1 Paragraph Response to 2 Classmate’s SPSS Posts: 2 Paragraphs Total

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By Day 5

Respond to at least two 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.

Classmate 1 (Natalie):

“Main Question Post – Discussion – Week 10

Variables

The dependent variable using the General Social Survey dataset is “Respondent Socioeconomic Index”. The two independent variables using the General Social Survey dataset are “R’s Occupational Prestige Score” which is measured on an interval/ratio level and “Married” which is the dummy variable measured on a nominal scale.

Research Questions

What is the relationship between the respondent’s occupational prestige score and their marital status of being married, and the respondent’s socioeconomic index?

Null Hypotheses

There is no relationship between the respondent’s occupational prestige score and marital status of being married, and the respondent’s socioeconomic index.

Research design

Although we have looked at building multiple regression models, we have not engaged with the assumptions and issues which are also vital to achieving valid and reliable results. This research design therefore seeks to recode categorical variables to be used in a regression model, and interpret the coefficients. The Model Summary table shows the Durbin-Watson value which provides information on the independence of errors. The Durbin-Watson value of 1.854 is between the values of 0 and 4.0 and indicates that there is no correlation between the residuals. The ANOVA table test the overall significance of the regression model. The p-value is 0.000 which is below the alpha level, therefore the model has statistical significance and the researcher can reject the null hypothesis and state that there is a relationship between the dependent variable and independent variables. The R-square value of .687 indicates there is a strong linear correlation.

Taking a look at the Coefficients output, the Variance Inflation Factor (VIF) requires that values close to 10 and above 10 indicate serious multicollinearity in the model and the independent variables have high levels of correlations between each other. The VIF values of 1.050 are below the 10.0 general rule and the researcher can assume that the assumption was met. The significance level of 0.000 is below the alpha level, therefore reject the null hypothesis and conclude that there is a relationship between the independent variables and dependent variable. The dummy variable was also statistically significant at the p < 0.05 level. The Coefficients output also indicates that being married has a predicted socioeconomic index of 1.806 units more than being widowed, divorced, separated, and never married.

The Residuals Statistics shows Cook’s Distance. Cases where the Cook’s distance is greater than 1 would be problematic. The values of Cook’s Distance are well below the value of 1.0, therefore the researcher can assume there is no undue influence in the model. The P-P Plot shows a bit of deviation from normality between the observed cumulative probabilities of 0.2 and 0.6 but it appears to be minor. There does not appear to be a severe problem with non-normality of residuals. The Scatter Plot shows no discernible pattern with the spread of scatter, and there is a linear relationship. The model does not seemingly violate the assumption of homoscedasticity.

The regression equation is as follows:

Respondent’s Socioeconomic Index = -14.089 + (1.358)Respondent’s occupational prestige score + (1.806)Marital Status: Married

Model Summaryb

Model

R

R Square

Adjusted R Square

Std. Error of the Estimate

Durbin-Watson

1

.829a

.687

.686

12.5464

1.854

a. Predictors: (Constant), Married, Rs occupational prestige score (2010)

b. Dependent Variable: R’s socioeconomic index (2010)

ANOVAa

Model

Sum of Squares

df

Mean Square

F

Sig.

1

Regression

836162.266

2

418081.133

2655.966

.000b

Residual

381566.922

2424

157.412

Total

1217729.188

2426

a. Dependent Variable: R’s socioeconomic index (2010)

b. Predictors: (Constant), Married, Rs occupational prestige score (2010)

Coefficientsa

Model

Unstandardized Coefficients

Standardized Coefficients

t

Sig.

Collinearity Statistics

B

Std. Error

Beta

Tolerance

VIF

1

(Constant)

-14.089

.863

-16.319

.000

Rs occupational prestige score (2010)

1.358

.019

.819

70.307

.000

.953

1.050

Married

1.806

.523

.040

3.451

.001

.953

1.050

a. Dependent Variable: R’s socioeconomic index (2010)

Collinearity Diagnosticsa

Model

Dimension

Eigenvalue

Condition Index

Variance Proportions

(Constant)

Rs occupational prestige score (2010)

Married

1

1

2.561

1.000

.01

.01

.06

2

.395

2.547

.03

.03

.94

3

.044

7.595

.95

.96

.01

a. Dependent Variable: R’s socioeconomic index (2010)

Residuals Statisticsa

Minimum

Maximum

Mean

Std. Deviation

N

Predicted Value

7.633

96.325

46.019

18.5652

2427

Std. Predicted Value

-2.068

2.710

.000

1.000

2427

Standard Error of Predicted Value

.347

.830

.434

.081

2427

Adjusted Predicted Value

7.600

96.338

46.018

18.5658

2427

Residual

-34.7917

43.8698

.0000

12.5412

2427

Std. Residual

-2.773

3.497

.000

1.000

2427

Stud. Residual

-2.776

3.498

.000

1.000

2427

Deleted Residual

-34.8634

43.9035

.0007

12.5558

2427

Stud. Deleted Residual

-2.780

3.506

.000

1.001

2427

Mahal. Distance

.855

9.621

1.999

1.230

2427

Cook’s Distance

.000

.008

.000

.001

2427

Centered Leverage Value

.000

.004

.001

.001

2427

a. Dependent Variable: R’s socioeconomic index (2010)”

Classmate 2 (Melvin):

“Independent variables (IV1 and IV2) and their Level of Measurement.

The 2 independent variables and their level of measurement “Are YOU A CITIZEN OF AMERICA and Married

Dependent variable and its Level of Measurement.

The Dependent variable and its level of measurement is “Rs occupational prestige score (2010)”

Research Question

What is the relationship between are you a citizen of American, marital status, and respondents occupational prestige score (2010)?

Null Hypothesis

There is no relationship between are you a citizen of American, marital status, and respondents occupational prestige score (2010).

Research Design

This research design is multiple linear regression model using a dummy variable from one categorical variable and more than two groups for our independent variable. Dummy coding a variable means representing each of its values by a separate dichotomous variable. When using dummy variables in multiple linear regression models it is easier to code a categorical variable into multiple dichotomous variables, in which variables take the value of “1” or zero. Dichotomous variables are defined as variables that split or group data into 2 distinctive categories as with the Married; 1 = married and all others = 0. The model summary tables shows the linear regression model summary and the overall fit statistics. We can interpret the model as followed: 7% “of the variability in a respondent’s socioeconomic status index is explained by the combination of are you a citizen of American and marital status. We can conclude since R = .262 (26%) this makes it a weak linear relationship and the R² = .069 (7%), would make it a very weak linear relationship between are you a citizen of American, marital status, and respondents occupational prestige score (2010)? The Durbin-Watson = 1.819, which is between the two critical values of 0 and 4, which “provides us with some information about the independent errors (Laureate Education, Inc., 2016). Thus, we can conclude there is no first order linear autocorrelation in the sample.

The Anova tests the overall significance of the regression model. The Anova’s significance level is 0.000, thus we can reject the null hypothesis and conclude there is a linear relationshipbetween are you a citizen of American, marital status, and respondents occupational prestige score (2010) and both are you a citizen of American and marital status are statistically significant predictors of the respondents occupational prestige score (2010). The information in the coefficients table allows for us to check multicollinearity in our multiple linear regression model. The values should be >0.1 or VIF < 10 for all variables, which our values are 1.000, therefore we can assume that the assumptions has been met. The significance level is 0.000, thus we can reject the null hypothesis and conclude there is a linear relationship between are you a citizen of American, marital status, and respondents occupational prestige score (2010). The Dummy variable is also below 0.05, which indicates statistically significance with the coefficient output married, which predicted respondents occupational prestige score (2010). In the residuals Statistic table the data is .000, thus concluding there is no bias influence on the model. Looking at the normal p-p plot we can check for normality of residuals. The plot shows that the points generally follow the normal diagonal line with no strong deviations, which indicates that the residuals are normally distributed concluding the assumption has been met. The scatter plot give us the information on homoscedasticity and “weather our residuals at each level the predictor are equal in variance” (Laureate Education, Inc., 2016). There is no discernible pattern with the spread of scatter, which concluded our model did not violate heteroscedasticity. Scatter, again, tells us that there is a linear relationship, if not you would have seen a nonlinear relationship, in which the scatter perform a u shaped pattern (Laureate Education, Inc., 2016).

Regression Equation

Rs occupational prestige score (2010) = 47.420+ YOU A CITIZEN OF AMERICA (-6.242) + Married (6.478)

Rs occupational prestige score (2010) = 47.420+ (-6.242) + (6.478)

Variables Entered/Removeda

Model

Variables Entered

Variables Removed

Method

1

Married, ARE YOU A CITIZEN OF AMERICA?b

.

Enter

a. Dependent Variable: Rs occupational prestige score (2010)

b. All requested variables entered.

Model Summaryb

Model

R

R Square

Adjusted R Square

Std. Error of the Estimate

Durbin-Watson

1

.262a

.069

.067

13.097

1.819

a. Predictors: (Constant), Married, ARE YOU A CITIZEN OF AMERICA?

b. Dependent Variable: Rs occupational prestige score (2010)

ANOVAa

Model

Sum of Squares

df

Mean Square

F

Sig.

1

Regression

15335.223

2

7667.611

44.700

.000b

Residual

208416.971

1215

171.537

Total

223752.194

1217

a. Dependent Variable: Rs occupational prestige score (2010)

b. Predictors: (Constant), Married, ARE YOU A CITIZEN OF AMERICA?

Coefficientsa

Model

Unstandardized Coefficients

Standardized Coefficients

t

Sig.

Collinearity Statistics

B

Std. Error

Beta

Tolerance

VIF

1

(Constant)

47.420

1.741

27.237

.000

ARE YOU A CITIZEN OF AMERICA?

-6.242

1.571

-.110

-3.973

.000

1.000

1.000

Married

6.478

.755

.238

8.580

.000

1.000

1.000

a. Dependent Variable: Rs occupational prestige score (2010)

Collinearity Diagnosticsa

Model

Dimension

Eigenvalue

Condition Index

Variance Proportions

(Constant)

ARE YOU A CITIZEN OF AMERICA?

Married

1

1

2.540

1.000

.01

.01

.06

2

.435

2.415

.01

.02

.93

3

.024

10.250

.98

.98

.01

a. Dependent Variable: Rs occupational prestige score (2010)

Residuals Statisticsa

Minimum

Maximum

Mean

Std. Deviation

N

Predicted Value

34.94

47.66

43.69

3.550

1218

Residual

-31.656

38.822

.000

13.086

1218

Std. Predicted Value

-2.465

1.118

.000

1.000

1218

Std. Residual

-2.417

2.964

.000

.999

1218

a. Dependent Variable: Rs occupational prestige score (2010)

 “