Multiple Linear Regression

Multiple linear regression (multiple regression) is a type of correlational test in which the research is interested in finding the strength of a correlation between multiple variables. In multiple linear regression, multiple variables are used as predictors. 'Here, the researcher is interested in the relationship between the predicted variables (dependent) and predictor variables (also known as the independent variables).

Independent variables in multiple regression are usually quantitatively measured variables using summative response, interval, or ratio scales (Lawrence, Meyer, & Guarino, 2017)

Multiple Linear Regression uses the same general equation as linear regression, but accommodates for multiple IV's.

contributed by Thomas Fox, WCSU Cohort 8

Reference

Lawrence, S., Meyer, G, & Guarino, A.J. (2017). Applied multivariate research: Design and interpretation. Thousand Oaks, CA: Sage Publications

Multiple Linear Regression interpreting results example

Pulled from completed Multiple Linear Regression assignment:

Research Question: To what extent and in what manner can variation in college readiness be explained by self regulation, engagement in reading, household income, and population density?

Independent Variables: Self regulation, Engagement in reading, Household income, population density Dependent Variable: College Readiness

Sample report interpreting results: Multiple linear regression was conducted with college readiness as the criterion variable and self regulation, engagement in reading, household income and population density as predictor variables. The model was significant F(4,45) = 17.88, p<.001. Together, the variables in the model explained 61.4% of the variation in parent income, f^2=[.614/.386], 1.59. Household income contributed significantly to the prediction of college readiness p<.001 while self regulation, engagement, and population density did not.

contributed by Scott Trungadi, WCSU Cohort 8

Collinearity

When conducting a multiple linear regression, you to see if the data meets the assumption of collinearity. Therefore, you need to locate the Coefficients table in your results under the heading Collinearity Statistics, under which are two subheadings, Tolerance and VIF.

If the VIF value is greater than 10, or the Tolerance is less than 0.1, then you have concerns over multicollinearity. Otherwise, your data has met the assumption of collinearity and can be written up something like this:

contributed by Sheri Prendergast, WCSU Cohort 8

Dart, A., (2013). Reporting Multiple Regressions in APA format-Part One. Retrieved from: http://www.adart.myzen.co.uk/reporting-multiple-regressions-in-apa-format-part-one/