Which of the following statements about the coefficient of determination R$2$ are correct? Select all that apply.

a$.$

The coefficient of determination R$2$ tells us what percentage of the variation in the response variable is explained by the model.

b$.$

R$2$ will be higher for good models and lower for worse models.

c$.$

In forecasting, we select the model with the highest R$2$ to get the most accurate forecasts.

d$.$

An R$2$ value close to $1$ indicates that generally predictions are very close to the actual values.

e$.$

A good R$2$ value in forecasting is $0\mathrm{.}8$ or higher.

f$.$

R$2$ can only increase when adding additional predictors.