Final answer:
A) Increases
Adding a variable to a regression model usually increases the Coefficient of Determination, which reflects the variance explained by the model, but it's important to avoid overfitting by only including relevant variables.
Step-by-step explanation:
When you add a variable to a regression model, the Coefficient of Determination, often represented by R², typically increases. This is because the Coefficient of Determination reflects the proportion of the variance in the dependent variable that is predictable from the independent variables. By adding another variable, the model may explain more of the variance, although this isn't always the case if the variable isn't actually associated with the outcome. Remember that adding too many irrelevant variables can lead to overfitting, where the model fits the sample data very well but may not perform well on new data.
The Coefficient of Determination is always a positive value, ranging from 0 to 1. An R² value closer to 1 indicates that the model explains a high proportion of the variance in the dependent variable. It's important to assess the relevance and contribution of each variable added to the model, as simply having a higher R² value doesn't necessarily mean the model is better, especially if it has become overly complex.