M303 Regression III and Conjoint Analysis

FALL 2026 · LECTURE 20
M303
Regression III & Conjoint Analysis
Apply multiple regression, then decompose preferences into attribute-level value.

Where we are

01Problem formulation

Management problem → research objectives → questions → hypotheses

02Research design

Exploratory · descriptive · causal

03Data collection

Secondary · observation · qualitative · survey · experiment · sampling

04Data analysis & recommendation

Regression applications → conjoint utilities → product decisions

Learning Objectives

01Apply

Multiple regression to category pricing and diamond valuation.

02Design

Product profiles from attributes and levels.

03Estimate

Part-worth utilities with dummy-coded regression.

04Calculate

Relative attribute importance and predicted preference shares.

Previous class review

01

Correlation measures the extent to which two continuous variables move together.

TRUE
02

Regression generates a mathematical function linking the dependent variable to the independent variable(s).

TRUE
03

A correlation coefficient by itself provides a prediction equation.

FALSE
04

Continuous predictors must be dummy coded, while categorical predictors can be entered directly.

FALSE

In-class exercise 1: category pricing

MULTIPLE REGRESSION APPLICATION

Estimate Pepsi demand.

SalesPepsi = a + b₁PriceCoke + b₂PricePepsi
01

Estimate the intercept and slopes.

02

Assume both wholesale costs are $1.

03

Test each brand’s price from $1.50 to $2.50 in $0.10 steps.

04

Find the pair that maximizes combined category profit.

In-class exercise 2: how much for a diamond?

◆

PRICE

Use DiamondData.xlsx to model price as a function of carat and cut.

CATEGORICAL PREDICTORM levels → M − 1 dummy variables
FairGoodVery GoodIdeal

Diamond regression: interpret and predict

Predictor
Coefficient
p-value
Intercept00.999 Carat5,1180.000 Cut_Good4460.026 Cut_Very_Good1,1280.000 Cut_Ideal1,9660.000

Interpret the intercept and slopes.

Predict prices for:

  1. 1 carat · Fair
  2. 1 carat · Ideal
  3. 2 carats · Very Good
$5,118$7,084$11,364
Price = 0 + 5,118(Carat) + 446(Good) + 1,128(Very Good) + 1,966(Ideal)

From regression to conjoint

Three unbranded ultrabook computers representing alternative product profiles
REGRESSION → CONJOINT Turn attribute levels into utility estimates.
Design profiles
Dummy-code levels
Estimate part-worths
Calculate importance
Predict preferences

Build an ultrabook from attributes and levels

BRAND · 3 LEVELSHPLenovoDell
PROCESSOR · 3 LEVELSi3i5i7
RAM · 2 LEVELS8 GB16 GB
STORAGE · 2 LEVELS256 GB SSD512 GB SSD
PRICE · 3 LEVELS$1,500$2,000$2,500

Profiles and response format

FULL FACTORIAL3 × 2 × 2 × 3 × 3= 108 profiles
01

Software chooses a smaller, informative set of profiles.

02

Respondents evaluate each selected profile.

03

Preference rating: 1–100
1 = worst · 100 = best

Data collection: 14 selected profiles

#
Brand
RAM
SSD
CPU
Price
Preference
1HP16GB256GBi3$1,50018 2Lenovo16GB256GBi3$1,50053 3HP8GB512GBi5$1,50051 4Dell8GB256GBi7$1,50064 5Dell16GB512GBi7$1,500100 6HP8GB512GBi3$2,00019 7Lenovo8GB256GBi5$2,00034 8Dell16GB512GBi5$2,00076 9HP16GB256GBi7$2,00051 10Dell8GB256GBi3$2,5008 11Lenovo8GB512GBi3$2,50010 12HP16GB256GBi5$2,50020 13HP8GB256GBi7$2,50013 14Lenovo16GB512GBi7$2,50061

Index coding: profiles 1–7

INDEX CODING

Each attribute has one column per level; the selected level receives 1.

#
HP
Dell
Len.
8G
16G
256
512
i3
i5
i7
$15
$20
$25
Pref.
1100011010010018 2001011010010053 3100100101010051 4010101000110064 50100101001100100 6100100110001019 7001101001001034

Index coding: profiles 8–14

INDEX CODING · CONTINUED

One active indicator within each attribute block.

#
HP
Dell
Len.
8G
16G
256
512
i3
i5
i7
$15
$20
$25
Pref.
8010010101001076 9100011000101051 1001010101000018 11001100110000110 12100011001000120 13100101000100113 14001010100100161

Dummy coding: profiles 1–7

DUMMY CODING

Reference levels: HP · 8GB · 256GB · i3 · $1,500.

#
Dell
Len.
16G
512
i5
i7
$20
$25
Pref.
10010000018 20110000053 30001100051 41000010064 510110100100 60001001019 70100101034

Dummy coding: profiles 8–14

DUMMY CODING · CONTINUED

The preference rating remains the dependent variable.

#
Dell
Len.
16G
512
i5
i7
$20
$25
Pref.
81011101076 90010011051 10100000018 110101000110 120010100120 130000010113 140111010161

Conjoint regression: model fit

MULTIPLE R0.988220851
R²0.976580451
ADJUSTED R²0.939109172
SIGNIFICANCE F0.001152106
Regression · df 8 · SS 10073.28784 · MS 1259.16098 · F 26.06210647Residual · df 5 · SS 241.5693032 · MS 48.31386064Total · df 13 · SS 10314.85714

Conjoint regression: part-worth estimates

Level
Coefficient
SE
t
p
Intercept11.158757065.0424391682.2129681070.077813358 Dell23.719397364.6387843485.1132787350.003728175 Lenovo16.558380414.6387843483.5695516690.016051305 16GB RAM16.949152543.8392475684.4147068510.006926083 512GB SSD16.111111113.8422088094.1931898850.008545463 Intel i520.38342754.9061688814.154652640.008869946 Intel i731.37796614.5964201336.8266096640.001028675 $2,000−10.794538614.906168881−2.2001971130.079074267 $2,500−29.97796614.596420133−6.52202480.001267018

Relative attribute importance

Calculate each attribute’s utility range, sum the five ranges, and divide each range by the total.
BRAND

HP 0 · Dell 23.7 · Lenovo 16.6

RAM

8GB 0 · 16GB 16.9

SSD

256GB 0 · 512GB 16.1

CPU

i3 0 · i5 20.4 · i7 31.4

PRICE

$1,500 0 · $2,000 −10.8 · $2,500 −30.0

BRANDRange 23.7

20.0%

RAMRange 16.9

14.3%

SSDRange 16.1

13.6%

CPURange 31.4

26.6%

PRICERange 30.0

25.4%

Importance = attribute range ÷ sum of ranges  ·  Σ ranges = 118.1

The preference equation

PART-WORTH UTILITY MODEL

Preference = 11.2 + 0(HP) + 23.7(Dell) + 16.6(Lenovo)

+ 0(8GB) + 16.9(16GB) + 0(256GB) + 16.1(512GB)

+ 0(i3) + 20.4(i5) + 31.4(i7)

+ 0($1,500) − 10.8($2,000) − 30.0($2,500)

Conjoint analysis estimates the utility weight of each attribute level.

Predict preferences and market shares

ULTRABOOK ADell

16GB · 512GB · i7 · $2,500

Preference = 69.3
ULTRABOOK BLenovo

8GB · 256GB · i3 · $1,500

Preference = 27.8

In-class exercise: conjoint analysis

#
Brand
RAM
SSD
CPU
Price
Pref.
1HP16256i3$1,500252Lenovo16256i3$1,500703HP8512i5$1,500614Dell8256i7$1,500845Dell16512i7$1,5001006HP8512i3$2,000237Lenovo8256i5$2,000428Dell16512i5$2,000889HP16256i7$2,0005110Dell8256i3$2,5001911Lenovo8512i3$2,5002412HP16256i5$2,5001713HP8256i7$2,5001414Lenovo16512i7$2,50075
Run the conjoint regression.Calculate relative attribute importance.Predict shares for A and B.

Exercise solution: conjoint regression

Before revealing the output: what would indicate strong model fit and a statistically significant conjoint model?
MULTIPLE R0.980260922
R²0.960911476
ADJUSTED R²0.898369837
SIGNIFICANCE F0.004006973
Regression · df 8 · SS 11226.80923 · MS 1403.351153 · F 15.3643476Residual · df 5 · SS 456.6907721 · MS 91.33815443Total · df 13 · SS 11683.5

Exercise solution: exact coefficients

Which attribute levels increase preference relative to the reference profile, and which decrease it?
Level
Coefficient
SE
t
p
Intercept20.328248596.9331550462.9320343270.032555847 Dell30.756120536.3781455844.8221101450.004789547 Lenovo26.688323926.3781455844.1843390940.008618757 16GB RAM13.610169495.2788140352.5782627310.049536327 512GB SSD16.277777785.2828856243.0812285060.027431314 Intel i518.64331456.7457887752.7636967480.039660446 Intel i729.064406786.3198964594.5988738840.005846296 $2,000−15.221092286.745788775−2.2563843590.073684799 $2,500−34.664406786.319896459−5.4849643510.002747893

Exercise solution: relative importance

Calculate each attribute range and its share of the total. Reveal the sum first, then the percentages.
BRAND30.8
RAM13.6
SSD16.3
CPU29.1
PRICE34.7
Σ ranges = 30.8 + 13.6 + 16.3 + 29.1 + 34.7 = 124.5
BRAND24.7%
RAM10.9%
SSD13.1%
CPU23.4%
PRICE27.9%

Exercise solution: predicted shares

ULTRABOOK ADell

16GB · 512GB · i7 · $2,500

Preference = 75.4
ULTRABOOK BLenovo

8GB · 256GB · i3 · $1,500

Preference = 47.0

To sum up

CORRELATION
  • Define the correlation coefficient.
  • Interpret its direction and strength.
  • Calculate r with M303 Web Tools.
SIMPLE REGRESSION
  • Use the notation Y, X, a, and b.
  • Estimate the model with M303 Web Tools.
  • Read R² and overall model significance.
  • Interpret intercept and slope estimates and their significance.
  • Make predictions from the estimated model.
MULTIPLE REGRESSION
  • Use the notation Y, X₁ … Xₖ, a, and b₁ … bₖ.
  • Estimate the model with M303 Web Tools.
  • Read R² and overall model significance.
  • Interpret intercept and slope estimates and their significance.
  • Make predictions.
  • Dummy-code categorical predictors.
CONJOINT ANALYSIS
  • Design product profiles from attributes and levels.
  • Dummy-code levels and estimate part-worth utilities.
  • Calculate relative attribute importance.
  • Predict preferences and market shares.

Course wrap-up and action

ONE LAST CHECKKeep every analysis tied to a research question and a decision.

Use Canvas for the current practice assignment, project milestone, and required data files.

01

For each research question, list the variables you will analyze.

02

Choose the method from the number, scale, structure, and roles of those variables.

03

For hypothesis tests, state H₀ and Hₐ before analyzing the data.

04

For regression, specify Y and the X variables; a separate H₀/Hₐ statement is not required for the source project-planning table.