Fire up graphlab create

In [20]:
import graphlab

Load some house sales data

Dataset is from house sales in King County, the region where the city of Seattle, WA is located.

In [22]:
sales = graphlab.SFrame('home_data.gl/')
In [23]:
sales
Out[23]:
id date price bedrooms bathrooms sqft_living sqft_lot floors waterfront
7129300520 2014-10-13 00:00:00+00:00 221900 3 1 1180 5650 1 0
6414100192 2014-12-09 00:00:00+00:00 538000 3 2.25 2570 7242 2 0
5631500400 2015-02-25 00:00:00+00:00 180000 2 1 770 10000 1 0
2487200875 2014-12-09 00:00:00+00:00 604000 4 3 1960 5000 1 0
1954400510 2015-02-18 00:00:00+00:00 510000 3 2 1680 8080 1 0
7237550310 2014-05-12 00:00:00+00:00 1225000 4 4.5 5420 101930 1 0
1321400060 2014-06-27 00:00:00+00:00 257500 3 2.25 1715 6819 2 0
2008000270 2015-01-15 00:00:00+00:00 291850 3 1.5 1060 9711 1 0
2414600126 2015-04-15 00:00:00+00:00 229500 3 1 1780 7470 1 0
3793500160 2015-03-12 00:00:00+00:00 323000 3 2.5 1890 6560 2 0
view condition grade sqft_above sqft_basement yr_built yr_renovated zipcode lat
0 3 7 1180 0 1955 0 98178 47.51123398
0 3 7 2170 400 1951 1991 98125 47.72102274
0 3 6 770 0 1933 0 98028 47.73792661
0 5 7 1050 910 1965 0 98136 47.52082
0 3 8 1680 0 1987 0 98074 47.61681228
0 3 11 3890 1530 2001 0 98053 47.65611835
0 3 7 1715 0 1995 0 98003 47.30972002
0 3 7 1060 0 1963 0 98198 47.40949984
0 3 7 1050 730 1960 0 98146 47.51229381
0 3 7 1890 0 2003 0 98038 47.36840673
long sqft_living15 sqft_lot15
-122.25677536 1340.0 5650.0
-122.3188624 1690.0 7639.0
-122.23319601 2720.0 8062.0
-122.39318505 1360.0 5000.0
-122.04490059 1800.0 7503.0
-122.00528655 4760.0 101930.0
-122.32704857 2238.0 6819.0
-122.31457273 1650.0 9711.0
-122.33659507 1780.0 8113.0
-122.0308176 2390.0 7570.0
[21613 rows x 21 columns]
Note: Only the head of the SFrame is printed.
You can use print_rows(num_rows=m, num_columns=n) to print more rows and columns.

Exploring the data for housing sales

The house price is correlated with the number of square feet of living space.

In [24]:
graphlab.canvas.set_target('ipynb')
sales.show(view="Scatter Plot", x="sqft_living", y="price")

Create a simple regression model of sqft_living to price

Split data into training and testing.
We use seed=0 so that everyone running this notebook gets the same results. In practice, you may set a random seed (or let GraphLab Create pick a random seed for you).

In [25]:
train_data,test_data = sales.random_split(.8,seed=0)

Build the regression model using only sqft_living as a feature

In [26]:
sqft_model = graphlab.linear_regression.create(train_data, target='price', features=['sqft_living'],validation_set=None)
Linear regression:
--------------------------------------------------------
Number of examples          : 17384
Number of features          : 1
Number of unpacked features : 1
Number of coefficients    : 2
Starting Newton Method
--------------------------------------------------------
+-----------+----------+--------------+--------------------+---------------+
| Iteration | Passes   | Elapsed Time | Training-max_error | Training-rmse |
+-----------+----------+--------------+--------------------+---------------+
| 1         | 2        | 0.011499     | 4349521.926170     | 262943.613754 |
+-----------+----------+--------------+--------------------+---------------+
SUCCESS: Optimal solution found.

Evaluate the simple model

In [27]:
print test_data['price'].mean()
543054.042563
In [28]:
print sqft_model.evaluate(test_data)
{'max_error': 4143550.8825285956, 'rmse': 255191.0287052738}

RMSE of about \$255,170!

Let's show what our predictions look like

Matplotlib is a Python plotting library that is also useful for plotting. You can install it with:

'pip install matplotlib'

In [29]:
import matplotlib.pyplot as plt
%matplotlib inline
In [30]:
plt.plot(test_data['sqft_living'],test_data['price'],'.',
        test_data['sqft_living'],sqft_model.predict(test_data),'-')
Out[30]:
[<matplotlib.lines.Line2D at 0x7fdaa66930d0>,
 <matplotlib.lines.Line2D at 0x7fdaa6693190>]

Above: blue dots are original data, green line is the prediction from the simple regression.

Below: we can view the learned regression coefficients.

In [31]:
sqft_model.get('coefficients')
Out[31]:
name index value stderr
(intercept) None -47114.0206702 4923.34437753
sqft_living None 281.957850166 2.16405465323
[2 rows x 4 columns]

Explore other features in the data

To build a more elaborate model, we will explore using more features.

In [32]:
my_features = ['bedrooms', 'bathrooms', 'sqft_living', 'sqft_lot', 'floors', 'zipcode']
In [33]:
sales[my_features].show()
In [57]:
sales.show(view='BoxWhisker Plot', x='zipcode', y='price')

Pull the bar at the bottom to view more of the data.

98039 is the most expensive zip code.

Build a regression model with more features

In [64]:
zip = '98039'
houseinZip = sales[(sales['zipcode']==zip)]
houseinZip['price'].mean()
Out[64]:
2160606.6000000006
In [74]:
livingbetween = sales[(sales['sqft_living'] <= 4000) & (sales['sqft_living'] >= 2000)]
print 9221/float(21613)
0.426641373248
In [35]:
my_features_model = graphlab.linear_regression.create(train_data,target='price',features=my_features,validation_set=None)
Linear regression:
--------------------------------------------------------
Number of examples          : 17384
Number of features          : 6
Number of unpacked features : 6
Number of coefficients    : 115
Starting Newton Method
--------------------------------------------------------
+-----------+----------+--------------+--------------------+---------------+
| Iteration | Passes   | Elapsed Time | Training-max_error | Training-rmse |
+-----------+----------+--------------+--------------------+---------------+
| 1         | 2        | 0.049763     | 3763208.270524     | 181908.848367 |
+-----------+----------+--------------+--------------------+---------------+
SUCCESS: Optimal solution found.

In [36]:
print my_features
['bedrooms', 'bathrooms', 'sqft_living', 'sqft_lot', 'floors', 'zipcode']

Comparing the results of the simple model with adding more features

In [37]:
print sqft_model.evaluate(test_data)
print my_features_model.evaluate(test_data)
{'max_error': 4143550.8825285956, 'rmse': 255191.0287052738}
{'max_error': 3486584.5093818563, 'rmse': 179542.4333126908}

The RMSE goes down from \$255,170 to \$179,508 with more features.

Apply learned models to predict prices of 3 houses

The first house we will use is considered an "average" house in Seattle.

In [38]:
house1 = sales[sales['id']=='5309101200']
In [39]:
house1
Out[39]:
id date price bedrooms bathrooms sqft_living sqft_lot floors waterfront
5309101200 2014-06-05 00:00:00+00:00 620000 4 2.25 2400 5350 1.5 0
view condition grade sqft_above sqft_basement yr_built yr_renovated zipcode lat
0 4 7 1460 940 1929 0 98117 47.67632376
long sqft_living15 sqft_lot15
-122.37010126 1250.0 4880.0
[? rows x 21 columns]
Note: Only the head of the SFrame is printed. This SFrame is lazily evaluated.
You can use sf.materialize() to force materialization.

In [40]:
print house1['price']
[620000, ... ]
In [41]:
print sqft_model.predict(house1)
[629584.8197281545]
In [42]:
print my_features_model.predict(house1)
[721918.9333272739]

In this case, the model with more features provides a worse prediction than the simpler model with only 1 feature. However, on average, the model with more features is better.

Prediction for a second, fancier house

We will now examine the predictions for a fancier house.

In [43]:
house2 = sales[sales['id']=='1925069082']
In [44]:
house2
Out[44]:
id date price bedrooms bathrooms sqft_living sqft_lot floors waterfront
1925069082 2015-05-11 00:00:00+00:00 2200000 5 4.25 4640 22703 2 1
view condition grade sqft_above sqft_basement yr_built yr_renovated zipcode lat
4 5 8 2860 1780 1952 0 98052 47.63925783
long sqft_living15 sqft_lot15
-122.09722322 3140.0 14200.0
[? rows x 21 columns]
Note: Only the head of the SFrame is printed. This SFrame is lazily evaluated.
You can use sf.materialize() to force materialization.

In [45]:
print sqft_model.predict(house2)
[1261170.4040999676]
In [46]:
print my_features_model.predict(house2)
[1446472.4690775052]

In this case, the model with more features provides a better prediction. This behavior is expected here, because this house is more differentiated by features that go beyond its square feet of living space, especially the fact that it's a waterfront house.

Last house, super fancy

Our last house is a very large one owned by a famous Seattleite.

In [47]:
bill_gates = {'bedrooms':[8], 
              'bathrooms':[25], 
              'sqft_living':[50000], 
              'sqft_lot':[225000],
              'floors':[4], 
              'zipcode':['98039'], 
              'condition':[10], 
              'grade':[10],
              'waterfront':[1],
              'view':[4],
              'sqft_above':[37500],
              'sqft_basement':[12500],
              'yr_built':[1994],
              'yr_renovated':[2010],
              'lat':[47.627606],
              'long':[-122.242054],
              'sqft_living15':[5000],
              'sqft_lot15':[40000]}

In [48]:
print my_features_model.predict(graphlab.SFrame(bill_gates))
[13749825.525718132]

The model predicts a price of over $13M for this house! But we expect the house to cost much more. (There are very few samples in the dataset of houses that are this fancy, so we don't expect the model to capture a perfect prediction here.)

In [50]:
advanced_features = [
'bedrooms', 'bathrooms', 'sqft_living', 'sqft_lot', 'floors', 'zipcode',
'condition', # condition of house				
'grade', # measure of quality of construction				
'waterfront', # waterfront property				
'view', # type of view				
'sqft_above', # square feet above ground				
'sqft_basement', # square feet in basement				
'yr_built', # the year built				
'yr_renovated', # the year renovated				
'lat', 'long', # the lat-long of the parcel				
'sqft_living15', # average sq.ft. of 15 nearest neighbors 				
'sqft_lot15'# average lot size of 15 nearest neighbors 
]
In [51]:
advanced_features_model = graphlab.linear_regression.create(train_data,target='price',features=advanced_features,validation_set=None)
Linear regression:
--------------------------------------------------------
Number of examples          : 17384
Number of features          : 18
Number of unpacked features : 18
Number of coefficients    : 127
Starting Newton Method
--------------------------------------------------------
+-----------+----------+--------------+--------------------+---------------+
| Iteration | Passes   | Elapsed Time | Training-max_error | Training-rmse |
+-----------+----------+--------------+--------------------+---------------+
| 1         | 2        | 0.110006     | 3469012.450487     | 154580.940732 |
| 2         | 3        | 0.177104     | 3469012.450673     | 154580.940735 |
+-----------+----------+--------------+--------------------+---------------+
SUCCESS: Optimal solution found.

In [52]:
print advanced_features_model.evaluate(test_data)
{'max_error': 3556849.4138490623, 'rmse': 156831.11680200786}

The RMSE goes down from \$255,170 to \$179,508 and now to \$156,831 with more features.

What is the difference in RMSE between the model trained with my_features and the one trained with advanced_features? Save this result to answer the quiz at the end.

In [56]:
156831 - 179508
Out[56]:
-22677
In [ ]: