Polynomial Regression

Polynomial Regression is a type of linear regression where the connection between the input variable (x) and the output variable (y) is shown using a polynomial equation of degree n. It works well when the data shows a curved pattern, letting the model create a curve that fits the data points closely.

Polynomial regression is used when the connection between the input and output isn't straight or linear. Instead of drawing a straight line like in linear regression, it uses a curved line made from a polynomial equation to better match shape of the data better.

USE CASE 1: Using Polynomial Regression with scikit-learn, predict the product price. The Production cost, Advertising spend, and Demand level are the independent variables.

import pandas as pd
from sklearn.linear_model import LinearRegression
from sklearn.model_selection import train_test_split
from sklearn.metrics import r2_score, mean_absolute_error, mean_squared_error

# -----------------------------------
# 1. Load data from Excel
# -----------------------------------
data = pd.read_excel("product_data.xlsx")

print("Dataset Preview:")
print(data.head())

# -----------------------------------
# 2. Define features and target
# -----------------------------------
X = data[['Production_Cost', 'Advertising_Spend', 'Demand_Level']]
y = data['Product_Price']

# -----------------------------------
# 3. Split into training and testing
# -----------------------------------
X_train, X_test, y_train, y_test = train_test_split(
    X, y, test_size=0.25, random_state=42
)

# -----------------------------------
# 4. Train the Linear Regression model
# -----------------------------------
model = LinearRegression()
model.fit(X_train, y_train)

# -----------------------------------
# 5. Model parameters
# -----------------------------------
print("\nIntercept:", model.intercept_)
print("Coefficients:")
for feature, coef in zip(X.columns, model.coef_):
    print(f"  {feature}: {coef}")

# -----------------------------------
# 6. Evaluate the model
# -----------------------------------
y_pred = model.predict(X_test)

r2 = r2_score(y_test, y_pred)
mae = mean_absolute_error(y_test, y_pred)
mse = mean_squared_error(y_test, y_pred)

print("\nModel Evaluation:")
print("R² Score:", r2)
print("Mean Absolute Error:", mae)
print("Mean Squared Error:", mse)

# -----------------------------------
# 7. Predict price for a new product
# -----------------------------------
new_product = pd.DataFrame({
    'Production_Cost': [68],
    'Advertising_Spend': [13],
    'Demand_Level': [37]
})

predicted_price = model.predict(new_product)

print("\nPredicted Product Price:", predicted_price[0])

import numpy as np
from sklearn.model_selection import train_test_split
from sklearn.linear_model import LinearRegression
from sklearn.metrics import mean_squared_error, r2_score

# -----------------------------------
# 1. Load data from Excel
# -----------------------------------
#sample data can be exported to 
#excel from the URL
# https://pythonPlaza.com/linear_school_grade_data.html

data = pd.read_excel("student_data.xlsx")

print("Dataset Preview:")
print(data.head())

# -----------------------------------
# 2. Define features and target
# -----------------------------------
X = data[['Hours_Studied', 'Attendance_%', 'Previous_Score']]
y = data['Final_Grade']

# -----------------------------------
# 3. Split into training and testing
# -----------------------------------
X_train, X_test, y_train, y_test = train_test_split(
    X, y, test_size=0.25, random_state=42
)

# -----------------------------------
# 4. Train the Linear Regression model
# -----------------------------------
model = LinearRegression()
model.fit(X_train, y_train)


# -----------------------------
# Predictions
y_pred = model.predict(X_test)

# -----------------------------
# Evaluation
print("Predicted grades:", y_pred)
print("Actual grades:   ", y_test)

print("\nMean Squared Error:", mean_squared_error(y_test, y_pred))
print("R² Score:", r2_score(y_test, y_pred))


Example: Predict a new student’s grade
# New student: [hours_studied, attendance %, previous_score]
new_student = np.array([[6, 85, 78]])

predicted_grade = model.predict(new_student)
print("Predicted final grade:", predicted_grade[0])

import numpy as np
from sklearn.model_selection import train_test_split
from sklearn.linear_model import LinearRegression
from sklearn.metrics import mean_squared_error, r2_score

# -----------------------------------
# 1. Load data from Excel
# -----------------------------------
#sample data can be exported to 
#excel from the URL

  
  Get the Profit Optimization data in Excel
  

data = pd.read_excel("profit_optimization.xlsx")

print("Dataset Preview:")
print(data.head())

# -----------------------------------
# 2. Define features and target  Price (P)	
# -----------------------------------
X = data[['Price', 'Advertising', 'Units_Sold']]
y = data['Profit']

# -----------------------------------
# 3. Split into training and testing
# -----------------------------------
X_train, X_test, y_train, y_test = train_test_split(
    X, y, test_size=0.25, random_state=42
)

# -----------------------------------
# 4. Train the Linear Regression model
# -----------------------------------
model = LinearRegression()
model.fit(X_train, y_train)


#Predict profit
y_pred = model.predict(X_test)

print("Predicted profit:", y_pred)
print("Actual profit:   ", y_test)

#Evaluate the model
print("\nMean Squared Error:", mean_squared_error(y_test, y_pred))
print("R² Score:", r2_score(y_test, y_pred))

#Profit equation (key for optimization)
print("Intercept:", model.intercept_)
print("Coefficients [Price, Advertising, Units Sold]:", model.coef_)


#Predict profit for a new business strategy
# Example: Price = 15, Advertising = 165, Units Sold = 460
new_strategy = np.array([[15, 165, 460]])

predicted_profit = model.predict(new_strategy)
print("Predicted profit:", predicted_profit[0])

import numpy as np
from sklearn.model_selection import train_test_split
from sklearn.linear_model import LinearRegression
from sklearn.metrics import mean_squared_error, r2_score

# -----------------------------------
# 1. Load data from Excel
# -----------------------------------
#sample data can be exported to 
#excel from the URL

  
  Get the Patient Response Data in Excel
  

data = pd.read_excel("patient_dosage_response.xlsx")

print("Dataset Preview:")
print(data.head())

# -----------------------------------
# 2. Define features and target  Price (P)	
# -----------------------------------
X = data[['Dosage', 'Age', 'Weight']]
y = data['Patient_Response']

# -----------------------------------
# 3. Split into training and testing
# -----------------------------------
X_train, X_test, y_train, y_test = train_test_split(
    X, y, test_size=0.25, random_state=42
)

# -----------------------------------
# 4. Train the Linear Regression model
# -----------------------------------
model = LinearRegression()
model.fit(X_train, y_train)


#Predict profit
y_pred = model.predict(X_test)

print("Predicted responses:", y_pred)
print("Actual responses:   ", y_test)

#Evaluate the model
print("\nMean Squared Error:", mean_squared_error(y_test, y_pred))
print("R² Score:", r2_score(y_test, y_pred))

#Profit equation (key for optimization)
print("Intercept:", model.intercept_)
print("Coefficients [Dosage, Age, Weight]:", model.coef_)


Predict response for a new patient
# New patient: Dosage=72mg, Age=36yrs, Weight=172lbs
new_patient = np.array([[72, 36, 172]])

predicted_response = model.predict(new_patient)
print("Predicted patient response:", predicted_response[0])