below is an overview of process

Copy_of_polynomial_regression.pdf

1. Training the Linear Regression Model

from sklearn.linear_model import LinearRegression
lin_reg = LinearRegression()
lin_reg.fit(X, y)

• Importing the Linear Regression Model: The LinearRegression class from Scikit-Learn is imported to create a linear regression model.
• Creating and Training the Model: An instance of LinearRegression is created and trained using the fit method on the original feature matrix X and target values y. This model learns the linear relationship between features and the target variable.

2. Training the Polynomial Regression Model

from sklearn.preprocessing import PolynomialFeatures
poly_reg = PolynomialFeatures(degree = 4)
X_poly = poly_reg.fit_transform(X)
lin_reg_2 = LinearRegression()
lin_reg_2.fit(X_poly, y)

• Importing Polynomial Features: The PolynomialFeatures class is imported to generate polynomial terms from the original features.
• Creating Polynomial Features: An instance of PolynomialFeatures with degree = 4 is created. This transforms the original feature matrix X into a new matrix X_poly that includes polynomial terms up to the 4th degree.
• Training the Polynomial Regression Model: A new LinearRegression model (lin_reg_2) is created and trained using the polynomial feature matrix X_poly and target values y. This model learns the relationship considering the polynomial terms.

3. Visualising the Linear Regression Results

plt.scatter(X, y, color = 'red')
plt.plot(X, lin_reg.predict(X), color = 'blue')
plt.title('Polynomial')
plt.xlabel('Truth or Bluff (Linear Regression)')
plt.ylabel('Salary')
plt.show()

• Plotting the Linear Regression:
  • plt.scatter creates a scatter plot of the original data points (features vs. target values) in red.
  • plt.plot overlays a line representing the predictions from the linear regression model (lin_reg). This line is drawn using the original feature values X and their corresponding predictions.
  • The title and labels are set, and the plot is displayed with plt.show().

4. Visualising the Polynomial Regression Results

plt.scatter(X, y, color = 'red')
plt.plot(X, lin_reg_2.predict(X_poly), color = 'blue')
plt.title('Polynomial')
plt.xlabel('Position level')
plt.ylabel('Salary')
plt.show()

• Plotting the Polynomial Regression:
  • plt.scatter again creates a scatter plot of the original data points.
  • plt.plot overlays a curve representing the predictions from the polynomial regression model (lin_reg_2). This uses X_poly to generate predictions, fitting a smooth curve.
  • The title and labels are set, and the plot is displayed.

5. Visualising the Polynomial Regression Results (Higher Resolution and Smoother Curve)

X_grid = np.arange(min(X), max(X), 0.1)
X_grid = X_grid.reshape((len(X_grid), 1))
plt.scatter(X, y, color = 'red')
plt.plot(X_grid, lin_reg_2.predict(poly_reg.fit_transform(X_grid)), color = 'blue')
plt.title('Polynomial')
plt.xlabel('Position level')
plt.ylabel('Salary')
plt.show()