I have some data and I want to build a model (say a linear regression model) out of this data. In a next step, I want to apply Leave-One-Out-Cross-Validation (LOOCV) on the model so see how good it performs.
If I understood LOOCV right, I build a new model for each of my samples (the test-set) using every sample except this sample (the training-set). Then I use the model to predict the test-set and calulate the errors $(predicted - actual)$.
In a next step I aggregate all the errors generated using a choose function, for example MSE, MAPE. I can use these values to judge on the qualitity (or goodness of fit) of the model.
Question: Which model is the model these qualitiy-values apply for, so which model should I choose if I find the metrics generated from LOOCV appropriate for my case? LOOCV looked at $n$ models (where $n$ is the sample count), which one is the model I should choose?
- Is it the model which uses all samples? This model was never calcuated during the LOOCV process!
- Is it the model which has the least error?
Have I understood something wrong?