How do you explain the concept of adjusted r squared to a non-technical audience?

3 Why use adjusted r squared?

Adjusted r squared is a better measure of model fit than r squared because it prevents you from being misled by a high r squared value that is due to overfitting. A model with a high r squared but a low adjusted r squared is likely to perform poorly on new data, because it has learned the quirks of the sample data rather than the general pattern. Adjusted r squared helps you compare different models with different numbers of predictors, and choose the one that has the highest explanatory power without being too complex. A good rule of thumb is to look for the model that maximizes adjusted r squared while minimizing the number of predictors.

4 How to interpret adjusted r squared?

Adjusted r squared can be interpreted in a similar way as r squared, but with a caveat. It tells you how much of the variation in the outcome variable is explained by the model, after accounting for the number of predictors. However, unlike r squared, adjusted r squared can be negative, which means that your model is worse than a simple average of the outcome variable. A negative adjusted r squared indicates that your model has no predictive value, and that you should either remove some predictors or try a different model.

5 How to report adjusted r squared?

When you report the results of your linear regression analysis, you should include both r squared and adjusted r squared, along with other statistics such as the coefficients, the standard errors, and the p-values. You should also explain what these values mean in plain language, and how they support your conclusions. For example, you could write something like this:

"We used linear regression to examine the effect of X, Y, and Z on W. The model explained 75% of the variation in W, as indicated by the r squared value of 0.75. However, after adjusting for the number of predictors, the adjusted r squared value was 0.72, which suggests that some of the predictors might not be necessary or relevant. The coefficients of X, Y, and Z were significant at the 0.05 level, and had positive effects on W."

6 How to improve adjusted r squared?

If you are not satisfied with your adjusted r squared value, there are some steps you can take to improve it. First, you should check the assumptions of linear regression, such as linearity, normality, homoscedasticity, and independence, and make sure that your data meets them. If not, you might need to transform your variables, remove outliers, or use a different type of regression. Second, you should explore different combinations of predictors, and use techniques such as variable selection, regularization, or cross-validation to find the optimal model. Third, you should consider adding interaction terms or polynomial terms to capture nonlinear or complex relationships between the variables.