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BA 555 Practical Business Analysis

Midterm Examination #1

Conjoint Analysis

Linear Programming (LP) Introduction LINDO and Excel-Solver

Agenda

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Residual Analysis (pp.33 – 34)

The three conditions required for the validity of the regression analysis are: the error variable is normally distributed with mean = 0. the error variance is constant for all values of x. the errors are independent of each other.

How can we identify any violation?

22110 XXY

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Residual Analysis (pp. 33 – 34)

Examining the residuals (or standardized residuals), help detect violations of the required conditions.

Residual = actual Y – estimated Y

YYe ˆ

We do not have (random error), but we can calculate residuals from the sample.

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Residuals, Standardized Residuals, and Studentized Residuals (p.33)

Residual from COST Regressed on UNITS and SWITCH

Case FactA Units Switch Cost Predicted Residual Standardized Studentized(1000) (million) Cost Residual Residual

1 1 1.104 8 1.155456 1.159550 -0.004097 -0.784498 -0.8303562 0 1.044 12 1.144198 1.146200 -0.002005 -0.383925 -0.3925333 1 1.020 12 1.141490 1.139270 0.002217 0.424535 0.4306614 1 0.986 6 1.119656 1.123490 -0.003836 -0.734607 -0.7730755 1 0.972 13 1.124815 1.126410 -0.001592 -0.304760 -0.312259: : : : : : : : :: : : : : : : : :

48 1 1.011 10 1.130929 1.134690 -0.003758 -0.719501 -0.72326049 1 1.016 9 1.136349 1.135140 0.001213 0.232184 0.23285850 0 1.008 9 1.140616 1.132830 0.007790 1.491579 1.53042051 0 1.059 11 1.154121 1.149540 0.004581 0.877094 0.90087852 0 1.019 13 1.142435 1.139980 0.002457 0.470480 0.484002

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The random error is normally distributed with mean = 0 (p.34)

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The error variance is constant for all values of X and estimated Y (p.34)

Constant spread !

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Constant Variance

When the requirement of a constant variance is violated we have a condition of heteroscedasticity.

Diagnose heteroscedasticity by plotting the residual against the predicted y, actual y, and each independent variable X.

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The spread increases with y

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Residual

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The errors are independent of each other (p.34)

Do NOT want to see any pattern.

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Residual Residual

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Note the runs of positive residuals,replaced by runs of negative residuals

Note the oscillating behavior of the residuals around zero.

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Non Independence of Error Variables

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Residual Plots with FACTA (p.34)

Which factory is more efficient?

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Dummy/Indicator Variables (p.36)

Qualitative variables are handled in a regression analysis by the use of 0-1 variables. This kind of qualitative variables are also referred to as “dummy” variables. They indicate which category the corresponding observation belongs to.

Use k–1 dummy variable for a qualitative variable with k categories. Gender = “M” or “F” → Needs one dummy variable. Training Level = “A”, “B”, or “C” → Needs 2 dummy variables.

Otherwise0,

B""evelTraining_L1,ummyBTraining_d

Otherwise0,

A""evelTraining_L1,ummyATraining_d

M"" Gender if0,

F"" Gender if1, my Gender_dum

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C""evelTraining_L if3,

B""evelTraining_L if2,

A""evelTraining_L if1,

ng_dummyTraing_wro

usejust not Why

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Dummy Variables (pp. 36 – 38)

FactABA

A Parallel Lines Model

Units

Cos

t

0.9 0.94 0.98 1.02 1.06 1.1 1.14 1.181.09

1.11

1.13

1.15

1.17

A Parallel Lines Model: Cost = 0 + 1 Units + 2 FactA + Least squares line: Estimated Cost = 0.86 + 0.27 Units – 0.0068 FactA

Two lines? Base level?

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Dummy Variables (pp. 36 – 38)

An Interaction Model : Cost = 0 + 1 Units + 2 FactA + 3 Units_FactA + Least squares line: Estimated Cost = 0.87 + 0.26 Units – 0.023 FactA + 0.016 Units_FactA

FactABA

An Interaction Model

Units

Cos

t

0.9 0.94 0.98 1.02 1.06 1.1 1.141.09

1.11

1.13

1.15

1.17

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Conjoint Analysis (pp. 55 – 56)

Conjoint analysis is a marketing tool used to determine the relative importance consumers attach to salient attributes and the utilities they attach to the levels of attributes. It has been used in marketing for a variety of purposes including the following: (1) determining the relative importance of attributes in the consumer choice process; (2) estimating market share of brands that differ in attribute levels; (3) determining the composition of the most preferred brand; (4) segmenting the market based on similarity of preferences for attribute levels. A good place to learn more about conjoint analysis can be found at www.sawtoothsoftware.com/techpap.shtml. A series of short research papers (easy reading) under the heading “General Conjoint Analysis” provides in-depth discussion on the topic.

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Data Preparation

Variable: Location Variable: SalaryY

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Regression Coefficients

Attributes Utilities

(Part Worths) Range Relative Importance

Location Seattle 4.3333

New York –8.3333 Denver –5.3333

L. A. –1.6667 Portland 6.0

S. F. (base level) 0

14.3333 33333.14

3333.1483.0

Salary

100K 3 90K 1.5

80K (base level) 0 3

33333.14

317.0

Estimated Utility = Constant + 4.33 X1_Seattle – 8.33 X2_NY – 5.33 X3_Denver –1.67 X4_LA + 6.0 X5_PDX + 3 X6_100K + 1.5 X7_90K

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Location is more important than Salary (Customer A13)

Attributes Utilities

(Part Worths) Range Relative Importance

Location Seattle -6

New York -3 Denver -12

L. A. -15 Portland -9

S. F. (base level) 0

15 0.918

Salary

100K 1.33 90K 0.67

80K (base level) 0 1.33 0.082

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Location is more important than Salary (Customer B20)

Attributes Utilities

(Part Worths) Range Relative Importance

Location Seattle 6

New York -3.67 Denver 3

L. A. -5.33 Portland 9

S. F. (base level) 0

14.33 0.851

Salary

100K 2.5 90K 1.5

80K (base level) 0 2.5 0.149

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Salary is more important than Location (Customer A2)

Attributes Utilities

(Part Worths) Range Relative Importance

Location Seattle 1.67

New York -1 Denver 0.33

L. A. -0.33 Portland 0.33

S. F. (base level) 0

2.67 0.182

Salary

100K 12 90K 6

80K (base level) 0 12 0.818

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Salary is a bit more important than Location (Customer B19)

Attributes Utilities

(Part Worths) Range Relative Importance

Location Seattle 4

New York -1 Denver 3

L. A. -2 Portland 5

S. F. (base level) 0

7 0.4

Salary

100K 10.5 90K 7.5

80K (base level) 0 10.5 0.6

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Location is most important, but … (Customer B24)

Attributes Utilities

(Part Worths) Range Relative Importance

Location Seattle 9

New York 6 Denver 15

L. A. 3 Portland 12

S. F. (base level) 0

15 1

Salary

100K 0 90K 0

80K (base level) 0 0 0

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An Irrational Customer? (I made this one up.)

Attributes Utilities

(Part Worths) Range Relative Importance

Location Seattle 6

New York –3 Denver 3

L. A. –6 Portland 9

S. F. (base level) 0

15 0.88

Salary

100K –2 90K –1

80K (base level) 0 2 0.12

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Market Segmentation

Relative ImportanceClusters of Customers

Location

Sa

lary

Cluster 12Centroids

0 0.2 0.4 0.6 0.8 10

0.2

0.4

0.6

0.8

1

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Decision-making under Uncertainty

Decision-making under uncertainty entails the selection of a course of action when we do not know with certainty the results that each alternative action will yield.

This type of decision problems can be solved by statistical techniques along with good judgment and experience.

Example: buying stocks/mutual funds.

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Decision-making under Certainty

Decision-making under certainty entails the selection of a course of action when we know the results that each alternative action will yield.

This type of decision problems can be solved by linear/integer programming technique.

Example: A company produces two different auto parts A and B. Part A (B) requires 2 (2) hours of grinding and 2 (4) hours of finishing. The company has two grinders and three finishers, each of which works 40 hours per week. Each Part A (B) brings a profit of $3 ($4). How many items of each part should be manufactured per week?

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Steps in Quantifying and Solving a Decision Problem Under Certainty Formulate a mathematical model:

Define decision variables, State an objective, State the constraints.

Input the model to a LP/ILP solver, e.g., LINDO or EXCEL Solver.

Obtain computer printouts and perform sensitivity analysis.

Report optimal strategy.

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What to prepare for our next topic?

Install LINDO or EXCEL Solver (do at least one.) LINDO: http://www.lindo.com/. Go to DOWNLOAD

HOMEPAGE. On the left-hand-side, chose LINDO FOR WINDOWS (not LINDO API, not LINGO.)

Its syntax is given on pp. 78 – 80 of the class packet.

EXCEL Solver: Under Tools / Add-Ins. Check the SOLVER ADD-INS box. Click OK.

It is supported by the textbook (Chapter 4, pp. 209 – 281)