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Raghu Iyengar Regression Analysis

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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

variables, called the independent variables

–  Uses a linear additive relation between the dependent and independent variables

Regression  Analysis  

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Example 1: Demand Analysis Price  ($) Demand4.0 73.5 75.0 56.0 46.5 47.0 42.0 84.0 65.5 53.0 73.5 72.0 82.0 83.0 83.0 71.5 93.0 84.8 55.0 54.0 74.5 74.0 87.5 34.0 76.5 44.0 77.0 35.5 57.0 53.5 77.0 52.0 8

Regression  Analysis  

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Demand Analysis –Plot

Regression  Analysis  

Regression  Analysis  

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Regression

•  Demand Analysis

–  Salest = a + b1 Pricet + et

•  Simple Regression

t1t1t eXbaY +× +=

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Demand Curve

The  regression  line  can  be  used  to  make  demand  predic8ons  

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Demand Prediction

Future    Prices  

Price ($) Demand Prediction4.0 7 6.53.5 7 7.05.0 5 5.66.0 4 4.76.5 4 4.37.0 4 3.82.0 8 8.34.0 6 6.55.5 5 5.23.0 7 7.43.5 7 7.02.0 8 8.32.0 8 8.33.0 8 7.43.0 7 7.41.5 9 8.83.0 8 7.44.8 5 5.95.0 5 5.64.0 7 6.54.5 7 6.14.0 8 6.57.5 3 3.44.0 7 6.56.5 4 4.34.0 7 6.57.0 3 3.85.5 5 5.27.0 5 3.83.5 7 7.07.0 5 3.82.0 8 8.3

Price2.751.505.756.757.10

Prediction7.668.784.964.063.74

Regression  Regression  

Regression  Analysis  

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Optimal Pricing

•  As predictions can be done for different prices, we can also determine optimal price

•  Optimal price - price that maximizes overall profit –  Intuition – for each price, we predict demand –  Demand à revenue and profit

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Multiple Regression

•  Multiple independent variables

•  Example –  Salest = a + b1 Pricet + b2* Advt + et

ikiiii eXbXbXbaY +×++×+× + = 2 κ....211

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Summary

•  Regression is an ideal tool for understanding the drivers of demand and for demand prediction.

•  It can be used for determining optimal prices.

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From Regression to Data mining

•  Regression is one way of doing predictive analytics

•  Lots of different approaches are present –  CART –  MARS –  Neural Networks

           Regression  Analysis