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update class 10 notebook and script
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@justmarkham
justmarkham committed Sep 18, 2015
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111 changes: 43 additions & 68 deletions code/10_linear_regression_nb.py
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#
# We'll be working with a dataset from Capital Bikeshare that was used in a Kaggle competition ([data dictionary](https://www.kaggle.com/c/bike-sharing-demand/data)).

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# read the data and set the datetime as the index
import pandas as pd
url = 'https://raw.githubusercontent.com/justmarkham/DAT8/master/data/bikeshare.csv'
bikes = pd.read_csv(url, index_col='datetime', parse_dates=True)


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bikes.head()

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# - What is the response variable (as defined by Kaggle)?
# - How many features are there?

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# "count" is a method, so it's best to name that column something else
bikes.rename(columns={'count':'total'}, inplace=True)


# ## Visualizing the data

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import seaborn as sns
import matplotlib.pyplot as plt
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plt.rcParams['font.size'] = 14


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# Pandas scatter plot
bikes.plot(kind='scatter', x='temp', y='total', alpha=0.2)


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# Seaborn scatter plot with regression line
sns.lmplot(x='temp', y='total', data=bikes, aspect=1.5, scatter_kws={'alpha':0.2})
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# ## Building a linear regression model

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# create X and y
feature_cols = ['temp']
X = bikes[feature_cols]
y = bikes.total


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# import, instantiate, fit
from sklearn.linear_model import LinearRegression
linreg = LinearRegression()
linreg.fit(X, y)


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# print the coefficients
print linreg.intercept_
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#
# How many bike rentals would we predict if the temperature was 25 degrees Celsius?

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# manually calculate the prediction
linreg.intercept_ + linreg.coef_*25


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# use the predict method
linreg.predict(25)
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#
# Let's say that temperature was measured in Fahrenheit, rather than Celsius. How would that affect the model?

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# create a new column for Fahrenheit temperature
bikes['temp_F'] = bikes.temp * 1.8 + 32
bikes.head()


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# Seaborn scatter plot with regression line
sns.lmplot(x='temp_F', y='total', data=bikes, aspect=1.5, scatter_kws={'alpha':0.2})


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# create X and y
feature_cols = ['temp_F']
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print linreg.coef_


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# convert 25 degrees Celsius to Fahrenheit
25 * 1.8 + 32


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# predict rentals for 77 degrees Fahrenheit
linreg.predict(77)


# **Conclusion:** The scale of the features is **irrelevant** for linear regression models. When changing the scale, we simply change our **interpretation** of the coefficients.

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# remove the temp_F column
bikes.drop('temp_F', axis=1, inplace=True)


# ## Visualizing the data (part 2)

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# explore more features
feature_cols = ['temp', 'season', 'weather', 'humidity']


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# multiple scatter plots in Seaborn
sns.pairplot(bikes, x_vars=feature_cols, y_vars='total', kind='reg')


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# multiple scatter plots in Pandas
fig, axs = plt.subplots(1, len(feature_cols), sharey=True)
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# Are you seeing anything that you did not expect?

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# cross-tabulation of season and month
pd.crosstab(bikes.season, bikes.index.month)


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# box plot of rentals, grouped by season
bikes.boxplot(column='total', by='season')
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# - A line can't capture a non-linear relationship.
# - There are more rentals in winter than in spring (?)

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# line plot of rentals
bikes.total.plot()
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#
# There are more rentals in the winter than the spring, but only because the system is experiencing **overall growth** and the winter months happen to come after the spring months.

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# correlation matrix (ranges from 1 to -1)
bikes.corr()


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# visualize correlation matrix in Seaborn using a heatmap
sns.heatmap(bikes.corr())
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# ## Adding more features to the model

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# create a list of features
feature_cols = ['temp', 'season', 'weather', 'humidity']


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# create X and y
X = bikes[feature_cols]
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print linreg.coef_


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# pair the feature names with the coefficients
zip(feature_cols, linreg.coef_)
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#
# $$\sqrt{\frac 1n\sum_{i=1}^n(y_i-\hat{y}_i)^2}$$

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# example true and predicted response values
true = [10, 7, 5, 5]
pred = [8, 6, 5, 10]


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# calculate these metrics by hand!
from sklearn import metrics
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#
# Here's an additional example, to demonstrate how MSE/RMSE punish larger errors:

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# same true values as above
true = [10, 7, 5, 5]
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# ## Comparing models with train/test split and RMSE

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from sklearn.cross_validation import train_test_split

Expand All @@ -405,23 +405,25 @@ def train_test_rmse(feature_cols):
return np.sqrt(metrics.mean_squared_error(y_test, y_pred))


# In[ ]:
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# compare different sets of features
print train_test_rmse(['temp', 'season', 'weather', 'humidity'])
print train_test_rmse(['temp', 'season', 'weather'])
print train_test_rmse(['temp', 'season', 'humidity'])


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# using these as features is not allowed!
print train_test_rmse(['casual', 'registered'])


# ## Comparing testing RMSE with null RMSE
#
# Null RMSE is the RMSE that could be achieved by **always predicting the mean response value**. It is a benchmark against which you may want to measure your regression model.

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# split X and y into training and testing sets
X_train, X_test, y_train, y_test = train_test_split(X, y, random_state=123)
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y_null


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# compute null RMSE
np.sqrt(metrics.mean_squared_error(y_test, y_null))
Expand All @@ -454,7 +456,7 @@ def train_test_rmse(feature_cols):
#
# For season, we can't simply leave the encoding as 1 = spring, 2 = summer, 3 = fall, and 4 = winter, because that would imply an **ordered relationship**. Instead, we create **multiple dummy variables:**

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# create dummy variables
season_dummies = pd.get_dummies(bikes.season, prefix='season')
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#
# Why? Because three dummies captures all of the "information" about the season feature, and implicitly defines spring (season 1) as the **baseline level:**

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# drop the first column
season_dummies.drop(season_dummies.columns[0], axis=1, inplace=True)
Expand All @@ -480,7 +482,7 @@ def train_test_rmse(feature_cols):
#
# If that's confusing, think about why we only need one dummy variable for holiday, not two dummy variables (holiday_yes and holiday_no).

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# concatenate the original DataFrame and the dummy DataFrame (axis=0 means rows, axis=1 means columns)
bikes = pd.concat([bikes, season_dummies], axis=1)
Expand All @@ -489,7 +491,7 @@ def train_test_rmse(feature_cols):
bikes.sample(n=5, random_state=1)


# In[ ]:
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# include dummy variables for season in the model
feature_cols = ['temp', 'season_2', 'season_3', 'season_4', 'humidity']
Expand All @@ -512,7 +514,7 @@ def train_test_rmse(feature_cols):
#
# **Important:** Dummy encoding is relevant for all machine learning models, not just linear regression models.

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# compare original season variable with dummy variables
print train_test_rmse(['temp', 'season', 'humidity'])
Expand All @@ -529,33 +531,6 @@ def train_test_rmse(feature_cols):
#
# Then, try using each of the three features (on its own) with `train_test_rmse` to see which one performs the best!

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# hour as a numeric feature
bikes['hour'] = bikes.index.hour


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# hour as a categorical feature
hour_dummies = pd.get_dummies(bikes.hour, prefix='hour')
hour_dummies.drop(hour_dummies.columns[0], axis=1, inplace=True)
bikes = pd.concat([bikes, hour_dummies], axis=1)


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# daytime as a categorical feature
bikes['daytime'] = ((bikes.hour > 6) & (bikes.hour < 21)).astype(int)


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print train_test_rmse(['hour'])
print train_test_rmse(bikes.columns[bikes.columns.str.startswith('hour_')])
print train_test_rmse(['daytime'])


# ## Comparing linear regression with other models
#
# Advantages of linear regression:
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