• Drivers?
• What is under Managerial/corporate control?
• Simple vs. complicated?

Enterprise Industries, owners of Fresh Detergent, want to predict demand for their product. In this case, the product is an extra large bottle of Fresh liquid detergent. Given a model for demand, Enterprise can:

• Plan a production schedule
• Estimate production requirements
• Plan inventory requirements
• Estimate sales revenue (and profits?)

Four indicators for 30 sales periods (4 weeks):

• The demand for the extra large sized bottle of Fresh (in 100,000s of bottles) in a sales period
• The price of Fresh in the sales period (in dollars)
• The average competitor price for similar products in the sales period (in dollars)
• Enterprise Industries' advertising expenditures (in $100,000s) targeted toward Fresh in the sales period.
• Later we might incorporate data on the advertising campaigns.

##    Fresh.Demand Fresh.Price Industry.Price Advertising.Spending
## 1          7.38        3.85           3.80                 5.50
## 2          8.51        3.75           4.00                 6.75
## 3          9.52        3.70           4.30                 7.25
## 4          7.50        3.70           3.70                 5.50
## 5          9.33        3.60           3.85                 7.00
## 6          8.28        3.60           3.80                 6.50
## 7          8.75        3.60           3.75                 6.75
## 8          7.87        3.80           3.85                 5.25
## 9          7.10        3.80           3.65                 5.25
## 10         8.00        3.85           4.00                 6.00
## 11         7.89        3.90           4.10                 6.50
## 12         8.15        3.90           4.00                 6.25
## 13         9.10        3.70           4.10                 7.00
## 14         8.86        3.75           4.20                 6.90
## 15         8.90        3.75           4.10                 6.80
## 16         8.87        3.80           4.10                 6.80
## 17         9.26        3.70           4.20                 7.10
## 18         9.00        3.80           4.30                 7.00
## 19         8.75        3.70           4.10                 6.80
## 20         7.95        3.80           3.75                 6.50

Let's have a look at the 3-D.

scatter3d(Fresh.Demand~Advertising.Spending+Price.Difference, 
  data=fresh.data, surface=FALSE, residuals=TRUE, bg="white", 
  axis.scales=TRUE, grid=TRUE, ellipsoid=FALSE)

Conforms to intuition:

• Demand is inversely related to own price.
• Demand is positively related to industry price.
• Advertising enhances demand.

Constructing na"ive confidence intervals:

• Own price and industry price may cancel out.
• -2.36 \(\pm t_{.975, 30-4}\)*0.64={-1.04,-3.68}
• 1.61 \(\pm t_{.025, 30-4}\)*0.30={0.99,2.23}.

How could we test this?

• We can either test a negative equality constraint (\(\beta_{1} = -\beta_{2}\)) or estimate a single parameter for a variable measuring the price difference.
• The former imposes a constraint.
• The latter involves a simple manipulation of the data. \(Fresh.Price - Industry.Price\) and then compare the two models. \[ y_{t} = \beta_{0} + \beta^{*}_{D}(F.P._{t} - I.P._{t}) + \beta_{3}Ad.Spend_{t} + \epsilon_{t} \]