Question

For each of parts (a) through (d), indicate whether we would generally expect the performance of a flexible statistical learning method to be better or worse than an inflexible method. Justify your answer.a. The sample size n is extremely large, and the number of predictors p is small. b. The number of predictors p is extremely large, and the number of observations n is small. c. The relationship between the predictors and response is highly non-linear. d. The variance of the error terms, i.e. Var(epsilon), is extremely high.

Answer 1

Step-by-step explanation:

First, note that a flexible statistical learning method refers to using models that take into account agree difference in the observed data set, and are thus adjustable. While the inflexible method usually involves a model that has no regard to the kind of data set.

a) The sample size n is extremely large, and the number of predictors p is small. (BETTER)

In this case since the sample size is extremely large a flexible model is a best fit.

b) The number of predictors p is extremely large, and the number of observations n is small. (WORSE)

In such case overfiting the data is more likely because of of the small observations.

c) The relationship between the predictors and response is highly non-linear. (BETTER)

The flexible method would be a better fit.

d) The variance of the error terms, i.e. σ2=Var(ϵ), is extremely high. (WORSE)

In such case, using a flexible model is a best fit for the error terms because it can be adjusted.