analysis example

How do you compare regression lines statistically? Imagine you are studying the relationship between height and weight and want to determine whether this relationship differs between basketball players and non-basketball players. You can graph the two regression lines to see if they look different. However, you should perform hypothesis tests to determine whether the visible differences are statistically significant. In this blog post, I show you how to determine whether the differences between coefficients and constants in different regression models are statistically significant. [Read more…] about Comparing Regression Lines with Hypothesis Tests

You’ve settled on a regression model that contains independent variables that are statistically significant. By interpreting the statistical results, you can understand how changes in the independent variables are related to shifts in the dependent variable. At this point, it’s natural to wonder, “Which independent variable is the most important?” [Read more…] about Identifying the Most Important Independent Variables in Regression Models

Data mining and regression seem to go together naturally. I’ve described regression as a seductive analysis because it is so tempting and so easy to add more variables in the pursuit of a larger R-squared. In this post, I’ll begin by illustrating the problems that data mining creates. To do this, I’ll show how data mining with regression analysis can take randomly generated data and produce a misleading model that appears to have significant variables and a good R-squared. Then, I’ll explain how data mining creates these deceptive results and how to avoid them. [Read more…] about Using Data Mining to Select Regression Models Can Create Serious Problems

P values and coefficients in regression analysis work together to tell you which relationships in your model are statistically significant and the nature of those relationships. The linear regression coefficients describe the mathematical relationship between each independent variable and the dependent variable. The p values for the coefficients indicate whether these relationships are statistically significant. [Read more…] about How to Interpret P-values and Coefficients in Regression Analysis

R-squared is a goodness-of-fit measure that tends to reward you for including too many independent variables in a regression model, and it doesn’t provide any incentive to stop adding more. Adjusted R-squared and predicted R-squared use different approaches to help you fight that impulse to add too many. The protection that adjusted R-squared and predicted R-squared provide is critical because too many terms in a model can produce results that you can’t trust. These statistics help you include the correct number of independent variables in your regression model. [Read more…] about How to Interpret Adjusted R-Squared and Predicted R-Squared in Regression Analysis

Multicollinearity occurs when independent variables in a regression model are correlated. This correlation is a problem because independent variables should be independent. If the degree of correlation between variables is high enough, it can cause problems when you fit the model and interpret the results. [Read more…] about Multicollinearity in Regression Analysis: Problems, Detection, and Solutions