[Term Entry] Python statsmodels: OLS

content/python/concepts/statsmodels/terms/ols/ols.md

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+---
+Title: 'Ordinary Least Squares' 
+Description: 'Uses Ordinary Least Squares (OLS) to perform linear regression in order to reduce prediction errors and evaluate associations between variables.' 
+Subjects:
+  - 'Computer Science'
+  - 'Data Science'
+  - 'Data Visualization'
+  - 'Machine Learning'
+Tags:
+  - 'Data'
+  - 'Linear Regression'
+  - 'Machine Learning'
+CatalogContent: 
+  - 'learn-python-3'
+  - 'paths/data-science-foundations'
+---
+
+**Ordinary least squares** (OLS) is a statistical method that reduces the sum of squared residuals to assess the correlation between independent and dependent variables. In linear regression, it is widely used to predict values and analyze correlations between variables.  
+
+## Syntax
+
+Here's syntax to implement Ordinary Least Squares in Python:
+
+```pseudo
+
+import statsmodels.api as sm  # Import the statsmodels library
+
+# Add a constant to the independent variable(s) for the intercept
+X = sm.add_constant(X)  # Method to add a constant to X
+
+# Fit the OLS model
+model = sm.OLS(y, X).fit()  # `OLS` function applied to y (dependent variable) and X (independent variables)
+
+# Access the model summary
+model.summary()  # Method to get summary statistics
+```
+- `sm.add_constant(x)`: Adds an intercept (constant term) to the independent variables X.
+- `sm.OLS(y, X)`: Creates the OLS model with y as the dependent variable and X as the independent variables.
+- `model.summary()`: Displays the model's results, including coefficients and `R-squared`values.
+
+## Example
+
+Here's an example predicting `test_scores` based on `hours_studied`:
+
+```py
+import statsmodels.api as sm
+import matplotlib.pyplot as plt
+import numpy as np
+
+# Hours studied and corresponding test scores
+hours_studied = [1, 2, 3, 4, 5]  
+test_scores = [50, 55, 60, 65, 70]
+
+# Add a constant to the independent variable
+hours_with_constant = sm.add_constant(hours_studied)
+
+# Fit the OLS model
+model = sm.OLS(test_scores, hours_with_constant).fit()
+
+# Display the summary of the model
+print(model.summary())
+
+# Predict the test scores using OLS model
+predicted_scores = model.predict(hours_with_constant)
+
+# Plot the data and line
+plt.scatter(hours_studied, test_scores, color='blue', label='Observed data')
+plt.plot(hours_studied, predicted_scores, color='red', label='Fitted line')
+
+# Displaying the plot
+plt.xlabel('Hours Studied')
+plt.ylabel('Test Scores')
+plt.title('OLS Regression: Test Scores vs Hours Studied')
+plt.legend()
+
+# Show the plot
+plt.show()
+```
+[Regression plot](https://raw.githubusercontent.com/Codecademy/docs/main/media/ols-model-example.png)