Multiple Regression Analysis

Class Outline
• Multiple Regression Analysis
• Application of Regression
– Substitute goods VS. Complimentary goods
• Group Exercise: Best Foods VS. Kraft

Example – Sales Data Continued
Market ID Sales Price Competitor Price
1 228 2.2 2.2
2 216 2.7 2.9
3 223 2.4 2.4
4 207 2.9 2.6
5 216 2.8 2.4
6 247 2.2 2.5
7 233 2.0 2.2
8 249 2.3 2.7
9 239 2.1 2.4
10 209 2.7 2.4
11 214 2.8 2.4
12 236 2.6 3.0
13 218 2.6 2.1
14 191 2.9 2.2
15 223 2.6 3.0

Example – Sales Data
SALES
COMPETITOR
PRICE
ADVERTISIGN
PROMOTION
COUPON
DISPLAY
••••••
PRICE

• SALES = f ( Price, Competitor Price, Other factors )
• Assumptions of Regression Model
1. Linear Relationship Between SALES and PRICE
2. Linear Relationship Between SALES and
COMPETITOR PRICE
3. Other factors follow N( )
2
,
),0(~
,CPricePriceSALES
2
21


Ni
iiii 
Competitor Price

• Using data, we make inferences on , , and .
• Our best guess on using the sample data: a
• Our best guess on using the sample data: b1
• Our best guess on using the sample data: b2
• Determine a, b1, and b2 by minimizing the sum of
squared errors
 1

iiii   CPricePriceSALES 21
2
1
2

Use of Regression Model
1. Prediction / Forecasting
eg.) Price = 3; CPrice = 2
Exp. Sales=284.86–46.60*3+22.40*2+ Expected Value of ε
=284.86–46.60*3+22.40*2
2. Relationship between variables
One Unit Increase in Price  46.60 Units Decrease in
Expected Sales
One Unit Increase in CPrice  22.40 Units Increase in
Expected Sales
Sales=284.86–46.60*Price+22.40*CPrice+ε

Exercise
• Use “Regression Exercise 3.xlsx => Multiple
Regression 1”
• Use Excel “Solver” and “Data Analysis”

In-Class Exercise
• Use “Regression Exercise 3.xlsx”  Multiple Regression
2
• Q1: Estimate a, b1,and b2
• Q2: Compute the average of errors
• Q3: Compute the expected sales when Price=3; CPrice=2
• Q4: Compute the expected sales when Price=2; CPrice=3
• Q5: Compute the R-Square
• Q6: Perform the same regression analysis using “Excel
Data Analysis”

Regression Statistics
Multiple R 0.85
R Square 0.73
Adjusted R Square 0.68
Standard Error 7.83
Observations 15.00
ANOVA
df SS MS F Significance F
Regression 2.00 1984.27992.13 16.19 0.00
Residual 12.00 735.33 61.28
Total 14.00 2719.60
Coefficients Standard Error t Stat P-value Lower 95% Upper 95%
Intercept 419.95 37.40 11.23 0.00 338.46 501.45
Price -42.80 8.30 -5.15 0.00 -60.89 -24.70
Cprice 4.39 9.74 0.45 0.66 -16.82 25.60

Application of Regression Model
Substitute Good VS. Complimentary Good
• Substitute goods: replace each other in use
Margarine and butter
Tea and coffee
Sales_Tea = a + b1 * Price_Tea + b2 * Price_Coffee + ε
• Complimentary goods: complement each other in use
Hotdog and hotdog bun
Hardware and software
Sales_Hard = a + b1 * Price_Hard + b2 * Price_Soft + ε
+ or - ?
+ or - ?

Application of Regression Model
Substitute Good VS. Complimentary Good
• Coke vs. Pepsi
• Coke vs. Sierra Mist (?)
• Why important?
– Identify _________________

Samuel Adams – Brewer & Patriot
• Relationship between Beer and Tea: Substitute goods
• Sales_Beer = a + b1 * Price_Beer + b2 * Price_Tea + ε
• b2: ( + ) or ( - ) ?
• Tea supply ↓ Tea price ↑  Sales_Beer ?
• For Sam, Good or Bad ?

Group Exercise
Analysis of Mayonnaise Market
Best Foods VS. Kraft
Strategic Pricing

Group Exercise: Best Foods VS. Kraft
• Use “PHXMayoData.xlsx”
• 173 weeks (2002-2005)
• A grocery store in Phoenix area
• Sales and Prices of Best Foods (BF) Mayo and Kraft (KR)
Mayo
Week Sales_BF Sales_KR Price_BF Price_KR
1 455 135 1.61 1.02
2 530 63 1.34 1.29
3 527 41 1.38 1.63
4 418 71 1.44 1.53
5 380 34 1.62 1.71
: : : : :

• Q1: Compute average sales and average prices for
both brands. What can we infer about this market
from these numbers?
 Use “=average( )”
Best Foods Kraft
Average Sales 350 73
Average Price 1.63 1.48

• Q2: Perform regression analysis
– Model1: Sales_BF = a + b1* Price_BF + b2* Price_KR + Error
– Model2: Sales_KR = a + b1* Price_BF + b2* Price_KR + Error
 Use “Data Analysis – Regression”
Model 1
Model 2

• Q3: Interpret the results – Model1 (Best Foods)
Sales_BF = a + b1* Price_BF + b2* Price_KR + ε

• Q3: Interpret the results – Model2 (Kraft)
Sales_KR = a + b1* Price_BF + b2* Price_KR + ε

• Q4: Compute the expected sales of both brands when
Price_BF = average of Price_BF’s
Price_KR = average of Price_KR’s
 Sales_BF = 900 - 393 * Price_BF + 61* Price_KR + ε
 Sales_KR = 155 + 55 * Price_BF – 116* Price_KR + ε

Best Foods Kraft
 Exp. Sales_BF = 900 - 393 * 1.63 + 61* 1.48 = 350
Exp. Sales_KR = 155 + 55 * 1.63 – 116* 1.48 = 73

• Q5: Now assume that Best Foods decrease its price
by $0.1. What will happen to the sales of both
brands?
Best Foods Kraft
 Exp. Sales_BF = 900 - 393 * 1.53 + 61* 1.48 = 389 (+11%)
Exp. Sales_KR = 155 + 55 * 1.53 – 116* 1.48 = 68 (-8%)
1.53

• Q6: Now assume that Kraft decrease its price by $0.1.
What will happen to the sales of both brands?
Best Foods Kraft
 Exp. Sales_BF = 900 - 393 * 1.63 + 61* 1.38 = 344 (-2%)
Exp. Sales_KR = 155 + 55 * 1.63 – 116* 1.38 = 85 (+16%)
1.38

Best Foods Kraft Total
Average Sales 350 73 423
Best Foods Price ↓ $0.1
389 68 457
(+11%) (-8%) (+8%)
Kraft Price ↓ $0.1
344 85 429
(-2%) (+16%) (+1%)

• Q7: Now assume that the cost of BF is $1. What is the
BF’s expected profit?
Exp.Profit = Exp.Sales * ( Price – Cost )
Coefficients Standard Error t Stat
Intercept 900.80 58.06 15.52
Price_BF -392.88 32.88 -11.95
Price_KR 61.25 23.29 2.63
Best Foods Kraft
Exp.Sales 350 =
Exp.Profit 221=
1
2
3
4 51 2 3+ +X X
X ( - 1)
4
4
5

• Q8: What is the optimal price that maximizes the BF’s
profit? Hint: Use “Solver”
Best Foods Kraft
Exp.Sales 299
Exp.Profit 228
Optimal
Solution

Multiple Regression Analysis

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