For a random forest, let p be the total number of features and m be the number of features selected at each split.

Determine which of the following statements is/are true.

• When [math]m = p[/math], random forest and bagging are the same procedure.
• [math]\frac{p-m}{p}[/math] is the probability a split will not consider the strongest predictor.
• The typical choice of [math]m[/math] is [math]\frac{p}{2}[/math]

• None
• I and II only
• I and III only
• II and III only
• The correct answer is not given by (A), (B), (C), or (D).

Determine which of the following statements about random forests is/are true?

• If the number of predictors used at each split is equal to the total number of available predictors, the result is the same as using bagging.
• When building a specific tree, the same subset of predictor variables is used at each split.
• Random forests are an improvement over bagging because the trees are decorrelated.

• None
• I and II only
• I and III only
• II and III only
• The correct answer is not given by (A), (B), (C), or (D).

Determine which of the following statements regarding statistical learning methods is/are true.

• Methods that are highly interpretable are more likely to be highly flexible.
• When inference is the goal, there are clear advantages to using a lasso method versus a bagging method.
• Using a more flexible method will produce a more accurate prediction against unseen data.

• I only
• II only
• III only
• I, II and III
• The correct answer is not given by (A), (B), (C), or (D).

You are given a dataset with two variables, which is graphed below. You want to predict y using x.

Determine which statement regarding using a generalized linear model (GLM) or a random forest is true.

• A random forest is appropriate because the dataset contains only quantitative variables.
• A random forest is appropriate because the data does not follow a straight line.
• A GLM is not appropriate because the variance of y given x is not constant.
• A random forest is appropriate because there is a clear relationship between y and x.
• A GLM is appropriate because it can accommodate polynomial relationships.

Determine which of the following statements is true

• Linear regression is a flexible approach
• Lasso is more flexible than a linear regression approach
• Bagging is a low flexibility approach
• There are methods that have high flexibility and are also easy to interpret
• None of (A), (B), (C), or (D) are true