Predictive Analytics and Machine Learning

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Exam practice exercises

Predictive Analytics and Machine Learning

Things to keep in mind

Today’s practice questions reflect the style of SOME questions in the exam.

It does not imply that different style of questions will not be asked.

Difficulty does not necessarily reflect the difficulty of questions in the exam.

This practice is just intended to further help you understand the methods.

You must still study and understand the content of the whole unit. Not just practice the questions in this lecture.

Example 1

A hospital has determined that the probability that emergency room (ER) patients have heart disease is given as

Pr(yi = 1|xi ) = g(4 + 0.02Agei 0.04MaxHRi ).

Where MaxHR denotes the maximum heart rate of the patient measured in a span of two minutes. When

the probability that a patient has heart disease is greater that 80%, the patient is immediately seen by a doctor. A 38 year old patient has been recently admitted to the ER. For what values of MaxHR would this patient need to be seen immediately by a doctor

Example 2

The data set in the plot below consists of the two predictors Walks and HmRun for 10 Baseball players.

HmRun

We want to fit a regression tree to this data in order to predict salary. We want to consider a tree with two leaves (or terminal nodes). The annual salary for these players is

X

Salary

-Mike Heath

650

-John Russell

155

-Pete Incaviglia

172

-Glenn Davis

215

-Frank White

750

-Rafael Santana

250

-Chili Davis

815

-Herm Winningham

90

-Robby Thompson

140

-Joe Carter

250

1. According to the overall SSE measure, which of the following is the best tree partition for this data

Partition 1 = {j = Walks, s = 50}; Partition 2 = {j = Walks, s = 35}; Partition 3 = {j =

HmRun, s = 10}; Partition 4 = {j = HmRun, s = 20}.

2. Using the optimal partition, what is the predicted salary for the player John Doe who has produced

15 home runs and a total number of 55 walks

Example 3

1. The figure below defines a neural network in R and presents some output in the R console window. Produce a network diagram of the neural network. Be explicit about the values of the weights and biases.

2. Based on the diagram, what are the values for the vectors β 1 and β 2

3. Use the neural network in question 1 to compute a prediction when xi1 = 1, xi2 = 3 and xi3 = 2 (show your workings on a piece of paper).

4. Discuss whether this neural network should be used for regression or classification.