A regression assesses whether predictor variables account for variability in a dependent variable. This page will describe regression analysis example research questions, regression assumptions, the evaluation of the R-square (coefficient of determination), the *F*-test, the interpretation of the beta coefficient(s), and the regression equation.

**Example questions answered by a regression analysis:**

Do age and gender predict gun regulation attitudes?

Do the five facets of mindfulness influence peace of mind scores?

**Assumptions:**

First, regression analysis is sensitive to outliers. Outliers can be identified by standardizing the scores and checking the standardized scores for absolute values higher than 3.29. Such values may be considered outliers and may need to be removed from the data.

Second, the main assumptions of regression are normality, homoscedasticity, and absence of multicollinearity. Normality can be assessed by examining a normal P-P plot. If the data form a straight line along the diagonal, then normality can be assumed. To assess homoscedasticity, the researcher can create a scatterplot of standardized residuals verses standardized predicted values. If the plot shows random scatter, the assumption is met. However, if the scatter has a cone shape, then the assumption is not met. Multicollinearity can be assessed by calculated variance inflation factors (VIFs). VIF values higher than 10 indicates that multicollinearity may be a problem.

*F*-test

When the regression is conducted, an* F*-value, and significance level of that *F*-value, is computed. If the *F*-value is statistically significant (typically *p* < .05), the model explains a significant amount of variance in the outcome variable.

**Evaluation of the R-Square**

When the regression is conducted, an R^{2} statistic (coefficient of determination) is computed. The* *R^{2} can be interpreted as the percent of variance in the outcome variable that is explained by the set of predictor variables.

**Evaluation of the Adjusted R-Square**

The adjusted R^{2} value is calculation of the R^{2} that is adjusted based on the number of predictors in the model.

Schedule a time to speak with an expert using the calendar below.

**User-friendly Software**

Transform raw data into written, interpreted, APA formatted regression results in seconds.

**Beta Coefficients**

After the evaluation of the* F*-value and R^{2}, it is important to evaluate the regression beta coefficients. The beta coefficients can be negative or positive, and have a *t*-value and significance of the *t*-value associated with each. The beta coefficient is the degree of change in the outcome variable for every 1-unit of change in the predictor variable. The *t*-test assesses whether the beta coefficient is significantly different from zero. If the beta coefficient is not statistically significant (i.e., the *t*-value is not significant), the variable does not significantly predict the outcome. If the beta coefficient is significant, examine the sign of the beta. If the beta coefficient is positive, the interpretation is that for every 1-unit increase in the predictor variable, the outcome variable will increase by the beta coefficient value. If the beta coefficient is negative, the interpretation is that for every 1-unit increase in the predictor variable, the outcome variable will decrease by the beta coefficient value. For example, if the beta coefficient is .80 and I statistically significant, then for each 1-unit increase in the predictor variable, the outcome variable will increase by .80 units.

**Equation**

Once the beta coefficient is determined, then a regression equation can be written. Using the example and beta coefficient above, the equation can be written as follows:

y= 0.80x + c, where y is the outcome variable, x is the predictor variable, 0.80 is the beta coefficient, and c is a constant.

**Statistics Solutions can assist with your quantitative analysis by assisting you to develop your methodology and results chapters. **The services that we offer include:

Edit your research questions and null/alternative hypotheses

Write your data analysis plan; specify specific statistics to address the research questions, the assumptions of the statistics, and justify why they are the appropriate statistics; provide references

Justify your sample size/power analysis, provide references

Explain your data analysis plan to you so you are comfortable and confident

Two hours of additional support with your statistician

*Quantitative Results Section** (Descriptive Statistics, Bivariate and Multivariate Analyses, Structural Equation Modeling, Path analysis, HLM, Cluster Analysis)*

Clean and code dataset

Conduct descriptive statistics (i.e., mean, standard deviation, frequency and percent, as appropriate)

Conduct analyses to examine each of your research questions

Write-up results

Provide APA 7^{th} edition tables and figures

Explain Chapter 4 findings

Ongoing support for entire results chapter statistics

**Please call 727-442-4290 to request a quote based on the specifics of your research, schedule using the calendar on this page, or email ****[email protected]**