M303 Regression III and Conjoint Analysis
Where we are
Management problem → research objectives → questions → hypotheses
Exploratory · descriptive · causal
Secondary · observation · qualitative · survey · experiment · sampling
Regression applications → conjoint utilities → product decisions
Learning Objectives
Multiple regression to category pricing and diamond valuation.
Product profiles from attributes and levels.
Part-worth utilities with dummy-coded regression.
Relative attribute importance and predicted preference shares.
Previous class review
Correlation measures the extent to which two continuous variables move together.
Regression generates a mathematical function linking the dependent variable to the independent variable(s).
A correlation coefficient by itself provides a prediction equation.
Continuous predictors must be dummy coded, while categorical predictors can be entered directly.
In-class exercise 1: category pricing
Estimate Pepsi demand.
Estimate the intercept and slopes.
Assume both wholesale costs are $1.
Test each brand’s price from $1.50 to $2.50 in $0.10 steps.
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.
Diamond regression: interpret and predict
Interpret the intercept and slopes.
Predict prices for:
- 1 carat · Fair
- 1 carat · Ideal
- 2 carats · Very Good
From regression to conjoint
Build an ultrabook from attributes and levels
Profiles and response format
Software chooses a smaller, informative set of profiles.
Respondents evaluate each selected profile.
Preference rating: 1–100
1 = worst · 100 = best
Data collection: 14 selected profiles
Index coding: profiles 1–7
Each attribute has one column per level; the selected level receives 1.
Index coding: profiles 8–14
One active indicator within each attribute block.
Dummy coding: profiles 1–7
Reference levels: HP · 8GB · 256GB · i3 · $1,500.
Dummy coding: profiles 8–14
The preference rating remains the dependent variable.
Conjoint regression: model fit
Conjoint regression: part-worth estimates
Relative attribute importance
HP 0 · Dell 23.7 · Lenovo 16.6
8GB 0 · 16GB 16.9
256GB 0 · 512GB 16.1
i3 0 · i5 20.4 · i7 31.4
$1,500 0 · $2,000 −10.8 · $2,500 −30.0
The preference equation
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)
Predict preferences and market shares
16GB · 512GB · i7 · $2,500
8GB · 256GB · i3 · $1,500
In-class exercise: conjoint analysis
Exercise solution: conjoint regression
Exercise solution: exact coefficients
Exercise solution: relative importance
Exercise solution: predicted shares
16GB · 512GB · i7 · $2,500
8GB · 256GB · i3 · $1,500
To sum up
- Define the correlation coefficient.
- Interpret its direction and strength.
- Calculate r with M303 Web Tools.
- 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.
- 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.
- 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
Use Canvas for the current practice assignment, project milestone, and required data files.
For each research question, list the variables you will analyze.
Choose the method from the number, scale, structure, and roles of those variables.
For hypothesis tests, state H₀ and Hₐ before analyzing the data.
For regression, specify Y and the X variables; a separate H₀/Hₐ statement is not required for the source project-planning table.