Regression Analysis

Regression analysis is a statistical method used to measure how strongly one dependent variable relates to one or more independent variables—and to quantify that relationship in ways that support prediction and explanation. It estimates how much variance in the dependent variable can be accounted for by the independent variable(s), producing a regression equation that links inputs to an expected outcome. In practice, regression is used to test whether changes in a predictor are associated with changes in an outcome, while also providing coefficients and fit statistics that indicate strength and significance.

A key distinction separates regression from correlation. Correlation focuses on association between two variables using a correlation coefficient, without labeling one variable as dependent or independent. Regression, by contrast, is built around prediction and explanation: it clearly distinguishes dependent and independent variables and uses inferential tests tied to regression outputs—such as regression coefficients, the intercept, and t statistics—to determine whether the relationship is statistically meaningful.

The transcript distinguishes two main forms. Bivariate regression involves exactly two variables: one dependent variable and one independent variable. It is often used to see how well scores on the dependent variable can be predicted from data on the independent variable. Multiple regression expands this framework to three or more variables, allowing researchers to evaluate the impact of several independent variables on a single dependent variable at once.

Before running models, several terms matter. Regression coefficients quantify how strongly each independent variable predicts the dependent variable. The unstandardized coefficient is used directly in the regression equation, while the standardized coefficient (beta value) expresses effects in standard deviation units; with a single predictor, beta aligns with the correlation coefficient between the dependent and independent variables. Model fit is summarized with R and R². R represents the correlation between observed and predicted values, while R² (the squared R) indicates the proportion of variance in the dependent variable explained by the chosen predictors. Because R² can look inflated as more predictors are added or with larger samples, adjusted R² offers a more conservative measure.

The walkthrough then demonstrates bivariate regression using servant leadership as the independent variable and life satisfaction as the dependent variable. The model summary reports R = .526, yielding R² = .276, meaning 27.6% of the variance in life satisfaction is accounted for by servant leadership. Significance is checked via the ANOVA table, where the p-value is reported as below .05 (described as 0.0 in the output). The coefficient interpretation follows: a positive beta (reported as .579) indicates that higher servant leadership is associated with higher life satisfaction, and the overall model fit is supported by an F statistic (reported around 83.599) with p < .01.

Finally, the transcript shows how multiple regression changes the output and reporting. When adding self-efficacy and job satisfaction alongside servant leadership, the overall model fit increases, with R² reported as .581 (58.1% variance explained). Significance is assessed again using the ANOVA p-value (< .05), while the coefficient table determines which predictors matter individually through t values and p values. Reporting guidance emphasizes writing results in text using a hypothesis template and presenting key statistics (beta, t, p, R², and F) in a table rather than copying raw software tables into a document.