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CS 6220 Data Mining — Assignment 6

Regression

This assignment will require you to implement and interpret some regression concepts intro-duced in this weeks lesson module. Keep in mind that the main objective of this assignment is to highlight the insights that we can derive from applying these techniques. While the coding aspect is important it is secondary. Accordingly, you are welcome to consult any online documentation and/or code that has been posted to the course website, so long as all references and sources are properly cited. You are also encouraged to use code libraries, so long as you acknowledge any source code that was not written by you by mentioning the original author(s) directly in your source code (comment or header).

Using the Boston House-Prices dataset, you will be asked to construct a linear regression us-ing different features of the dataset to predict the target. You will then be asked to evaluate the performance of the regression with visual outputs.

Objectives:

1. Apply linear regression to a dataset containing numerical features

2. Evaluate the performance of linear regression using R-squared metric and Mean Squared Error

Submission:

Submit your ipynb file on the Assignment submission portal.

Grading Criteria:

Follow the instructions in the pdf, and complete each task. You will be graded on the ap-plication of the modules’ topics, the completeness of your answers to the questions in the assignment notebook, and the clarity of your writing and code.

Assignment Description

The Data The given dataset contains information of Boston housing-prices. The dataset has 13 numeric/categorical predictive attributes. Median Value (attribute 14) is usually the target. You can know more about the dataset from https://scikit-learn.org/stable/datasets/index.html#toy-datasets.

The dataset can be loaded using the sklearn datasets module. You cam get the feature names from the provided link.

The Idea: Linear Regression on Boston House-Prices Dataset

Here, we want to predict the “Median value of owner-occupied homes”, which is the feature14. In this assignment, we will predict the target feature using all the other features. And then we will use single features to predict the target feature.

What to Do

First, load the dataset from sklearn dataset using the following code snippet.

To generate a linear regression model, you may use the linear_model.LinearRegression() func-tion available via the scikit-learn library. To run the model on the Boston data, first divide the dataset into training and testing sets(80 and 20 percent, respectively), then fit the model on the training set and predict with the fitted model on the testing set. scikit-learn provides several functions for dividing datasets in this manner, including cross_validation.KFold and cross_validation.train_test_split.

Several statistics can be generated from a linear model. Given a fitted linear model, the following code outputs the model coefficients (the parameter values for the fitted model), the residual sum of squares (the model error), and the explained variance or R square or Variance Score(the degree to which the model explains the variation present in the data):

You can use these scores to measure the efficacy of a particular linear model.

What to do

Step 1 Split the dataset into training and test sets (80, 20).

Step 2(a) Use all the features (1-13) to fit the linear regression model for feature 14 using the training set.

Step 2(b) Report the coefficients, mean squared error and variance score for the model on the test set.

Step 3(a) Use each feature alone - to fit a linear regression model on the training set.

Step 3(b) Report the coefficient, mean squared error and variance score for the model on the test set. Also report the thirteen plots of the linear regression models generated on each feature. Each plot should distinctly show the training points, test points and the linear regression line.

Step 4(a) Perform 10 iterations of (Step 1, Step 2(a), and Step 3(a)).

Step 4(b)

● During each iteration of Step4(a), gather the metrics - mean squared error and variance score for the 14 models on the test set.

● For each feature, compute the average, over the 10 iterations, of each evaluation metric. Do the same for the metrics corresponding to ’all features’.

● To compare the model performance, provide the following plots

1. mean square error vs features

2. variance score vs features

● In the above mentioned two plots, make sure to designate a point on the features axis for ’all 13 features’ so you can include the metrics corresponding to the models gener-ated in the 10 iterations of Step 2(a). E.g., You may designate it as feature 0.

What to Provide

Your output should contain the following:

● Report generated in Step 2(b)

● Thirteen sets of metrics and plots generated in Step 3(b)

● Two plots generated in Step 4(b)

● Given this output, respond to the following questions:

1. Based upon the linear models you generated, which feature appears to be most predictive for the target feature? Note that you can answer this question based upon the output provided for the linear models.

2. Suppose you need to select two features for a linear regression model to predict the target feature. Which two features would you select? Why?

3. Examine all the plots and numbers you have, do you have any comments on them? Do you find any surprising trends? Do you have any idea about what might be causing this surprising trend in the data? This is a descriptive question meant to encourage you to interpret your results and express yourself.