Early on, the most common treatment for breast cancer was removal of the breast. It is now usual to remove only the tumor and nearby lymph nodes, followed by radiation. The change in policy was due to a large medical experiment that compared the two treatments. Some breast cancer patients, chosen at random, were given one or the other treatment. The patients were closely followed to see how long they lived following surgery. What are the explanatory and response variables? Are they categorical or quantitative?

In this problem, there are two variables to consider. The sort of treatment each patient received is the explanatory variable. The response variable would be the length of time each patient lived after surgery.

The explanatory variable can be regarded of as something that aids in the explanation or prediction of the response variable. The influence of the explanatory variable can be described by the response variable.

The explanatory variable is a categorical variable because the treatment kind cannot be specified by a number. The response variable is quantitative since the number of years lived following surgery may be quantified given a number.

Quantitative variables have numerical values, but categorical variables place people into one of several classes.