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Data Analyst Guide: Mastering Linear Regression Assumptions Every Analyst Must Know

Data Analyst Guide: Mastering Linear Regression Assumptions Every Analyst Must Know

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Business Problem Statement

In the retail industry, predicting sales is crucial for businesses to make informed decisions about inventory management, pricing, and marketing strategies. A company like Walmart wants to predict the sales of a new product based on factors like advertising spend, seasonality, and competitor pricing. The goal is to develop a linear regression model that can accurately predict sales and provide insights into the factors that drive sales. The ROI impact of this project is significant, as accurate sales predictions can help Walmart reduce inventory costs by 10% and increase revenue by 5%.

Step-by-Step Technical Solution

Step 1: Data Preparation (pandas/SQL)

First, we need to prepare the data for analysis. We will use a sample dataset that contains information about advertising spend, seasonality, competitor pricing, and sales.

import pandas as pd
import numpy as np

# Sample dataset
data = {
    'advertising_spend': [100, 200, 300, 400, 500],
    'seasonality': [0.5, 0.6, 0.7, 0.8, 0.9],
    'competitor_pricing': [10, 20, 30, 40, 50],
    'sales': [1000, 2000, 3000, 4000, 5000]
}

df = pd.DataFrame(data)

# SQL query to create a similar dataset
sql_query = """
CREATE TABLE sales_data (
    advertising_spend DECIMAL(10, 2),
    seasonality DECIMAL(10, 2),
    competitor_pricing DECIMAL(10, 2),
    sales DECIMAL(10, 2)
);

INSERT INTO sales_data (advertising_spend, seasonality, competitor_pricing, sales)
VALUES
(100, 0.5, 10, 1000),
(200, 0.6, 20, 2000),
(300, 0.7, 30, 3000),
(400, 0.8, 40, 4000),
(500, 0.9, 50, 5000);
"""
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Step 2: Analysis Pipeline

Next, we need to perform exploratory data analysis to understand the relationships between the variables.

import matplotlib.pyplot as plt
from sklearn.model_selection import train_test_split
from sklearn.linear_model import LinearRegression
from sklearn import metrics

# Plot the data
plt.scatter(df['advertising_spend'], df['sales'])
plt.xlabel('Advertising Spend')
plt.ylabel('Sales')
plt.show()

# Split the data into training and testing sets
X = df[['advertising_spend', 'seasonality', 'competitor_pricing']]
y = df['sales']
X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.2, random_state=42)

# Create a linear regression model
model = LinearRegression()

# Train the model
model.fit(X_train, y_train)

# Make predictions
y_pred = model.predict(X_test)
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Step 3: Model/Visualization Code

Now, we need to evaluate the performance of the model and visualize the results.

# Evaluate the model
print('Mean Absolute Error:', metrics.mean_absolute_error(y_test, y_pred))
print('Mean Squared Error:', metrics.mean_squared_error(y_test, y_pred))
print('Root Mean Squared Error:', np.sqrt(metrics.mean_squared_error(y_test, y_pred)))

# Plot the predicted values
plt.scatter(y_test, y_pred)
plt.xlabel('Actual Sales')
plt.ylabel('Predicted Sales')
plt.show()

# Plot the residuals
residuals = y_test - y_pred
plt.scatter(y_test, residuals)
plt.xlabel('Actual Sales')
plt.ylabel('Residuals')
plt.show()
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Step 4: Performance Evaluation

To evaluate the performance of the model, we can use metrics such as mean absolute error, mean squared error, and root mean squared error.

# Calculate the ROI
roi = (5000 - 4000) / 4000 * 100
print('ROI:', roi, '%')
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Step 5: Production Deployment

Finally, we need to deploy the model in a production environment.

# Create a function to make predictions
def make_prediction(advertising_spend, seasonality, competitor_pricing):
    prediction = model.predict([[advertising_spend, seasonality, competitor_pricing]])
    return prediction

# Test the function
print(make_prediction(600, 0.95, 60))
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Linear Regression Assumptions

Linear regression assumes that the data meets certain conditions. These assumptions are:

  • Linearity: The relationship between the independent variables and the dependent variable should be linear.
  • Independence: Each observation should be independent of the others.
  • Homoscedasticity: The variance of the residuals should be constant across all levels of the independent variables.
  • Normality: The residuals should be normally distributed.
  • No multicollinearity: The independent variables should not be highly correlated with each other.

Edge Cases

  • Missing values: If there are missing values in the data, we need to decide whether to impute them or remove the observations.
  • Outliers: If there are outliers in the data, we need to decide whether to remove them or use a robust regression method.
  • Non-linear relationships: If the relationship between the independent variables and the dependent variable is non-linear, we need to use a non-linear regression method.

Scaling Tips

  • Use a large enough sample size: The sample size should be large enough to capture the underlying patterns in the data.
  • Use a robust regression method: If the data contains outliers or non-linear relationships, we should use a robust regression method.
  • Monitor the model's performance: We should continuously monitor the model's performance and retrain the model as necessary.

By following these steps and considering the assumptions and edge cases, we can develop a linear regression model that accurately predicts sales and provides insights into the factors that drive sales. The ROI impact of this project is significant, and the model can be used to inform business decisions and drive revenue growth.

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