Topic for Discussion 4:

Let's say you have collected lots of data from an online source with a large number of predictors available for you to consider building a model with. The following prompts will get you thinking about how one might approach developing a model in this setting and in what order it might make sense to apply certain techniques:

• If we are going to perform a hypothesis test, when would we want to check for model violations? Which model violations would we be most interested in verifying? Can you think of an example of how not checking the assumptions at the right time would lead you to an incorrect conclusion?
• If we start with the biggest model we could build with these predictors, what might be some of the issues we would encounter when trying to check our assumptions (in terms of practicality)? Should we avoid checking all our assumptions in every possible way due to this?
• If we start with the biggest model we could build with these predictors, would we need to continue checking the additional conditions every time we change our model? Why or why not? Think up an example to support your answer.
• What if we already found model violations in a model, performed some transformations to correct them, but then decided we don't want a few predictors in this model? Would you expect that we would need to change our transformations at all once we've removed the predictors from the model? Why or why not?
• Should we examine our model for violated assumptions before or after we check whether we have leverage points, outliers, or influential points? What might happen if we change the order that we check these problems?
• While it's not a good idea to delete observations without a contextual reason (i.e. not just because the model would be better without them), what would change in our model if we were to delete some leverage points, or some outliers, or some influential points?