A regression assesses whether predictors account for variability in a dependent variable. Statistics Solutions is a consulting company with regression expertise. This page will describe examples where regression analyses can be used, regression assumptions, the evaluation of the R-square, the F-test, the interpretation of the beta coefficient(s), the regression equation.
Regression example. The are numerous applications of regression. For example, a school has two types of reading programs (tradition program and a novel program), and would like to examine if program type influences (predicts) test scores. This regression example will be used throughout this page.
Regression assumptions. First, regression analysis is very sensitive to outliers. The researcher should first standardize the scores to see if a value is +/- 3 standard deviations from the other scores and consider deleting that score.
Second, the main assumptions of regression are linearity and constant variance. To assess regression assumptions the researcher should plot the standardized residuals verses the predicted values. If the plot shows random scatter, the regression assumptions are met. However, there is a curvilinear (e.g., U-shape) then linearity is not met, and if the scatter has a cone shape, then constant variance of the regression analysis is not met.
Regression F-test. When the regression is conducted, a F-value and significance level of that F-value will be in the output. If the F-value is statistically significant (typically p < .05), this signifies that the regression model (the predictors) did a good job of predicting the outcome variable.
Evaluation of the R-Square. When the regression is conducted, a R-square is presented. The R-square in regression really answers the question, “of all of the reasons why the outcome variable can vary, what percent of those reasons can be accounted for by the predictor(s) variables.”
Evaluation of the Adjusted R-Square. The regression output will also present an adjusted R-square value. The interpretation of this value is that if the researcher used this regression model on a new data set, this would be the amount of variability accounted for in the new data set.
Regression beta coefficients. After the evaluation of the F-value and R-square, it is important to evaluate the regression beta coefficient(s). The beta coefficient can be negative or positive, and have a t-value and significance of that t-value associated with it. Think of the regression beta coefficient as the slope of a line: the t-value and significance assesses the extent to which the magnitude of the slope is significantly different from the line laying on the X-axis. If the regression beta coefficient is not statistically significant (i.e., the t-value is not significant), do not interpret that predictor. If the beta coefficient, examine the sign of the beta. If the regression beta coefficient is positive, the interpretation is that for every 1-unit increase in the predictor variable, the dependent variable will increase by the beta coefficient. For example, if the regression beta coefficient is .80 and significant, then for each unit increase in the predictor variable, the outcome variable will increase by .80 units.
Regression equation. Once the beta coefficeint is determined, then a regression equation can be written. Using the example and beta coefficient above, the equation can be written as follows:
Y=.80X + c, where Y is the outcome variable, X is the predictor variable, .80 is the beta coefficient, and c is a constant.
Regression consulting. Statistics Solutions provides complete solutions for your dissertation or thesis proposal and results chapters (including all types of regressions–linear, multiple, logistic, ordinal, and multinominal regression), from inception to defense. As professional methodologists and statistical consultants, we ensure satisfaction with your dissertation consulting services and the successful completion of your study and your degree!
