Regression
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Regression Overview Regression is similar to correlation in that it is trying to fit data values along a best-fit straight line, but regression can be used to predict the value of one variable given the value of another variable. In other words, regression lets you predict what your dependent variable value will be from one or more independent variables. Hypotheses H0: The proportion of variance the independent variables account for in the dependent variable is 0. (no relationship) H1: The proportion of variance the independent variables account for in the dependent variable is not 0. (there is a relationship) Equation Trust me, you don’t want to do this one by hand. Use a statistical analysis program.
Warning! • There are several different kinds of regression. This handout just covers linear regression. • Unstandardized coefficients cannot be compared to each other. Use the standardized or Beta coefficients to compare the effects of the predictor variables. • The following example is actually multiple regression because I used two independent variables. I also left out the scatterplots that are sometimes used to check the relationships between the variables before the analysis. See the SPSS help section for links to more thorough resources. SPSS • Click Analyze > Regression > Linear. . . • Select the dependent variable and one or more independent variables. In this example, the dependent variable is the grade students received on a research assignment, and the independent variables are the time in minutes they spent searching for articles and the number of articles they found.
UT Southwestern Medical Center Library—October 2007
R square tells us that the independent variables explain 40.6% of the variance of the dependent variable.
The F statistic tests to see if the null hypothesis is 0, i.e., the R square statistic is not significant, and there is no relationship between the independent and dependent variables. We can see that the null hypothesis was not supported. Our results are significant at .001, so we know that our independent variables are accounting for a significant proportion of the variance of our dependent variable.
The Coefficients table gives us information about the effects of each of the individual predictor variables. The unstandardized coefficients show us the increase in the value of the dependent variable for each unit increase in the independent variable. For each minute of searching, the student’s grade will increase by .212 points. We cannot compare the relative influences of the UT Southwestern Medical Center Library—October 2007
independent variables with the unstandardized coefficients, however. We must use the Beta coefficients because they are standardized instead of being on multiple scales like the unstandardized coefficients. From the Beta coefficients, we can see that the time spent searching has about six times the effect on grade than the number of results found. The Coefficients table also gives us a significance test for each of the independent variables’ influence on the dependent variable. We can see that the time spent searching accounts for a significant amount of variance in the grade. The number of results returned does not account for a significant amount of the variance in the grade. Thus, when we look at the results in the ANOVA table, we know that the time spent searching is accounting for most of the model’s effect on the dependent variable. SPSS Help For additional examples of how to perform regression analysis in SPSS, please see the following sites. • http://www.american.edu/cte/docs_pdfs/training/SPSS_Regressionand Correlation.pdf : An explanation of how to perform and interpret regression and correlation analyses from American University. • http://www.indstate.edu/cirt/research/statsoftware/spss13_regression .pdf : Thorough explanations with plenty of screenshots of how to perform linear and other kinds of regression from Indiana State University. • http://www.visualstatistics.net/SPSS%20workbook/multiple_regressio n.htm : A thorough but brief explanation from Cruise Scientific of how to create and read scatterplots and perform multiple regression analyses.
UT Southwestern Medical Center Library—October 2007
Warning! • There are several different kinds of regression. This handout just covers linear regression. • Unstandardized coefficients cannot be compared to each other. Use the standardized or Beta coefficients to compare the effects of the predictor variables. • The following example is actually multiple regression because I used two independent variables. I also left out the scatterplots that are sometimes used to check the relationships between the variables before the analysis. See the SPSS help section for links to more thorough resources. SPSS • Click Analyze > Regression > Linear. . . • Select the dependent variable and one or more independent variables. In this example, the dependent variable is the grade students received on a research assignment, and the independent variables are the time in minutes they spent searching for articles and the number of articles they found.
UT Southwestern Medical Center Library—October 2007
R square tells us that the independent variables explain 40.6% of the variance of the dependent variable.
The F statistic tests to see if the null hypothesis is 0, i.e., the R square statistic is not significant, and there is no relationship between the independent and dependent variables. We can see that the null hypothesis was not supported. Our results are significant at .001, so we know that our independent variables are accounting for a significant proportion of the variance of our dependent variable.
The Coefficients table gives us information about the effects of each of the individual predictor variables. The unstandardized coefficients show us the increase in the value of the dependent variable for each unit increase in the independent variable. For each minute of searching, the student’s grade will increase by .212 points. We cannot compare the relative influences of the UT Southwestern Medical Center Library—October 2007
independent variables with the unstandardized coefficients, however. We must use the Beta coefficients because they are standardized instead of being on multiple scales like the unstandardized coefficients. From the Beta coefficients, we can see that the time spent searching has about six times the effect on grade than the number of results found. The Coefficients table also gives us a significance test for each of the independent variables’ influence on the dependent variable. We can see that the time spent searching accounts for a significant amount of variance in the grade. The number of results returned does not account for a significant amount of the variance in the grade. Thus, when we look at the results in the ANOVA table, we know that the time spent searching is accounting for most of the model’s effect on the dependent variable. SPSS Help For additional examples of how to perform regression analysis in SPSS, please see the following sites. • http://www.american.edu/cte/docs_pdfs/training/SPSS_Regressionand Correlation.pdf : An explanation of how to perform and interpret regression and correlation analyses from American University. • http://www.indstate.edu/cirt/research/statsoftware/spss13_regression .pdf : Thorough explanations with plenty of screenshots of how to perform linear and other kinds of regression from Indiana State University. • http://www.visualstatistics.net/SPSS%20workbook/multiple_regressio n.htm : A thorough but brief explanation from Cruise Scientific of how to create and read scatterplots and perform multiple regression analyses.
UT Southwestern Medical Center Library—October 2007
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