Linear regression models

(a) Tree. Draw a decision tree that can be used for this classification task. Label each node in order to make it clear how to use this tree for classification. What is the training error rate of this tree?

(b) Prunning. Suppose the tree is pruned to just one split. If “speed” is the only variable used, what split minimizes the Gini idex? What is the Gini index for this split, and what is the training error rate of this tree?

(c) Bagging. Four bootstrap samples from the given data are (listed by the party number): Bootstrap sample #1 − (1, 1, 2, 3, 4, 5, 6)

Bootstrap sample #2 − (3, 4, 4, 5, 5, 7, 7)

Bootstrap sample #3 − (3, 3, 4, 6, 7, 7, 7)

Bootstrap sample #4 − (1, 2, 2, 2, 5, 5, 6)

Draw a tree based on each bootstrap sample. Predict the out-of-bag data by the majority vote. Use these results to estimate the testing error rate of this method.

Problem 2. (10 points)

(To be done by hand) Multiple linear regression models are studied for eight different sets of data. Below are various kinds of residual plots. For each case, give a brief dignostics of the regression model and suggest a way to improve the model, if necessary.

 

 

 

Sample Solution

Pain is not an unfamiliar experience to any one person. It’s important to not think of pain just as physical pain from a stubbed toe or broken bone, but also pain from the loss of a loved one or a failure. Often times, the sensation of pain is associated with misery and suffering throughout the existence of the supposed discomfort. However, Colin Klein details how that actually is not the case through his Imperative Theory of Pain. In it, he discusses how suffering is merely a consequence of pain and that the two are not synonymous. Using an Imperativist stance and a theory composed of relative simplicity, he presents a compelling argument. Throughout the entirety of this paper, I will detail Klein’s argument and discuss how he presents a theory of the relationship between pain and suffering that is correct.

Colin Klein looks at pain and suffering from an imperativist point of view. Imperativism concludes, according to Klein, that motivation is an intrinsic, or naturally belonging, feature of pain. Colin Klein begins his argument by discussing the two senses in which he believes pains motivate. He acknowledges pains do many things and the pains motivate the one who is experiencing said pain. Primary motivational force, Klein explains, is simply the command of the body to protect the affected and pained body part. He explains that the primary motivational force is simply derived from the content of the pain. Secondary motivation, however, is deeper than the idea of primary motivation. Secondary motivation contrasts primary motivation completely and includes all motivations that are extrinsic to pain. Klein explains how pain can often cause emotional and mental states directed toward or caused by the pain itself, but since secondary motivations are not always present, the emotions and motivational states can also be absent when pain is present. Klein describes situations in which pains arouse emotions and cause actions related to specific pains.

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