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Regression Analysis The Basics of Regression Professor Raghu Iyengar
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 Analysis - Regression
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Demand Analysis - 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
Professor Raghu Iyengar
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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Price Elasticity• The percentage change in sales with 1% change in price.
• Sales = 0.90 *Price + 10.13
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Price Elasticity• The percentage change in sales with 1% change in price.
• 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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Price Elasticity• The percentage change in sales with 1% change in price.
• 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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Price Elasticity• The percentage change in sales with 1% change in price.
• 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
Professor Raghu Iyengar
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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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.
• Attractiveness of a NPD project proposal changes over time
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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.
• 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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New Product Development
Development ?Review• Concept
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New Product Development
Development ?Review
PrototypeDevelopment
• Concept
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New Product Development
Development ?Review
PrototypeDevelopment
?Review
• Concept
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New Product Development
Development ?Review
PrototypeDevelopment
?Review
AdvertisingDevelopment
• Concept
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New Product Development
Development ?Review
PrototypeDevelopment
?Review
AdvertisingDevelopment
?Review
• Concept
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New Product Development
Development ?Review
PrototypeDevelopment
?Review
AdvertisingDevelopment
?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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Regression Using Data From Both Stages
Higher than 0.55
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Regression Using Data From Both Stages
Higher than 0.55
Useful to combine the additional data from the Prototype stage?
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Regression Using Data From Both Stages
Higher than 0.55
Useful to combine the additional data from the Prototype stage?
YES!
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Empirical Lessons• One can determine whether adding more variables is helpful or
not
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Empirical Lessons• One can determine whether adding more variables is helpful or
not
• 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)
Professor Raghu Iyengar
Example 3: CPG Context• Are more variables always better?
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Example 3: CPG Context• Are more variables always better?
• Dependent Variable – Sales
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Example 3: CPG Context• Are more variables always better?
• 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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Separate Regressions
No problem at all
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Separate Regressions
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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
Professor Raghu Iyengar
Example 4: Regression and Time Trends
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Example 4: Regression and Time Trends
Salsa demand in a retail store over time
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Example 4: Regression and Time Trends
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
Professor Raghu Iyengar
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
lagprom -3.191780961 0.855723945 -3.72991895 0.001666007
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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
lagprom -3.191780961 0.855723945 -3.72991895 0.001666007
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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
lagprom -3.191780961 0.855723945 -3.72991895 0.001666007
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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
lagprom -3.191780961 0.855723945 -3.72991895 0.001666007
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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
lagprom -3.191780961 0.855723945 -3.72991895 0.001666007
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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
lagprom -3.191780961 0.855723945 -3.72991895 0.001666007
Carry over effects!
Net-Net – advertising is more powerful
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Dynamics Effects of Promotions / Advertising • Carry-over from the marketing mix variable
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Dynamics Effects of Promotions / Advertising • Carry-over from the marketing mix variable
• The following equation can help in capturing the short term and longer term effect• Salest = a + b Xt + c Xt-1
• If X is advertising, then the above equation captures the carry over effect of advertising
• If X is promotions, then the above equation captures the carry over effect of promotions.
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Overall Empirical Lessons• Be mindful marketing dynamics
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Overall Empirical Lessons• Be mindful marketing dynamics
• Advertising and Promotions• There is a tradeoff
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Regression AnalysisAdvertising and Promotions
Professor Raghu Iyengar
Validation of Model Predictions• Split Sample
• Run two regressions on half of the sample and cross-predict
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Validation of Model Predictions• Split Sample
• Run two regressions on half of the sample and cross-predict• Prediction in hold out samples
• Most obvious alternative if you have the data
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Validation of Model Predictions• Split Sample
• Run two regressions on half of the sample and cross-predict• Prediction in hold out samples
• Most obvious alternative if you have the data• Good to test against overfitting
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Summary• Regression is a simple tool. Keep the following in mind :
• Multicollinearity of variables• Adding more variables is not always better• Time trend and dynamics are important
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Summary• Regression is a simple tool. Keep the following in mind :
• Multicollinearity of variables• Adding more variables is not always better• Time trend and dynamics are important
• Model validation is important
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