I attached the homework assignment and textbook for reference if needed.
IS 603 Homework 3, Due Sunday 3/28/2021 (11:59pm) Points 1. For this question, consider the Weather dataset in the table below, where the goal is to predict whether we will play an outdoor sports game on a particular day (yes or no). The class attribute is the last column, Play. The Day ID attribute is not used for the predictions. As we proceed through this question, we will work toward predicting the class label for Day F using the nearest neighbor classifier. Day ID Temperature Humidity Wind Speed Play (class) A 85 85 5 no B 80 90 25 no C 83 86 10 yes D 70 96 7 yes E 68 80 3 yes F 65 70 20 ? (a) Briefly explain (in around 2-3 sentences, your own words) the main conceptual idea of the nearest neighbor classifier, and how it could be used to predict the class label for the Weather problem. (1) (b) Your task for this sub-question is to calculate the Euclidean distances between each of the data points (i.e. days) from Day F. For this question, ignore the Day ID when calculating distances. First, let’s calculate the distance for Day A together. Recall that the general formula for Euclidean distance between points A = [d1,A, d2,A, . . . , dn,A] and B = [d1,B , d2,B , . . . , dn,B ] is: d(A,B) = √ (d1,A − d1,B)2 + (d2,A − d2,B)2 + . . . + (dn,A − dn,B)2 . Guided example for Day A: We want to calculate the Euclidean distance between A = [85, 85, 5] and F = [65, 70, 20]. Note, we did not include either the Day ID or the class attribute here. Plugging these numbers into the formula, we must calculate d(A,F ) = √ (85− 65)2 + (85− 70)2 + (5− 20)2. Open wolframalpha.com, which we will use as a calculator. At the prompt, enter: sqrt((85 - 65)^2 + (85 - 70)^2 + (5 - 20)^2). Read off the first few decimal places of the answer under decimal approximation, confirming that you get 29.15. Using similar calculations, please provide the distances for Days B, C, D, and E. (4) (c) Based on the distances you calculated, which day is the nearest neighbor for Day F? Hence, what is the predicted class label for Day F according to the nearest neighbor classifier? (2) (d) Based on the distances you calculated, which are the three nearest neighbors? Hence, what is the predicted class label for Day F according to the K-nearest neighbor classifier, where K = 3? (2) Homework continues overleaf. 2. For this question, suppose you have a larger version of the Weather dataset from Question 1, which contains approximately one year’s worth of data. The goal of this question will be to evaluate the performance of the nearest neighbor classifier and K-nearest neighbor classifiers discussed in Question 1 in the context of this version of the Weather problem. (a) Briefly explain (in 2-3 sentences, your own words) the concept of overfitting. (1) (b) Briefly explain (in 2-3 sentences, your own words) why it would not be appropriate to evaluate the performance of the nearest neighbor classifiers by simply measuring the accuracy of the models on the training dataset. Be sure to use the concept of overfitting in your answer. (1) (c) Briefly explain (in 2-3 sentences, your own words) the concept of a hold-out set, and how it can help to address the problem you described in your answer to Question 2b. (1) (d) Suppose we train a K-nearest neighbor classifier on the training data for the Weather problem with different several different values of the number of nearest neighbors, K = {1, 3, 5, 7, 9, 11}. We select the best value of K which performs the best on the hold-out set. Going forward, we plan to use the model with the best value of K to predict the class labels (Play) on each new day from now on. Briefly explain (in 2-3 sentences, your own words) why the accuracy of the model, estimated based on the hold-out set, may be an over-estimate of the model’s true accuracy on future days. (1) (e) Briefly explain (in 2-3 sentences, your own words), the concept of a validation set, and how it can help to address the problem you described in your answer to Question 2d. (1) (f) Briefly explain (in 2-3 sentences, your own words) a possible use-case/application of clustering methods such as K-means to the Weather problem. In your answer, be sure to explain what the output of the clustering method would be used for. Feel free to make any assumptions you want to about the broader context of the scenario and who is using the model (e.g. which particular sport is being played and whether it is professional or amateur), though it would be best to explain any assumptions you make. (1) Total: 15 Data Science for Business Praise “A must-read resource for anyone who is serious about embracing the opportunity of big data.” — Craig Vaughan Global Vice President at SAP “This timely book says out loud what has finally become apparent: in the modern world, Data is Business, and you can no longer think business without thinking data. 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