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BASIC STATISTICS

REGRESSION

REGRESSION--To determine the (standardized or unstandardized) slope(s) of the regression line which predicts a dependent variable given knowledge of one or more independent variables.  For Asimple@ regression (i.e., one dependent and one independent variable), this REGRESSION option reproduces the information available in the SCATTERPLOT option without the actual scatterplot; REGRESSION also provides standardized regression coefficients (the same as Pearson r with two variables; the same as the partial correlation coefficient with one dependent variable and multiple independent variables) as well as unstandardized regression coefficients (expressed in raw score units).  REGRESSION is most useful when you have multiple independent variables, when you desire a multiple regression equation or the multiple correlation coefficient (R).

1.  When you select REGRESSION, the window screen will ask you for your dependent variable and a list of independent variables (you must supply at least one).  As with previous statistical options, you may elect to run the analysis on a subset of the full sample.  As with the CORRELATION option, there is no way to eliminate outliers in this version of regression analysis except through the subset function.  When you have indicated your dependent variable, your independent variable(s), and any subset variables, click on OK in the upper right hand corner of the window.

2.  The summary screen shows the BETA weight (standardized multiple regression coefficient; partial correlation coefficient) for the relationship between the dependent variable and each independent variable when the effects of the other variables in the model have been eliminated or controlled.  The BETA can be compared to the zero-order Asimple@ correlation coefficient (r) which describes the relationship between the dependent variable and the independent variable when the effects of the other variables have been allowed to impact the independent and dependent variables.  The summary screen also shows the R-squared which tells you the amount of the variation in the dependent variable which can be attributed to all the independent variables considered together.

3.  ANOVA (on the left side of the screen) provides the ANOVA summary table used to test the probability that an R-squared of that magnitude could occur by random sampling error alone.  ANOVA also provides a chart of the regression coefficients--both standardized (BETAs) and unstandardized; this chart also provides the standard errors and the t-values to allow you to test whether each of the regression coefficients is statistically different from zero (i.e., is statistically significant).

4.  CORRELATION (on the left side of the screen) provides the zero-order correlation matrix for all the variables in the regression analysis.  
A.  This CORRELATION screen also reports Cronbach
=s Alpha, a measure of internal consistency for a set of variables, which is often used to assess the reliability of a set of questions.  (Cronbach=s alpha is calculated only if all the variables in the regression analysis are positively related to one another.)

5.  MEANS (on the left side of the screen) provides the number of cases, the mean, and the standard deviation for each variable in the analysis.

for questions or comments contact me at mduncombe@coloradocollege.edu
last updated on November 25, 2002