Reference no: EM132225850
Homework -
Q1. For each part below 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.
(i) The sample size n is extremely large, and the number of predictors p is small.
(ii) The number of predictors p is extremely large, and the number of observations n is small.
(iii) The relationship between the predictors and response is highly non-linear.
(iv) The variance of the error terms, i.e. σ2 = Var(∈), is extremely high.
Q2. We have data from the questionnaires survey (to ask people opinion) and objective testing with two attributes (acid durability and strength) to classify whether a special paper tissue good or not. The following table gives the training sample
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X1 = Acid Durability (seconds)
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X2 = Strength (kg/square meter)
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Y
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7
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7
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Bad
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7
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4
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Bad
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3
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4
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Good
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1
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4
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Good
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5
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3
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Good
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7
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5
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Good
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Now the factory produces a new paper tissue that pass laboratory test with X1 = 3 and X2 = 7. Suppose we wish to use this data set to make a prediction for Y when X1 = 3 and X2 = 7 using K-nearest neighbors.
(i) Compute the Euclidean distance between each observation and the test point X1 = 3 and X2 = 7.
(ii) What is our prediction with K = 1? Why?
(iii) What is our prediction with K = 3? Why?
(iv) If the Bayes decision boundary in this problem is highly non-linear, then would we expect the best value for K to be large or small? Why?
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