Regression Analysis: Linear & Multiple Regression

If you’re stepping into data analysis, regression analysis is one of the first predictive techniques you’ll use. Whether you’re analyzing sales trends, forecasting business growth, or understanding customer behavior, regression helps you understand the relationship between variables and predict future outcomes.

In this guide, I’ll walk you through linear regression and multiple regression in the simplest way—using explanations, visuals-in-words, examples, and real-world applications. By the end, you’ll understand not just the formulas, but how regression fits into your data analytics work.

What Is Regression Analysis?

Regression analysis is a statistical method used to identify the relationship between a dependent variable (the outcome you want to predict) and one or more independent variables (factors that influence the outcome).

You can think of regression as answering two main questions:

1. How much does X affect Y?
2. Can I use X to predict Y?

This makes regression one of the most widely used techniques in data analytics, business intelligence, data science, and forecasting.

Related read: Excel for Data Analysis (Advanced Excel Skills)

Why Data Analysts Use Regression

As a data analyst, you use regression to:

• Understand trends
• Measure the strength of relationships
• Forecast future values
• Identify key business drivers
• Build predictive models
• Support data-driven decision-making

Regression analysis is the backbone of predictive analytics—if you’re learning machine learning later, regression is the perfect starting point.

Understanding Linear Regression

Linear regression is the simplest form of regression. It analyzes the relationship between:

• One independent variable (X)
• One dependent variable (Y)

The relationship is modeled as a straight line.

Linear Regression Formula

Y = a + bX

Where:

• Y = predicted value
• a = intercept (value of Y when X = 0)
• b = slope (how much Y changes when X increases by 1 unit)
• X = independent variable

Example: Predicting Sales Using Marketing Spend

Let’s say you’re analyzing a dataset:

Marketing Spend (X)	Sales (Y)
1000	8000
1500	9500
2000	12000
2500	15000

A linear regression model might learn:

Y = 4000 + 4X

Meaning:

• When marketing spend increases by ₹1, sales increase by ₹4.
• Even without spending anything, estimated baseline sales = ₹4000.

This kind of insight is pure gold for business teams.

Visualization (Explained in Words)

Imagine a scatter plot of all data points (sales vs marketing). Linear regression draws the best-fit straight line through these points, minimizing errors. This line becomes your prediction model.

When to Use Linear Regression

You should use linear regression when:

• The relationship looks like a straight line
• There’s only one predictor
• You need a simple, interpretable model
• The dataset is small or medium sized
• You want to detect basic trends

Understanding Multiple Regression

Multiple regression is an extension of linear regression.

Here, you use two or more independent variables to predict a single dependent variable.

Multiple Regression Formula

Y = a + b₁X₁ + b₂X₂ + b₃X₃ + … + bₙXₙ

Where each b measures the impact of each variable while keeping others constant.

Example: Predicting House Prices

Imagine a dataset with:

• X1 = House size (sq ft)
• X2 = Number of bedrooms
• X3 = Distance from city center
• Y = House price

A model may output:

Y = 50,000 + 150(X₁) + 5,000(X₂) – 800(X₃)

Interpretation:

• Every extra sq ft increases price by ₹150
• Each extra bedroom increases price by ₹5,000
• Each kilometer farther reduces price by ₹800

Multiple regression gives you a deeper, more realistic understanding of real-world scenarios where multiple factors drive outcomes.

Related read: Formulas and Functions in Excel: Explanations, and Differences

Visualization (Explained in Words)

Instead of a straight line, multiple regression forms a plane (or hyperplane). Picture a 3D chart where the surface predicts house prices from size and distance. Add more variables and that surface becomes multi-dimensional.

When to Use Multiple Regression

Use multiple regression when:

• You have multiple factors influencing the outcome
• You need more accurate predictions
• You want to measure the effect of each predictor
• The business scenario is complex
• You want to find hidden patterns

Key Similarities Between Linear & Multiple Regression

• Both use statistical modeling to predict outcomes
• Both assume linear relationships
• Both use least squares to minimize prediction errors
• Both require clean, numeric data
• Both build interpretable, easy-to-explain models

Differences Between Linear & Multiple Regression

Feature	Linear Regression	Multiple Regression
Number of predictors	1	2 or more
Model output	Straight line	Multidimensional plane
Analysis complexity	Simple	Advanced
Accuracy	Basic	Higher
Real-world usage	Limited	Very common

Related read: Data visualization Fundamentals: How to Present Data Effectively

Real-World Use Cases of Regression for Data Analysts

1. Sales Forecasting

Predict future sales using:

• Marketing spend
• Seasonality
• Prices
• Promotions

2. Customer Churn Prediction

Predict which customers will leave using:

• Usage metrics
• Customer support data
• Demographics
• Payment history

3. Demand Planning

Estimate inventory needs based on:

• Weather
• Location
• Festival seasons
• Promotions

4. Business Performance Analysis

Analyze how factors like:

• Employee count
• Experience
• Training hours

impact performance outcomes.

5. Finance & Risk Modeling

Predict:

• Credit risk
• Loan defaults
• Insurance premium pricing

Regression is everywhere—in business dashboards, analytics tools, Power BI, Excel modeling, and machine learning workflows.

Related read: Making Professional Dashboards for Data Analysis

How Data Analysts Perform Regression Step-by-Step

1. Collect Data

From SQL, Excel, CRM platforms, APIs, or BI tools.

2. Prepare the Data

• Handle missing values
• Remove outliers
• Convert categories to numbers
• Normalize or scale data

3. Explore Variables (EDA)

Look for:

• Correlations
• Trends
• Patterns

4. Build the Regression Model

Using:

• Excel
• Python (scikit-learn)
• R
• Power BI
• SPSS

5. Evaluate the Model

Common metrics:

• R² (explains variance)
• Adjusted R²
• RMSE
• MAE
• P-values

6. Deploy or Use Model Insights

Share findings with business teams or integrate the models into dashboards.

Common Mistakes Beginners Make

• Using highly correlated variables (multicollinearity)
• Ignoring outliers
• Not checking assumptions
• Using too many predictors
• Misinterpreting coefficients

Understanding these helps you build cleaner and more trustworthy models.

Related read: Predictive Analytics: Basics of Machine Learning

Conclusion

Regression analysis is one of the most powerful tools you’ll use as a data analyst. Linear regression gives you simple trend insights, while multiple regression helps you understand the combined effect of multiple variables—and predict outcomes more accurately.

If you want to move toward advanced analytics or machine learning later, mastering regression is your first major step. With practice, you’ll learn to interpret coefficients confidently, build predictive models, and support business decisions with real data.