Use SPSS to answer the research question. Post your response to the following:
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- If you are using the Afrobarometer Dataset, report the mean of Q1 (Age). If you are using the HS Long Survey Dataset, report the mean of X1SES.
- What is your research question?
- What is the null hypothesis for your question?
- What research design would align with this question?
- What dependent variable was used and how is it measured?
- What independent variables are used and how are they measured? What is the justification for including these predictor variables?
- If you found significance, what is the strength of the effect?
- Explain your results for a lay audience, explain what the answer to your research question.
Use the General Social Survey data set and construct a research question that can be answered using multiple regression. To do this you will need to select three variables that are measured on an interval or ratio level. In SPSS they will be listed as scale data in the variable view.
Select two IVs (AKA predictor variables) that could be used to predict the value of the DV (AKA, criterion variable or outcome variable). For example, the length and the weight of a car (predictor variables) could be used to predict its miles per gallon (outcome variable). Use an alpha level of .05 for these analyses.
In this week’s video example, 3 variables were selected from the GSS data set. Note that our data set has been edited and is not exactly the same as theirs. You can follow along and you should get similar results, but you will not get exactly the same values. That is OK, remember, we have a revised data set that is a little different than the one used for the video example. Here are the variables used in the example:
DV = sei10, R’s socioeconomic index (2010)
IV 1 = prestg10, Rs occupational prestige score (2010)
IV 2 = educ, HIGHEST YEAR OF SCHOOL COMPLETED
Do Not use these variables for your discussion or application assignment for multiple regression.
Here is an overview of how to run the Multiple Regression
Analyze > Regression > Linear
Enter your 1 (and only 1) DV into the Dependent box.
Enter your 2 (and only 2) IVs into the Independent(s) box.
Reading the Output & Reporting Results
The overall Model Summary shows the R, R Square, and Adjusted R Square. In my experience, we typically report the R Square value. Yet our video recommends reporting the Adjusted R square. For this example, R square and Adjusted R square are the same, R2 = .787. However, sometimes they will be different.
Because we have conflicting information, you may report either. However, clearly state whether you are reporting R square or the adjusted R square.
Figure 1. Model Summary for multiple regression in SPSS
The next box shows the ANOVA summary.
Figure 2. ANOVA summary of the overall model for multiple regression
This is for the overall model with your two independent variables and your one dependent variable. Notice that the Sig. column shows .000, we would report the results like this:
The purpose of this standard regression analysis was to examine the combined and relative effects of the respondents’ occupational prestige score and highest year of school completed in predicting their socioeconomic status. The combined effect of prestg10 and educ statistically significantly predicted sei10, F(2, 1404) = 2595.24, p < .001, adjusted R2 = .787. The two predictors combined, explained about 79% of the variability in socioeconomic status index scores. This is a large effect.
By convention, 2% is considered a small effect, 13% is medium, and 26% is large.
Here is a resource: http://core.ecu.edu/psyc/wuenschk/docs30/EffectSizeConventions.pdf
Figure 3. Coefficients
The B coefficient for the RS occupational prestige score, 1.055, is significantly different from zero because the sig column shows .000. We could report this as:
While holding the effects of the other predictor constant, the RS occupational prestige score significantly predicts socioeconomic index values, t(1404) = 52.30, p < .001. For each 1- point increase in prestige score, socioeconomic status index values are expected to increase by 1.055 points.
The B coefficient for Highest year of school completed, 1.226, was significantly different from 0 because the Sig. column shows .000. We could report this as:
While holding the effects of the other predictor constant, the highest year of school completed significantly predicts socioeconomic index values, t(1404) = 13.60, p < .001. For each 1- point increase in prestige score, socioeconomic status index values are expected to increase by 1.226 points.
As we saw in Week 8, the Constant B of -13.373 is the y-intercept. At point (0, -13.373) the regression line will cross the y-axis (the vertical line).
The Multiple Regression Equation
For this analysis, we could report the Multiple Regression equation as
Predicted sei10 = -13.373 + 1.055(prestg10) + 1.226(educ)
For example, if someone had a prestige score of 1 and an education score of 15 we could predict their sei10 score:
Predicted sei10 = -13.373 + 1.055(prestg10) + 1.226(educ)
Predicted sei10 = -13.373 + 1.055(1) + 1.226(15)
Predicted sei10 = -13.373 + 1.055 + 18.39
Predicted sei10 = 6.062
A person with a prestige score of 1, who attended 15 years of schooling is predicted to have a socioeconomic index score of 6.062.
The Null Hypotheses for Multiple Regression is not in any of our course materials.
I don’t recall seeing this explicitly stated in our course materials. Technically, there is one null hypothesis for the combined model, and then one for each of the IVs.
Here is an example for a Multiple Regression model with 2 IVs and one DV.
Null 1: The combined effect of the two IVs will not significantly predict the DV.
Null 2: The First IV is not a significant predictor of the DV, while controlling for the second IV.
Null 3: The Second IV is not a significant predictor of the DV, while controlling for the first IV.
Hopefully it is obvious that this is a generic example and you would insert the names of your variables in place of First IV, Second IV, and DV.
This is an introduction
This week we learn how to run a multiple regression and how to interpret the results and report them. However, there is much more to learn on this topic. I have greatly oversimplified the information we typically report for a multiple regression analysis.
Next week you will learn about the assumptions of multiple regression. That is, you will learn about several additional statistics that we must check ahead of time to ensure it is appropriate to run and interpret a multiple regression analysis. For now, just focus on the general idea of multiple regression and what the results tell you.
– all three variables should be interval or ratio variables. They should be listed as scale variables in your data set
– the variable you wish to predict should be entered as the DV
– leave the Method as “Enter”, this is referred to as a standard regression and it enters all of the IVs at the same time, whether or not they are significantly related to the DV
– select Only 2 IVs for the discussion and assignments for multiple regression.
You should address all of the following:
– State your research question
– State your null hypothesis
– Describe your outcome variable (DV) and how it was measured.
– Describe the predictor variables (IVs) and how they were measured. (Select 2 and only 2 IVs)
– explain whether one IV was a control and if so, why
– explain the rationale for selecting IVs
– clearly identify the name of the variables as they appear in the data set
– Indicate whether the overall model was significant or not, explain how you know
– indicate whether each of your two predictors were significant or not, explain how you know
– report the results of your multiple regression analysis in APA format, interpret the effect size using R square (see pp. 440 – 441, and p. 450 in your text and my example below)
– ensure you clearly explain whether the variables are significant predictors or not and state the regression equation for for your results (use my example above as a guide).
– Discuss implications for positive social change