGREE, and RESPONDENTS INCOME

 The regression equation might be:

                                     R's socioeconomic index = b0 + b1X1+ b2X2+ b3X3    

where b0, b1, and b2 are regression coefficients. X1 and X2 are regression coefficients defined as:

· X1 = 1, if Age of Respondent; X1 = 0, otherwise.

· X2 = 1, if RS Highest Degree; X2 = 0, otherwise.

· X3 = 1, if Respondents Income; X3 = 0, otherwise.

Age of Respondent, RS Highest Degree, and Respondents Income are all dummy variables. Dummy variables allow the use of a single regression equation to represent multiple groups.

1. 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.

From the Model Summary, the assumption of the independence of error, Durbin-Winston, is 1.999.  The number is more than one and less than three; therefore, the assumption is confirmed. The regression analysis on the ANOVA table shows that the overall regression is statistically significant regarding whether R's socioeconomic index depends on the Age of Respondent, RS Highest Degree, and Respondents Income.

1. Is there any possible remedy for one of the assumption violations?

The smaller the p-value, the stronger the evidence that should reject the null hypothesis. A p-value less than 0.05 is significant. From the Coefficients Table, the p- values for Age of Respondent, RS Highest Degree, and Respondents Income are less than 0.05. Thus, they are regressors that affect the R's socioeconomic index. On the other hand, a p-value higher than 0.05 is not statistically significant and indicates strong evidence that the Age of Respondent variable does not affect the R's socioeconomic index.

Model Summaryb
Model	R	R Square	Adjusted R Square	Std. Error of the Estimate	Durbin-Watson
1	.598a	.357	.351	17.6290	1.999
a. Predictors: (Constant), AGE OF RESPONDENT, RS HIGHEST DEGREE, RESPONDENTS INCOME
b. Dependent Variable: R's socioeconomic index (2010)

ANOVAa
Model	Sum of Squares	df	Mean Square	F	Sig.
1	Regression	50602.351	3	16867.450	54.274	.000b
	Residual	91058.739	293	310.781
	Total	141661.091	296
a. Dependent Variable: R's socioeconomic index (2010)
b. Predictors: (Constant), AGE OF RESPONDENT, RS HIGHEST DEGREE, RESPONDENTS INCOME

Coefficientsa
Model	Unstandardized Coefficients	Standardized Coefficients	t	Sig.
	B	Std. Error	Beta
1	(Constant)	12.276	4.596		2.671	.008
	RESPONDENTS INCOME	1.557	.385	.203	4.040	.000
	RS HIGHEST DEGREE	9.693	.934	.505	10.372	.000
	AGE OF RESPONDENT	.039	.077	.024	.505	.614
a. Dependent Variable: R's socioeconomic index (2010)

Residuals Statisticsa
	Minimum	Maximum	Mean	Std. Deviation	N
Predicted Value	14.690	72.454	46.221	13.0749	297
Residual	-46.1123	48.2433	.0000	17.5394	297
Std. Predicted Value	-2.412	2.006	.000	1.000	297
Std. Residual	-2.616	2.737	.000	.995	297
a. Dependent Variable: R's socioeconomic index (2010)