Predicting House Prices¶
Your neighbor is a real estate agent and wants some help predicting housing prices for regions in the USA. It would be great if you could somehow create a model for her that allows her to put in a few features of a house and returns back an estimate of what the house would sell for.
She has asked you if you could help her out with your new data science skills. You say yes, and decide that Linear Regression might be a good path to solve this problem!
Your neighbor then gives you some information about a bunch of houses in regions of the United States,it is all in the data set: USA_Housing.csv.
The data contains the following columns:
- 'Avg. Area Income': Avg. Income of residents of the city house is located in.
- 'Avg. Area House Age': Avg Age of Houses in same city
- 'Avg. Area Number of Rooms': Avg Number of Rooms for Houses in same city
- 'Avg. Area Number of Bedrooms': Avg Number of Bedrooms for Houses in same city
- 'Area Population': Population of city house is located in
- 'Price': Price that the house sold at
- 'Address': Address for the house
Import Libraries¶
import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
import seaborn as sns
%matplotlib inline
sns.set_style("darkgrid")
Checking out the data¶
USAHousing = pd.read_csv('USA_Housing.csv')
USAHousing.head()
USAHousing.info()
USAHousing.describe()
USAHousing.columns
EDA¶
sns.pairplot(USAHousing)
sns.distplot(USAHousing['Price'])
sns.heatmap(USAHousing.corr())
Training Linear Regression Model¶
Let's now begin to train out regression model! We will need to first split up our data into an X array that contains the features to train on, and a y array with the target variable, in this case the Price column. We will toss out the Address column because it only has text info that the linear regression model can't use.
X and y arrays¶
X = USAHousing[['Avg. Area Income', 'Avg. Area House Age', 'Avg. Area Number of Rooms', 'Avg. Area Number of Bedrooms',
'Area Population']]
y = USAHousing['Price']
Train Test Split¶
Now let's split the data into a training set and a testing set. We will train out model on the training set and then use the test set to evaluate the model.
from sklearn.model_selection import train_test_split
X_train, X_test, y_train, y_test = train_test_split(X, y , test_size = 0.4, random_state = 101)
Creating and Training Model¶
from sklearn.linear_model import LinearRegression
lm = LinearRegression()
lm.fit(X_train, y_train)
Model Evaluation¶
Let's evaluate the model by checking out it's coefficients and how we can interpret them.
# print the intercept
print(lm.intercept_)
coeff_df = pd.DataFrame(lm.coef_,X.columns, columns=["Coefficient"])
coeff_df
Interpreting the coefficients:
- Holding all other features fixed, a 1 unit increase in Avg. Area Income is associated with an increase of \$21.52 .
- Holding all other features fixed, a 1 unit increase in Avg. Area House Age is associated with an increase of \$164883.28 .
- Holding all other features fixed, a 1 unit increase in Avg. Area Number of Rooms is associated with an increase of \$122368.67 .
- Holding all other features fixed, a 1 unit increase in Avg. Area Number of Bedrooms is associated with an increase of \$2233.80 .
- Holding all other features fixed, a 1 unit increase in Area Population is associated with an increase of \$15.15 .
Predictions from our model¶
Let's grab predictions off our test set and see how well it did!
predictions = lm.predict(X_test)
plt.scatter(y_test, predictions,edgecolors= 'darkblue')
Residual Histogram¶
sns.distplot((y_test-predictions),bins = 50)
Regression Evaluation Metrics¶
Here are three common evaluation metrics for regression problems:
Mean Absolute Error (MAE) is the mean of the absolute value of the errors:
$$\frac 1n\sum_{i=1}^n|y_i-\hat{y}_i|$$Mean Squared Error (MSE) is the mean of the squared errors:
$$\frac 1n\sum_{i=1}^n(y_i-\hat{y}_i)^2$$Root Mean Squared Error (RMSE) is the square root of the mean of the squared errors:
$$\sqrt{\frac 1n\sum_{i=1}^n(y_i-\hat{y}_i)^2}$$Comparing these metrics:
- MAE is the easiest to understand, because it's the average error.
- MSE is more popular than MAE, because MSE "punishes" larger errors, which tends to be useful in the real world.
- RMSE is even more popular than MSE, because RMSE is interpretable in the "y" units.
All of these are loss functions, because we want to minimize them.
from sklearn import metrics
print('MAE :',metrics.mean_absolute_error(y_test,predictions))
print('MSE :',metrics.mean_squared_error(y_test,predictions))
print('RMSE :',np.sqrt(metrics.mean_squared_error(y_test,predictions)))