CSC 4780/6780 Homework 06

Description

• What are we doing?

Often the data that we are given is not what we should feed into our model. So we might manufac-ture some new features from the data we have. And we might delete some irrelevant or redundant features. This is known as “Feature engineering” and “Feature selection”.

• Analyze the features

You are given data.csv which is, once again, real estate data that you will use to predict prices.

There are ve columns:

• property id Use this as the index of the dataframe.

• sqft hvac This is the square foot measurement of the interior of the house.

• lot width This is the width of the lot in feet.

• lot depth This is the depth of the lot in feet.

• age of roof This is the age of the roof in years.

• miles to school This is the number of miles to the nearest elementary school.

• price This is the price that the house sold for.

Create a program called analysis.py to do feature selection.

Speci cally, analysis.py should do the following:

• Read the csv into a dataframe.

• Get the input (X) and target (Y ) as numpy arrays.

• Use PolynomialFeatures to expand X into 2nd degree polynomials. (This will automatically add a column of 1s)

• Create a loop that:

{ Calculates the p-value of the Pearson correlation between each input and the current residual. (The rst time through the residual will just be Y .)

{ Sorts the inputs so that the p-values are in ascending order.

{ Add the input with the lowest p-value to the list of inputs you are going to actually use. { Do linear regression using that list of inputs.

{ Print the R² value.

{ Calculate a new residual.

• Finally, make two scatter plots:

{ ResidualMiles.png that compares the nal residual and the texttmiles to school { ResidualRoof.png which compares the residual and the age of roof

The output should look like this:

> python3 analysis.py data.csv

First time through: using original price data as the residual

“sqft_hvac” vs residual: p-value=0.0

“sqft_hvac^2” vs residual: p-value=0.0

“sqft_hvac lot_width” vs residual: p-value=0.0

“sqft_hvac lot_depth” vs residual: p-value=0.0

“sqft_hvac age_of_roof” vs residual: p-value=8.731082754175303e-55

“lot_width lot_depth” vs residual: p-value=4.1868028438284917e-41

“lot_depth^2” vs residual: p-value=1.1014229237235183e-34

“lot_depth” vs residual: p-value=1.349112505398765e-32

“lot_width^2” vs residual: p-value=5.993692365884732e-22

“lot_width” vs residual: p-value=7.502300252189193e-22

“sqft_hvac miles_to_school” vs residual: p-value=9.519591803622703e-21

“lot_depth age_of_roof” vs residual: p-value=9.568489304909097e-09

“miles_to_school” vs residual: p-value=6.314415223095078e-08

“miles_to_school^2” vs residual: p-value=4.169604800671784e-06

“lot_width miles_to_school” vs residual: p-value=3.3260830318919526e-05

“age_of_roof miles_to_school” vs residual: p-value=0.002206196824401264

“lot_width age_of_roof” vs residual: p-value=0.014189712836334

“age_of_roof” vs residual: p-value=0.2204854707886266

“age_of_roof^2” vs residual: p-value=0.37721705725549765

“lot_depth miles_to_school” vs residual: p-value=0.6902534566522582

**** Fitting with [“1” “sqft_hvac” ] ****

R2 = 0.8285362066724605

Residual is updated

“lot_width lot_depth” vs residual: p-value=4.63867435576096e-226

“lot_depth” vs residual: p-value=1.2511219230454328e-213

“lot_depth^2” vs residual: p-value=7.007419749277197e-210

“sqft_hvac lot_depth” vs residual: p-value=1.3573402394546474e-79

“miles_to_school” vs residual: p-value=1.143866412662615e-60

“lot_width miles_to_school” vs residual: p-value=3.1979675246627807e-48

“miles_to_school^2” vs residual: p-value=4.278477233456872e-46

“sqft_hvac miles_to_school” vs residual: p-value=2.2362041512664205e-42

“lot_depth age_of_roof” vs residual: p-value=5.324817730838837e-34

“lot_width^2” vs residual: p-value=1.6087269118146826e-30

“lot_width” vs residual: p-value=1.894797058154101e-30

“age_of_roof miles_to_school” vs residual: p-value=3.073565041879731e-21

“lot_width age_of_roof” vs residual: p-value=0.0024146107224859237

“sqft_hvac lot_width” vs residual: p-value=0.007708854025643736

“lot_depth miles_to_school” vs residual: p-value=0.012927560709559626

“age_of_roof” vs residual: p-value=0.1250566876903974

“sqft_hvac age_of_roof” vs residual: p-value=0.14177548490199277

“age_of_roof^2” vs residual: p-value=0.20592884268913036

“sqft_hvac^2” vs residual: p-value=0.955142095666689

“sqft_hvac” vs residual: p-value=1.0000000000004001

**** Fitting with [“1” “sqft_hvac” “lot_width lot_depth” ] ****

R2 = 0.9278909375846092

Residual is updated

Making scatter plot: age_of_roof vs final residual

Making a scatter plot: miles_from_school vs final residual

So, you will go through the loop twice to get an X with two columns of input (and a column of 1s).

• Make Predictions

Now stare at the two plots you made. Can you make a new variable that will let linear regression t better? (Keep reading; there is a heavy-handed hint in the next couple of paragraphs.)

Now, make another program: prediction.py. Using the list of features that you found in analysis.py, this program should read in the csv, manufacture the meaningful variables, and

remove the less useful ones. The X matrix should have three columns. (Or four if you have a column of 1s.)

Do not use sklearn.preprocessing.PolynomialFeatures or scipy.stats.pearsonr in prediction.py.

Use this 3-column X and Y to make a formula for prediction. The output should look like this:

• python3 prediction.py data.csv Making new features…

Using only the useful ones: [’sqft_hvac’, ’lot_size’, ’is_close_to_school’]…

R2 = 0.96941

*** Prediction ***

Price = $23,846.11 + (sqft x $119.01) + (lot_size x $11.01)

Less than 2 miles from a school? You get $49,300.87 added to the price!

• Criteria for success

If your name is Fred Jones, you will turn in a zip le called HW06 Jones Fred.zip of a directory called HW06 Jones Fred. It will contain:

• analysis.py

• prediction.py

• data.csv

• ResidualRoof.png

• ResidualMiles.png

Be sure to format your python code with black before you submit it.

We will run your code like this:

cd HW06_Jones_Fred

python3 analysis.py data.csv

python3 prediction.py data.csv

Do this work by yourself. Stackover ow is OK. A hint from another student is OK. Looking at another student’s code is not OK.

The template les for the python programs have import statements. Do not use any frameworks not in those import statements.

• Reading

You should have read through Chapter 10 : Preparing Data for Machine Learning: Feature Se-lection, Feature Engineering, and Dimensionality Reduction. (You can skip the dimensionality reduction for now { we will talk about that later.)

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