What is a measure used to evaluate how well a model fits the data? F-statistic R-squared Mean absolute error Adjusted R-squared

All of the options you provided are measures used to evaluate how well a model fits the data. Here's a brief explanation of each:

1. F-statistic: This is a statistical test used to compare our model with a simpler model to see if our added variables are meaningful. The higher the F-statistic, the more likely it is that the variables we added in our model provide value.

2. R-squared: This is a statistical measure that represents the proportion of the variance for a dependent variable that's explained by an independent variable or variables in a regression model. If the R-squared of a model is 0.50, then approximately half of the observed variation can be explained by the model's inputs.

3. Mean Absolute Error (MAE): This is a measure of errors between paired observations expressing the same phenomenon. It's an average of the absolute differences between the predicted and actual values. It gives an idea of how wrong the predictions were. The measure gives an idea of the magnitude of the error, but no idea of the direction (e.g. over or under predicting).

4. Adjusted R-squared: This is a modified version of R-squared that has been adjusted for the number of predictors in the model. The adjusted R-squared increases only if the new term improves the model more than would be expected by chance. It decreases when a predictor improves the model by less than expected by chance.

Each of these measures can be useful in different scenarios, and they often need to be considered together to get a full picture of a model's performance.