Predicting the Future¶
In this assignment, we'll attempt to make a prediction of a timeseries dataset using a linear prediction.
First, the code below will create a pandas dataframe of noisy timeseries data. To keep things simple, the x-axis won't actually be a datetime, but rather just a number starting at 0 and going to 100 (but we can imagine ways to convert datetime axis into numeric ones in the future).
Don't change this code but take a look at the dataframe to get familiar with it.
import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
from sklearn.linear_model import LinearRegression
# Set seed for reproducibility
np.random.seed(42)
# Generate a time series with a linear trend and some noise
x = np.arange(0, 100) # X-axis: 0 to 99
trend = 2 * x # Linear trend
noise = np.random.normal(0, 10, size=len(x)) # Random noise
data = trend + noise
# Create a DataFrame
df = pd.DataFrame({'Time': x, 'Value': data})
df.info()
<class 'pandas.core.frame.DataFrame'> RangeIndex: 100 entries, 0 to 99 Data columns (total 2 columns): # Column Non-Null Count Dtype --- ------ -------------- ----- 0 Time 100 non-null int64 1 Value 100 non-null float64 dtypes: float64(1), int64(1) memory usage: 1.7 KB
1. Visualize the Data¶
For this step, use matplotlib and seaborn to visualize the data.
Here's a reminder on how to do a line-plot using Seaborn.
Set x_col_name and y_col_name accordingly.
import seaborn as sns
import matplotlib.pyplot as plt
# Set the plot size and shape
plt.figure(figsize=(10, 6))
# Lineplot of col_name where x is the dataframe index
sns.lineplot(x=x_col_name,y=y_col_name, data=df)
import matplotlib.pyplot as plt
import seaborn as sns
plt.figure(figsize=(10,6))
sns.lineplot(x="Time", y="Value", data=df)
<Axes: xlabel='Time', ylabel='Value'>
2. Fit a Linear Regression¶
Refresher¶
A Linear Regression is a method to calculate the line for a sample of data-points.
To do this:
The slope $b_1$ is calculated using the formula: $$ b_1 = \frac{\sum{(X - \bar{X})(Y - \bar{Y})}}{\sum{(X - \bar{X})^2}} $$
The intercept $b_0$ is calculated using the formula: $$ b_0 = \bar{Y} - b_1 \bar{X} $$
The linear regression equation $Y$ is given by: $$ Y = b_0 + b_1X $$
From there, we would use these $b_0$ and $b_1$ values to calculate new values in the future.
However, the sklearn python package can do this for us using the LinearRegression model.
Use the code below to generate a forecast_df.
from sklearn.linear_model import LinearRegression
# Prepare the data for linear regression
X = df[['Time']]
y = df['Value']
# Fit the linear regression model
model = LinearRegression()
model.fit(X, y)
# Generate future values
future_steps = 20
future_X = pd.DataFrame({'Time': range(100, 100 + future_steps)})
# Predict future values
future_y = model.predict(future_X)
# Create a DataFrame for the forecast
forecast_df = future_X
forecast_df['Value'] = future_y
As you do, inspect each line and try to guess what's happening here. This is your first Machine Learning code.
from sklearn.linear_model import LinearRegression
# Prepare the data for linear regression
X = df[['Time']]
y = df['Value']
# Fit the linear regression model
model = LinearRegression()
model.fit(X, y)
# Generate future values
future_steps = 100
future_X = pd.DataFrame({'Time': range(0, 100 + future_steps)})
# Predict future values
future_y = model.predict(future_X)
# Create a DataFrame for the forecast
forecast_df = future_X
forecast_df['Value'] = future_y
- Plot the Results
Finally, plot the results. To do this, plot both the original df and the new forcast_df. Use seaborn's sns.lineplot method but pass a color=red to the forcast so that it looks different.
Here's an example of calling sns.lineplot.
import seaborn as sns
sns.lineplot(data=..., x=..., y=..., label=..., color=...)
import seaborn as sns
sns.lineplot(data=df, x="Time", y="Value", label="past", color="Blue")
sns.lineplot(data=forecast_df, x="Time", y="Value", label="forecast", color="Red")
<Axes: xlabel='Time', ylabel='Value'>
