Midterm MATH 260

AIC

an estimate of the distance (or discrepancy or divergence) between a candidate model and the true model, on a log-scale

The AIC is optimized (smallest) for a model that contains the optimal balance of simplicity of the model with quality of fit to the observations

If two models are similarly good on AIC, then select the simpler of the two models since it is more likely to be correct in general than the more complicated model.

A rule of thumb is that a 2 unit difference on AICs is moderate evidence of a difference in the models and more than 4 units is strong evidence of a difference

bootstrapping

key assumption: the sample is intended to represent the population of interest

Create many different datasets based on original sample - because if original sample is representative of the population, subsets of the sample should also be representative of the population

Takes random pairs from data, with replacement:

• Good if dataset is smaller

  • And you don’t want to break up pairs of data, like we would do in randomization

when would you decide to use logistic regression?

y (response) is a yes or no (binary) variable

x (explanatory) is any kind of variable

simple linear regression: assumptions and types of variables

multiple linear regression: assumptions and types of variables

ANOVA: types of variables

when to use scatterplots

when to use other diagnostic plots (Q-Q, residuals vs fitted)