regression

Business Analytics: Diagnostic Analytics and Regression

Diagnostic Analytics Overview

• Definition of Diagnostic Analytics in business decision-making primarily focuses on understanding the cause of certain outcomes.

• Importance in addressing common business questions in the context of marketing analytics.

Common Business Questions

• What will be the impact on sales due to a price increase or decrease?

• Should the company increase advertising investments (which increases awareness) or run consumer promotions (which provides short-term incentives to consumers)?

• Will sales increase if the distribution is improved (i.e., making products available in more outlets)?

Example Inquiry: Impact of Advertising on Sales

Standard Business Question

• Question: Does advertising boost sales?
      - Variables of Interest:
          - X: Advertising expenses (ad exp)
          - Y: Sales

Assessing Impact of Advertising Expenses on Sales

Needed Information

• Key Question: If the answer to advertising impacting sales is affirmative, what is the effect of increasing advertising expenses?
      - For instance, increasing ad expenses by $1, what effect will this have on sales?

Ideal Method for Assessment

• Methodology: Randomized controlled trials are the ideal method but pose challenges:
      - Expenses: High, potentially limiting feasibility.
      - Time Consumption: Lengthy process to conduct effectively.
      - Design Difficulty: Complex experimental design.

• Questioning feasibility of observational data (non-experimental), a common resource for firms.
      - Example: Retail measurement studies as an approach to estimating the effect of advertising on sales.

Visualization of Data

• The first step in analyzing the association between two variables is visual representation.

• Typical Initial Step: Create a scatter plot to illustrate the relationship.

• Illustration: Advertising expenses plotted against sales volume for Nescafe, showing data points for analysis.

Analyzing the Scatter Plot

Initial Analysis

• Question: What can be inferred about the association between sales and advertising expenses from the scatter plot?

Statistical Tools for Analysis

• Beyond visualization, simple statistical tools such as correlation analysis can enhance understanding.

Correlation Explained

• Correlation: A statistic that quantifies how two variables move together linearly.

• Important Note: Non-linear relationships are not captured through simple correlation metrics.

Evaluating Advertising Impact

• Query: Can the correlation coefficient predict sales impact from a $100,000 increase in advertising expenses?

Steps for Evaluating Advertising Boost

1. Visualization through scatter plot.

2. Add a trendline to estimate further insights.

Regression Analysis

Defining the Regression Model

• A regression model provides a trendline representing the best fit to estimate relationships.
      - Equation:
          $Sales volume = 142.6 + 13.934 imes Advertising Expenses$
          - Here, 142.6 is the intercept (constant) and 13.934 is the slope (change in sales per unit change in expenses).

Regression Equation Principles

• General Form:
      $y = c + mx$
          - Where:
              - y: Dependent variable (Sales volume)
              - c: Intercept (base sales volume)
              - m: Slope (effect of changes in x)
              - x: Explanatory variable (Advertising expenses)

### Interpretation of the Slope

    - The slope ('m') indicates how much the dependent variable (sales volume) changes with a 1-unit change in the independent variable (advertising expenses).
    

Assumption in Simplest Regression Model

• The dependent variable (DV) is treated as a linear function of the explanatory variable:
      - Example Function:
          $Sales volume = \beta_0 + \beta_1 imes Advertising Expenses + ext{error term}$
          - Here,
              -
                  - $\beta_1$ indicates the expected change in sales from a 1 unit change in advertising expenses, confirming the significance of regression.

Error Term in Regression Analysis

• Error term captures effects from all other variables not included in regression.

Interpreting the Slope Estimate

• An increase in Advertising Expenses leads to approximately 14 units increase in sales volume.
      - Example Regression Output:
          $Sales volume = \beta_0 + \beta_1 imes Advertising Expenses + ext{error}$
          - Shows association and interpreted impact.

Statistical Significance of Estimates

• Caveat: Not all estimates may be statistically significant.

• p-value Perspective:
      - If the p-value < 0.05, it's considered statistically significant at the 5% level.
      - Lower p-values indicate higher reliability of the estimates.
      - Example Analysis: A p-value below 0.05 for $\beta_1$ indicates a statistically significant impact of Advertising Expenses on Sales.

Multivariate Analysis Necessity

• Conclusion: Can we conclusively claim Advertising Expenses affect sales?
      - Considerations: There may be confounding factors (e.g., price changes, competitor actions, and other marketing strategies) that could impact sales beyond advertising alone.
      - Suggested approach for clarity: Conduct a multivariate analysis.

Extending Regression Models

Multivariate Regression Model Formulation

• Example:
      $Sales volume = \beta_0 + \beta_1 imes Price + \beta_2 imes Consumer Promotion + \beta_3 imes Display + \beta_4 imes Discount + \beta_5 imes Advertising Expenses + ext{error}$
      

Significance Interpretation in the Multivariate Context

Summary Output from Regression Statistics

• Dimension of Regression Statistics: Multiple R, R Square, Standard Error, Observations, ANOVA tables describing variance and significance across coefficients.

Elasticity Analysis

• Price-Elasticity: Quantifying how price changes affect sales quantities.
      - Fundamental Definitions:
          - Slope: 1 unit change in price results in how many units change in sales volume.
          - Elasticity: 1% change in price results in how many % changes in sales volume, indicating responsiveness.
          

Elasticity Estimation Techniques

Utilizing Log Transformations

• Applying log transformations of sales volume and price provides direct elasticity estimates:
      $ext{ln}(Sales) = \beta_0 + \beta_1 imes ext{ln}(Price) + ext{other factors} + ext{error}$

Implications on Own Price Elasticity

• Own price elasticity considers the direct effect of its price change on sales quantity.

Demand Types

1. Elastic Demand: A 1% increase in price results in more than 1% decrease in sales volume.

2. Unit Elastic Demand: A 1% increase in price results in a precise 1% decrease in sales volume.

3. Inelastic Demand: A 1% increase in price leads to a less than 1% decrease in sales volume.

Scenario Analysis Principles

Utilizing Regression for Scenario Projections

• Scenario: When evaluating Nescafe's actions, regression analysis can predict sales implications based on various configurations of price changes, promotions, and advertising expenditures.

Estimating Revenue Change

• Formula: For minor price changes, approximate revenue change as:
       ext{% change in Revenue} ext{≈ % change in Price + % change in Quantity}

Final Insights on Recommendations

• Recommendations based on regression analysis must involve competitive activities integrated into scenario analysis, evaluating overall sales quantity and examining monetary actions to maximize revenue against constraints.

Use of GenAI in Business Analytics

• Reminder to use proprietary data cautiously, outlining the need for specific requests regarding regression models to obtain relevant elasticity measures.

• Provide necessary variables to optimize outcomes based on the broader market understanding and competition.