M303 Simple and Multiple Regression II
Where we are
Management problem → research objectives → questions → hypotheses
Exploratory · descriptive · causal
Secondary · observation · qualitative · survey · experiment · sampling
Correlation → simple regression → multiple regression
Learning Objectives
A simple regression with the course Web Tools.
R², overall model significance, coefficients, and coefficient p-values.
Outcomes with an estimated regression equation.
From one predictor to multiple predictors.
Categorical predictors with M − 1 dummy variables.
Previous class review
Correlation distinguishes a dependent variable from an independent variable.
FALSEr = −0.86 indicates a strong negative linear association.
TRUESimple regression predicts one continuous Y from one X.
TRUEIn Y = a + bX, b is the predicted value of Y when X = 0.
FALSEBest Buy regression data
Estimate simple regression with Web Tools
Load the Best Buy data.
Select StoreTraffic as Y.
Select AdSpending as X.
Run the model and inspect all three output sections.
Interpret simple regression output
R² = 0.744
74.4% of variation in store traffic is explained by advertising spending.Significance F = 9.97 × 10⁻⁷
Below 0.05 → the regression model is statistically significant.a = 14,864
b = 0.154
Simple regression output: full source table
Interpret the equation
If advertising spending is $0, predicted store traffic is 14,864.
Each additional $1 of advertising predicts 0.154 additional store visits.
What if ad spending is $100,000?
14,864 + 0.154(100,000) = 30,264What if ad spending is $500,000?
14,864 + 0.154(500,000) = 91,864Correlation vs. regression
In-class exercise: simple regression
How does weekly Coke demand respond to its price?
Estimate a and b.
Predict demand when Coke costs $2.
With a $1 wholesale cost, test prices from $1.50 to $2.50 in $0.10 steps and identify the profit-maximizing price.
Repeat the exercise for Pepsi.
One predictor is not always enough
What is multiple regression?
Multiple linear regression predicts one continuous dependent variable Y from multiple independent variables X₁, X₂, …, Xₖ.
Motivating example: competing prices
What important information is missing?
Coke demand should depend on both Coke’s own price and Pepsi’s price.
SalesCoke = a + b₁PriceCoke + b₂PricePepsiEstimate multiple regression with Web Tools
Load WeeklySoftDrinkSales.xlsx.
Select Sales_Coke as Y.
Select Price_Coke and Price_Pepsi as X variables.
Run the model and read fit, significance, and coefficients.
Weekly soft-drink source rows
Interpret multiple regression output
29.5% of Coke-sales variation is explained.
Adjusted R² = 0.291 · n = 416Significance F = 4.64 × 10⁻³²
Below 0.05 → significant.−414.14 · Coke price
+188.59 · Pepsi price
Multiple regression output: full source table
Interpret the multiple regression equation
If both prices were $0, predicted Coke sales would be 672.17 units.
A $1 increase in Coke’s price predicts 414.14 fewer units, holding Pepsi’s price fixed.
A $1 increase in Pepsi’s price predicts 188.59 more Coke units, holding Coke’s price fixed.
To sum up
Read regression output in order: fit → overall significance → coefficients → prediction.
Simple regression uses one predictor; multiple regression uses X₁ … Xₖ.
Interpret each slope while holding the other predictors fixed.
A fitted equation turns estimated relationships into explicit predictions and decision inputs.
Next class
- Optimize a category-pricing decision with two demand equations.
- Dummy-code a categorical predictor.
- Translate part-worth utilities into attribute importance and predicted preference shares.