Week 13 - Multiple Regression Analysis with Dummy Variables Study Guide

Overview of Multiple Regression Analysis with Dummy Variables

• Date: 02.06.2026
• Presented by: Petar Zivkovic
• Subject Focus: Understanding how numerical and categorical predictors contribute to outcomes within a regression framework.

Learning Objectives

• Understand how multiple predictors, both numerical and categorical, influence the outcome in a regression model.
• Know how to encode categorical variables as dummy variables and include them correctly in regression models.
• Know how to interpret coefficients, evaluate model quality, and use regression results for practical decision-making.

Business Case Applications

Multiple linear regression is applied across various industries to translate raw data into actionable insights. The following table identifies typical use cases, their variables, and strategic goals:

• Streaming Service Analysis

  • Outcome (Dependent Variable): Weekly hours watched (Numerical).
  • Predictors (Independent Variables): Preferred content type (Categorical — e.g., series, films); Recommendation exposure rate (Numerical — % of content suggested to user); Autoplay usage rate (Numerical — % of sessions using autoplay).
  • Goal: Identify which factor most drives watch time and suggest improvements to recommendation algorithms.

• Electric Car Battery Longevity

  • Outcome (Dependent Variable): Battery degradation (%).
  • Predictors (Independent Variables): Miles driven (Numerical); Charging frequency (Numerical); Driving style score (Categorical); Battery type (Categorical).
  • Goal: Determine which factors accelerate degradation to recommend maintenance or warranty adjustments.

• Hotel Occupancy Forecast

  • Outcome (Dependent Variable): Room occupancy rate (%) (Numerical).
  • Predictors (Independent Variables): Month (Categorical); Average room rate (Numerical); Number of local events (Numerical); Online review rating (Numerical).
  • Goal: Identify drivers of occupancy and advise on pricing or promotional strategies.

• Restaurant Menu Sales

  • Outcome (Dependent Variable): Number of dishes sold per week (Numerical).
  • Predictors (Independent Variables): Dish price (Numerical); Day of the week (Categorical); Promotional campaign (Categorical).
  • Goal: Determine which factors increase sales to optimize promotions.

• Online Retail Customer Spend

  • Outcome (Dependent Variable): Monthly spending per customer ($) (Numerical).
  • Predictors (Independent Variables): Number of emails received (Numerical); Previous purchase amount (Numerical); Website visits (Numerical); Product rating (Numerical).
  • Goal: Identify what encourages spending to recommend targeted marketing strategies.

Encoding Categorical Variables

To include non-numerical data in a regression model, categorical variables must be converted into dummy variables (binary indicators).

• Binary Variables (2 Categories)

  • Represents the presence or absence of a specific condition.
  • Example: Room has a lake view (Yes/No).
  • Encoding: Requires 1 dummy variable.
  • Formula Logic:
    • $1$ = Presence of condition (e.g., Lake View exists).
    • $0$ = Absence of condition (e.g., No Lake View).
  • Interpretation: The coefficient ($\beta$) represents how much a lake view changes the outcome (e.g., price or rating) compared to rooms without it, keeping all other variables constant.

• Categorical Variables with Multiple Levels (3+ Categories)

  • All effects are measured relative to a designated reference category.
  • Example: Property condition rating (5 levels: Important renovations needed, renovations needed, well maintained, recently renovated, in mint condition).
  • The (k-1) Rule: If there are $k$ categories, you must create $k-1$ dummy variables.
  • Procedure:
    1. Choose a reference category (e.g., "well maintained").
    2. Create dummies for all other categories: "Important renovations needed," "renovations needed," "recently renovated," and "in mint condition."
  • Interpretation: Each coefficient represents the specific difference in the outcome compared to the reference category.

Data Transformation Example: Property Encoding

Below is an illustration of how original categorical data for properties is transformed into binary numerical columns for regression analysis.

Original Data Structure

• P1: LakeView-Yes, Condition-Important renovations needed.
• P2: LakeView-No, Condition-renovations needed.
• P3: LakeView-Yes, Condition-well maintained.
• P4: LakeView-No, Condition-recently renovated.
• P5: LakeView-Yes, Condition-in mint condition.

Encoded Data Table

Note: P3 has zeros for all condition dummies because it represents the reference category ("well maintained").

Regression Output Interpretation

Interpreting the output involves looking at the coefficients ($\beta$) and the $p$-values to determine the impact and reliability of each predictor.

Comparing Model Variations

Initial Regression (Model 1):

• Intercept: $200'000$ (represents no lakeview and well maintained). $p < 0.001$.
• Lakeview: $22'000$ ($p = 0.002$).
• Important renovations needed: $-40'000$ ($p = 0.001$).
• Renovations needed: $-20'000$ ($p = 0.12$).
• Recently renovated: $18'000$ ($p = 0.01$).
• In mint condition: $38'000$ ($p = 0.001$).
• Observation: The variable "renovations needed" has a $p$-value of $0.12$, which is not statistically significant. This suggests it does not reliably explain price variation compared to the reference category.

Refined Regression (Model 2):

• The non-significant predictor ("renovations needed") is removed.
• New Intercept: $200'000$. This now represents the base price for a property that is either well maintained or only needs minor renovations (as the latter is now absorbed into the intercept) and has no lake view.
• Lakeview: $22'000$. ($p = 0.002$).
• Important renovations needed: $-40'000$. ($p = 0.001$).
• Recently renovated: $18'000$. ($p = 0.01$).
• In mint condition: $38'000$. ($p = 0.001$).

Key Interpretation Rules

• Coefficient ($\beta$): In the presence of the condition (compared to the state defined in the intercept), the dependent variable ($Y$) varies on average by the value of the coefficient, assuming all other variables remain equal.
• P-Value: Indicates the probability that the coefficient is equal to $0$. A high $p$-value means there is a high probability that there is no meaningful difference between that category and the reference category.