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​ Regression Analysis

Picture

There are broadly two ways in which we can think about quantifying data:
  • Making predictions one period ahead.
  • Making predictions more than two periods ahead.
Making predictions one period ahead
This is done through regression analysis.
Regression is about quantifying the relationship between two or more variables.
Example: Suppose you're looking at demand or data of people purchasing, and you know how prices were changing. What you'd like to do is to think about how you can start thinking about how price is changing demand.
What we are trying to do is to explain a dependent variable (sales or demand), as a function of independent variables (price).
  • With regression we try to make predictions of what would be the demand at different prices.
  • Regression is a technique that uses simple linear additive model to make these kinds of predictions.
 
Example: Demand Analysis
What this firm was trying to do is to try and understand how their prices might change demand. So they changed the prices and then observed the demand.
 
Price ($)
Demand

4.0
7

3.5
7

5.0
5

6.0
4

6.5
4

7.0
4

2.0
8

4.0
6

5.5
5

3.0
7

3.5
7

2.0
8

2.0
8

3.0
8

3.0
7

1.5
9

3.0
8

4.8
5

5.0
5

4.0
7

4.5
7

4.0
8

7.5
3

4.0
7

6.5
4

4.0
7

7.0
3

5.5
5

7.0
5

3.5
7

7.0
5

2.0
8




​
 



​We see that as prices go up, the demand goes down.
What regression helps with here, is that it gives specific numbers. With regression, we can tell by how much the sales will reduce for a certain increase in price.
Question answered: If I increase price by 1 $, by how much does the sales come down?
Demand Analysis
Salest = a + b1 Pricet + et
Here,
  • Sales is the dependent variable
  • Price is the independent variable.
  • b = price sensitivity à captures how sensitive your demand is to price
  • a = intercept à captures the baseline level of demand
  • e = error term à captures the increase/decrease in demand due to factors other than price (For example, they could be promotions, advertising, competitive actions, and so on)
If the model is good, then the error term will be small
 
Simple Regression:
Yt = a + b1 * X1t + et
This is the more general form of what we discussed above. This is termed as simple regression. The idea here is that the dependent variable, y, which is on the left-hand side, is related to the independent variable, x, which is on the right-hand side.
 
How does regression work?
Regression tries to fit a straight line, in this case, the demand equation, to the data that we have.

The regression line is downward sloping à higher prices, lower demand
Value of a = 10.13
Value of b = -0.9 à If price is increased by $1, then the demand will fall by 0.9 units
R2 = 0.87 or 87% à it is a metric of how good the regression model is
à varies from 0-1
à higher numbers are better since it shows that the model is able to capture a lot of variation in sales
à Typical threshold for a good regression model is R2 = 0.7 or 70%
à Here, we can say that 87% of the variation in sales is captured by price
 
Now, we can start making predictions using this regression.
We can first take the prices that are already in our dataset, and compare how our predicted regression line or making predictions from the regression is comparing with actual data. The below chart shows exactly that. We can see that the actual data and the predicted regression line are quite close to each other. This is not surprising, since the R-square of the regression is quite high.

We can also start looking at demand predictions at prices that were not there in the dataset. This way, managers can use regression to make predictions about demand for prices that have not been tested yet.
 
 
 
 
 
 
 
Once we are able to make predictions, we can move to optimum pricing.
 
 

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  • Home
  • Applied Analytics
    • Analytics for Decision Making >
      • What is Cluster Analysis
      • Data Reduction and Unsupervised Learning
      • Preparing Data and Measuring Dissimilarities
      • Hierarchical and k-Means Clustering
      • Defining Output Variables and Analyzing the Results
      • Using Historical Data to Model Uncertainty
      • Models with Correlated Uncertain Variables
      • Creating and Interpreting Charts
      • Using Average Values versus Simulation
      • Optimization and Decision Making
      • Formulating an Optimization Problem
      • Developing a Spreadsheet Model
      • Adding Optimization to a Spreadsheet Model
      • What-if Analysis and the Sensitivity Report
      • Evaluating Scenarios and Visualizing Results to Gain Practical Insights
      • Digital Marketing Application of Optimization
      • Advanced Models for Better Decisions
      • Business Problems with Yes/No Decisions
      • Formulation and Solution of Binary Optimization Problems
      • Metaheuristic Optimization
      • Chance Constraints and Value At Risk
      • Simulation Optimization
    • Analytics for Marketing >
      • Marketing Analytics and Customer Satisfaction
      • Customer Satisfaction
      • Measurements and Scaling Techniques – Introduction
      • Primary Scales of Measurement
      • Comparative Scaling
      • Non-Comparative Scaling
      • Experiment Design: Controlling for Experimental Errors
      • A/B Testing: Introduction
      • A/B Testing: Types of Tests
      • ANOVA – Introduction
      • Example -Inspect Spray and Tooth Growth
      • Logit Model - Binary Outome and Forecastign linear regression
      • Text Summarization
      • Social media Microscope
      • N-Gram - Frequcy Count and phase mining
      • LDA Topic Modeling
      • Machine-Learned Classification and Semantic Topic Tagging
    • Data Engine >
      • Understanding The Growth Of Data
      • Evaluating Methods Of Data Access
      • Communication journey
      • Data Journey
      • Planning for data visualisation
      • Visualisation Component
      • Content Connection and Chart Legitibility
    • Customer Insights >
      • Introduction
      • What is Descriptive Analytics?
      • Survey Overview
      • Net Promoter Score and Self-Reports
      • Survey Design
      • Passive Data Collection
      • Media Planning
      • Data Visualization
      • Causal Data Collection and Summary
      • Asking Predictive Questions
      • Regression Analysis
      • Data Set Predictions
      • Probability Models
      • Results and Predictions
      • Perspective Analytics (Maximize Revenue and Market Structure Competitions)
    • Analytics for Advance Marketing >
      • Visualisation and statistics (Political Advertising,Movie Theater and Data Assembly)
      • Excel Analysis of Motion Picture Industry Data
      • Displaying Conditional Distributions
      • Analyzing Qualitative Variables
      • Steps in Constructing Histograms
      • Common Descriptive Statistics for Quantitative Data
      • Regression-Based Modeling
      • Customer Analytics
      • Illustrating Customer Analytics in Excel
      • Customer Valuation Excel Demonstration
  • Soft Skills
    • Adaptability
    • Confidence
    • Change Management
    • Unlearning and Learning
    • Collaboration and Teamwork
    • Cultural Sensitivity
  • Marketing
  • Finance
  • Economics
    • Introduction to Managerial Economics >
      • Basic Techniques
      • The firm: Stakeholders, Objectives and Decision Issues
      • Demand and Revenue Analysis >
        • Demand Estimation and Forecasting
        • Demand Elasticity
        • Demand Concepts and Analysis >
          • Formulation and Solution of Binary Optimization Problems
      • Scope of Managerial Economics
    • Prodution and Cost Analysis >
      • Production Function
      • Estimation of Production and Cost Functions
      • Cost Concepts and Analysis I
      • Cost Concepts and Analysis II
    • Pricing Decisions >
      • Pricing strategies >
        • Adding Optimization to a Spreadsheet Model
      • Market structure and microbes barriers to entry
      • Pricing under pure competition and pure monopoly
      • Pricing under monopolistic and oligopolistic competition
    • Narendra Modi Development Model of Gujarat
  • JBDON Golf
    • Digital Marketing Application of Optimization
  • Let's Talk
  • MBA Project Sharing
  • About Us
    • Good Read >
      • IIMC says PepsiCo CEO Indra Nooyi was an average student
      • India’s middle class figures in Fortune’s Top Ten list of those who matter
      • The Start-Up of you.
      • BUYING AND MERCHANDISING
      • HUMAN RESOURCE MANAGEMENT
      • Do You Suffer From Decision Fatigue?
      • New Page
      • About social media and web 2.0
      • Building Your Own Start-up Technology Company, Part 1
      • Building Your Own Start-up Technology Company, Part 2
      • Building Your Own Start-up Technology Company, Part 3
      • Building Your Own Start-up Technology Company, Part 4
      • Renewable energy is no longer alternative energy
      • What Makes an Exceptional Social Media Manager?
      • The Forgotten Book that Helped Shape the Modern Economy
      • Home
      • How to Think Creatively
      • A Lighthearted Looks at Project Management and Sports Analogies
      • Why Trust Matters More Than Ever for Brands
  • CET Knowledge Zone
    • Tips From JBIMS Students >
      • Prasad Sawant
      • Chandan Roy
      • Ram
      • Ashmant Tiwari
      • Rajesh Rikame
      • Ami Kothari
      • Ankeet Adani
      • Sonam Jain
      • Marketing Analytics and Customer Satisfaction
      • Mitesh Thakker
      • Tresa Sankoorikal
    • Speed Techniques
    • CET Workshops
  • Untitled
  • New Page
    • Cluster analysis using excel and excel miner
    • Chance Constraints and Value At Risk
    • Adding Uncertainty to a Spreadsheet Model
  • Adidas