The Basics of Regression - d37djvu3ytnwxt.cloudfront.net · • Highlight the usefulness of...

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Regression AnalysisThe Basics of Regression

Professor Raghu Iyengar

Regression Analysis• Several Examples

• Highlight the usefulness of regression for key managerial decisions

• Issues one must be careful about

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Regression Analysis• Several Examples

• Highlight the usefulness of regression for key managerial decisions

• Issues one must be careful about

• Managerial Relevance• Demand Analysis• Optimal Pricing and Price Elasticity• Dynamics of promotions

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What is the Purpose of Regression• Quantify the relationship among two or more variables

• Explain a dependent variable, from a set of predictor variable, called the independent variables

• Uses a linear additive relation between the dependent and independent variable.

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Example 1: Simple Demand Analysis

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Demand Analysis - Plot

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Regression• Demand Analysis

Salest = a + b1 Pricet + et

• Simple Regression

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Demand Analysis - Regression

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Demand Curve

The regression line can be used to make demand predictions

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Demand Prediction

Regression

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Demand Prediction

Regression

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Demand Prediction

Regression

Future Prices

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Demand Prediction

Regression

Future Prices

Regression

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Regression AnalysisOptimal Pricing (Price Sensitivity) and Price Elasticity

Optimal PricingPredicted Profit = (Price-MC) *(Predicted Demand)

If MC = 0 then

Predicted Revenue- (Price) *(Predicted Demand)

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Optimal PricingPredicted Profit = (Price-MC) *(Predicted Demand)

If MC = 0 then

Predicted Revenue- (Price) *(Predicted Demand)

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Price Elasticity• The percentage change in sales with 1% change in price.

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• Sales = 0.90 *Price + 10.13

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• Sales = 0.90 *Price + 10.13

• Price Elasticity at Price = $3.0?• Sales at Price = $3 : -0.90 *3 + 10.13 = 7.43

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• Sales = 0.90 *Price + 10.13

• Price Elasticity at Price = $3.0?• Sales at Price = $3 : -0.90 *3 + 10.13 = 7.43• Sales at Price = $3.03: -0.90*3.03 + 10.13 = 7.40

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• Sales = 0.90 *Price + 10.13

• Price Elasticity at Price = $3.0?• Sales at Price = $3 : -0.90 *3 + 10.13 = 7.43• Sales at Price = $3.03: -0.90*3.03 + 10.13 = 7.40• Elasticity = (7.40 – 7.43)/7.43*100 = -0.40

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Regression AnalysisMultiple Regression

Multiple Regression

Multiple independent variables

ExampleSalest = a + b1 Pricet + b2* Advt + et

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Example 2: Multiple Regression and New Product Sales• Imagine many new product development (NPD) project

proposals (> 100) but resources are only sufficient for launching of 20 new products.

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• Attractiveness of a NPD project proposal changes over time

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• Attractiveness of a NPD project proposal changes over time

• Which projects to pick and which projects to kill during the NPD Process?

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New Product Development

Development• Concept

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Development ?Review• Concept

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Development ?Review

PrototypeDevelopment

• Concept

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Development ?Review

?Review

• Concept

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Development ?Review

?Review

AdvertisingDevelopment

• Concept

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Development ?Review

?Review

• Concept

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Development ?Review

?Review

• Actual vs. Projected

Post-LaunchAnalysis

Return

• Concept

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History of Product Launches – New Soup

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Regression Using Data From the Concept Stage

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History of Product Launches – New Soup

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Regression Using Data From the Both Stages

Useful to combine the additional data from the Prototype stage?

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How to Decide When to Stop Adding Variable?• R2

• It cannot decrease as more independent variables are added

• Adjusted R2

• Corrects for number of independent variables.

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Regression Using Data From Both Stages

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Higher than 0.55

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Higher than 0.55

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Higher than 0.55

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Empirical Lessons• One can determine whether adding more variables is helpful or

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Empirical Lessons• One can determine whether adding more variables is helpful or

• Think about adjusted R-squared as a metric for determining when to stop adding variables

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Regression AnalysisConsumer Packaged Goods Example (Multicollinearity)

Example 3: CPG Context• Are more variables always better?

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• Dependent Variable – Sales

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• Dependent Variable – Sales

• Independent Variables• Ad Spend• Price

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Scatter Plots

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Scatter Plots

Both AdSpend and Prices are highly correlated with Sales

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Regression Results

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Regression Results

What’s going on here?

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Scatter Plot (AdSpend vs Price)

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Scatter Plot (AdSpend vs Price)

Almost perfect correlation!

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Multicollinearity• Multicollinearity - Xs are collinear with each other

• Look at correlation matrix of Xs• Solution: Do not include all of the Xs

• More variables are not always be better!

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Separate Regressions

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No problem at all

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VIF – Variance Inflation Factor

VIF > 5 is a typical cut off

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Overall Empirical Lessons• Always look out for multicollinearity when you see regression

results.

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Overall Empirical Lessons• Always look out for multicollinearity when you see regression

results.

• It is particularly important if there are several variables you are putting into a model.

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Regression AnalysisRegression and Time Trends

Example 4: Regression and Time Trends

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Salsa demand in a retail store over time

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Salsa demand in a retail store over time

Question:What is the price sensitivity?

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Regression

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Regression

Positive Impact of Price?!

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Salsa Data – Monthly Category Demand

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Salsa Data – Monthly Category Demand

Overall demand is increasing over time

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Regression

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Regression

Reasonable impact of price after accounting for overall increase in demand

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Overall Empirical Lessons• Be mindful of market size and economic conditions

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Overall Empirical Lessons• Be mindful of market size and economic conditions

• Be mindful of seasonality and other time trends

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Regression AnalysisAdvertising and Promotions

Data and Questions• Data

• Quarterly Sales Data of Cereal (thousands of dollars)• Promotion and Advertising Spending (thousands of dollars)

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Data and Questions• Data

• Quarterly Sales Data of Cereal (thousands of dollars)• Promotion and Advertising Spending (thousands of dollars)

• Question• What is the impact of promotions and advertising

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What is the $ impact of promotion / adv?

Should we put all our money in promotions?

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What is the $ impact of promotion / adv

Coefficients Standard Error t Stat P-valueIntercept 757.3168569 274.9484797 2.754395506 0.013542618prom 5.915436041 0.874022866 6.768056391 3.28474E-06

adv 2.29581158 0.746485388 3.075494332 0.006855015lagadv 2.622828289 0.776793776 3.376479538 0.003585691