You had the chance earlier in the course to practice with multiple regression and obtain peer feedback. Now, it is time once again to put all of that good practice to use and answe

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Assignment: Testing for Multiple Regression

You had the chance earlier in the course to practice with multiple regression and obtain peer feedback. Now, it is time once again to put all of that good practice to use and answer a social research question with multiple regression. As you begin the Assignment, be sure and pay close attention to the assumptions of the test. Specifically, make sure the variables are metric level variables.

Part 1

To prepare for this Part 1 of your Assignment:

· Review this week 9 and 10 Learning Resources and media program related to multiple regression.

· Using the SPSS software, open the Afrobarometer dataset or the High School Longitudinal Study dataset (whichever you choose) found in the Learning Resources for this week.

· Based on the dataset you chose, construct a research question that can be answered with a multiple regression analysis.

· Once you perform your multiple regression analysis, review Chapter 11 of the Wagner text to understand how to copy and paste your output into your Word document.

For this Part 1 Assignment:

Write a 1- to 2-page analysis of your multiple regression results for each research question. In your analysis, display the data for the output. Based on your results, provide an explanation of what the implications of social change might be.

Use proper APA format, citations, and referencing for your analysis, research question, and display of output.

Week Nine: Multiple Regressions

Posted on: Friday, July 22, 2022 9:31:03 AM EDT

As social scientists, we frequently have questions that require the use of multiple predictor variables. Moreover, we often want to include control variables (i.e., workforce experience, knowledge, education, etc.) in our model. Multiple regression allows the researcher to build on bivariate regression by including all of the important predictor and control variables in the same model. This, in turn, assists in reducing error and provides a better explanation of the complex social world.

Example: a local school system is trying to mitigate poor attendance. The researchers may look at several, possible interventions. In the end, a study may find a combination of interventions will work better than any single one. This finding is a typical product of multiple regression. In addition, because combinations of data may need to combined, a researcher can  infer. The word is a power word in social sciences as it empowers a researcher to synthesize and speculate based upon responsible use of data.

In the end, having concluded your analysis of a regression, what has been learned? In two sentences or less what can you share with others?

Introduction

Consider the two research studies and the challenges they presented.

In a classic research study by Ellen Langer and Judith Rodin (1976), elderly individuals who resided in nursing homes were assigned to one of two groups; one group was granted much more personal control and the other much less. For example, in the first group, individuals were given latitude to have a say in how their furniture was arranged and given a plant to take care of if they wished. The results were striking in that the group granted greater personal control showed much better health outcomes than the group given less control.  

In this study, each group of participants lived on a different floor of the nursing home, and researchers randomly selected which floor would be placed into which group (Langer & Rodin, 1976). The two floors were similar in pre-existing characteristics that might impact their health outcomes. The researchers were, therefore, able to control, at the start, other factors besides being in one of the two groups that might relate to health outcomes. That is, control in this study was achieved through the research design.

Langer, E., & Rodin, J. The effects of choice and enhanced personal responsibility for the aged: A field experiment in an institutional setting. Journal of Personality and Social Psychology.34/ 2. 1976.

In many research studies, however, it is simply not feasible to design a study that sufficiently controls other factors besides the independent variable that might help to explain the dependent variable. Researchers often must find statistical methods of controlling for confounding variables when conducting correlational research.

Consider research conducted by Angela Duckworth and her colleagues (2007). Duckworth focused on a construct called grit, which she has found to be related to achievement. She and her colleagues define grit as “perseverance and passion for long-term goals.” Duckworth was interested in what types of individual qualities might be related to achievement besides academic ability such as that measured by IQ tests. Why is it that people of about the same level of intelligence differ in their degree of achievement and their degree of persevering in tasks that are difficult?  

Previous research on personality factors linked to achievement had already supported the idea that those who are more conscientious show advantageous achievement. In one study, therefore, Duckworth wanted to examine whether grit offered a unique predictive ability of educational attainment over and above the personality trait of conscientiousness and other personality traits (Duckworth, Peterson, Matthews, & Kelly, 2007)[2]. That is, she wanted to control for certain personality traits to better assess whether grit showed the unique prediction of educational attainment. What if those who were higher in grit showed higher educational attainment simply because of other factors such as other personality traits and not the characteristic of grit per se?

In this type of research, it would be quite difficult to simply control for preexisting differences in personality between participants using a strategy like a random assignment. For example, it would be difficult to assign some to have high grit randomly and some to have low grit as grit is a personal attribute. Duckworth and her colleagues, therefore, controlled for personality factors when conducting their statistical analyses to examine if grit is associated with educational attainment beyond other personality factors. Note: They did, in fact, find that grit was related to educational attainment even after controlling for other personality traits (Duckworth et al., 2007).

Duckworth, A. L., Peterson, C., Matthews, M. D., & Kelly, D. R. Grit: Perseverance and passion for long-term goals. Journal of Personality and Social Psychology. 92/6. 2007.

The focus of this Skill Builder is on the purpose of control variables in regression models and on how to interpret regression results when there is more than one (1) predictor in the model. 

Multiple Regression Models

Topic 2 of 4

Learning Objective: Interpret regression results when the regression model has more than one predictor.

The Purpose of Control Variables

A control variable in a statistical model is a variable that we are attempting to “hold constant” while we examine the association among other variables in our model. In essence, we want to know if our independent variable of interest (e.g., grit) is associated with our dependent variable after factoring in other variables (e.g., personality factors) that could also be related to the dependent variable.

In addition to our independent variables of interest, in regression models, we also include control variables as predictor variables because we suspect the control variable is related to our outcome variable and could explain the association between our independent variable and the outcome.

For example, suppose we want to understand factors that might predict an individual's income. Education level seems like an obvious predictor variable that we would want to examine as it is probably a predictor of income. Might there be other variables, however, that would predict income besides education? And, if we find that education level is associated with income, could it partially be because those with more education are also likely to be older and more accomplished/established and therefore earn more money?  For this reason, we probably want to include age as a control variable in our regression model predicting income with education.

Take a look at the output below from SPSS, which shows the results of a regression model based on data from the 2004 General Social Survey ( http://sda.berkeley.edu/archive.htm  ). Use an alpha value of .05 to interpret the results.

Model Summary A model summary showing the results of a regression model based on data from the 2004 General Social Survey. Highest year of school completed, age of respondent. 

a. Predictors: (Constant), HIGHEST YEAR OF SCHOOL COMPLETED, AGE OF RESPONDENT.

Interpreting the Regression Coefficient

So, how would we interpret the regression coefficient in this model for education level, if we are controlling for age? Researchers would say that holding age constant, education level has a weak, positive association with income,  β = .21,  p < .05. Recall that a positive association indicates that as education level increases, the income also increases. Another way to say the same thing is to say that education level predicts income above and beyond an individual's age.  

Recall, too, that we need to look at the  p-value for each predictor in the model in order to discern whether the predictor shows a statistically significant association with the outcome variable and that we can use the standardized regression coefficients to gauge the effect size for each predictor. In our results below, we can see that each predictor, age, and education level is statistically significant as the  p-value is less than the alpha value of .05.

Coefficientsa Table of coefficients showing both unstandardized coefficients and standardized coefficients for age of respondent, highest year of school completed. 

If you look at the standardized regression coefficients, you can see that each predictor shows a weak relationship with income, as each predictor has a standardized regression coefficient that is about .1 or .2; stronger effects would be indicated if the regression coefficients had values closer to 1. Of the two predictors, the education level has a greater value for its standardized regression coefficient, indicating that it is a stronger predictor of income than age.

R-squared

Aside from looking at the individual regression coefficients and the  p-values, another thing to note when you are discussing your multiple regression results is the R-squared value.  R-squared is an important statistic that tells you the proportion of variability in the dependent variable that is accounted for by your model. In other words, it tells you how good of a job your predictors are doing at predicting your outcome variable. The R-squared value ranges from 0 to 1 and can be expressed as a percent.  In the output shown below, you can see that the R-squared value is .066.  

Model Summary

a. Predictors: (Constant), HIGHEST YEAR OF SCHOOL COMPLETED, AGE OF RESPONDENT.

Numbered divider 1

Consider the following scenario when answering the question below.

Using the SPSS output above, and assuming an alpha level of .05, suppose we wanted to control for education level instead of age this time around.

Hint: Look at the  p -value in the “sig.” column of the output for age. Is that value less than the alpha value of .05?

How would we interpret the results if we were interested in predicting income with age while controlling for education level?

Holding education level constant, an increase in age predicts an increase in income.

Education level is a stronger predictor of income than age, indicating that age is not related to income after controlling for education level

Age does not predict income after controlling for education level.

SUBMIT

TAKE AGAIN

How Predictors Are Related to the Dependent Variable?

The above question emphasizes the fact that regardless of whether the researcher is thinking of age or education level as the control variable, the mathematical interpretation of how the predictors are related to the dependent variable does not change. When we interpret the coefficient for one predictor in the model, it is always in the context of holding the other variables “constant,” regardless of which variable, conceptually, we are thinking of as a control variable.

Sometimes, researchers include multiple predictors in a model and are not thinking of any of them, conceptually, as control variables. They are simply interested in how the predictors, together, are related to the outcome variable, or they may be interested in seeing which predictor variables show the strongest relationships with the outcome.

Numbered divider 2

Consider the following scenario when answering the question below.

Suppose we wanted to predict the number of slices of pepperoni pizza people ate at a party based on how many slices their friends ate. Suppose we also gathered data on three (3) additional variables: individual's mood, how much they like pepperoni, and how hungry they reported being when they arrived at the party. Take a look at the correlation results below from SPSS, which is based on fictitious data.

Correlations

Blank	number of slices	positive mood	friends' number of slices	like pepperoni	hunger
number of slices	Pearson Correlation	1	.036	.791**	.806**	-.080
	Sign. (2-tailed)	blank	.864	.000	.000	.702
	N	25	25	25	25	25
positive move	Pearson Correlation	.036	1	-.106	.174	.238
	Sig. (2-tailed)	.864	blank	.613	.406	.253
	N	25	25	25	25	25
friends' number of slices	Pearson Correlation	.791**	-.106	1	.638**	-.139
	Sig. (2-tailed)	.000	.613	blank	.001	.507
	N	25	25	25	25	25
like pepperoni	Pearson Correlation	.806**	-.174	.638**	1	-.198
	Sig. (2-tailed)	.000	.613	blank	.001	.507
	N	25	25	25	25	25
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