Single Regression

Advanced techniques can be used when there is trend or seasonality, or when other factors (such as price discounts) must be considered.

What is Single Regression?
EXAMPLE: 16 Months of Demand History
EXAMPLE: Building a Regression Model to Handle Trend and Seasonality
EXAMPLE: Causal Modeling

h2. What is Single Regression?

• Develops a line equation y = a + b(x) that best fits a set of historical data points (x,y)
• Ideal for picking up trends in time series data

• Once the line is developed, x values can be plugged in to predict y (usually demand)

• For time series models, x is the time period for which we are forecasting
• For causal models (described later), x is some other variable that can be used to predict demand: o Promotions
  • Price changes
  • Economic conditions
• Etc.

• Software packages like Excel can quickly and easily estimate the a and b values required for the single regression model

h2. EXAMPLE: 16 Months of Demand History

There is a clear upward trend, but also some randomness.

Forecasted demand = 188.55 + 69.43*(Time Period)

Notice how well the regression line fits the historical data,
BUT we aren’t interested in forecasting the past…

Forecasts for May ’05 and June ’05:

May: 188.55 + 69.43*(17) = 1368.86
June: 188.55 + 69.43*(18) = 1438.29

• The regression forecasts suggest an upward trend of about 69 units a month.

• These forecasts can be used as-is, or as a starting point for more qualitative analysis.

h2. EXAMPLE: Building a Regression Model to Handle Trend and Seasonality

Quarter	Period	Demand
Winter 04	1	80
Spring	2	240
Summer	3	300
Fall	4	440
Winter 05	5	400
Spring	6	720
Summer	7	700
Fall	8	880

Regression picks up the trend, but not seasonality effects

Calculating seasonal index: Winter Quarter

• (Actual / Forecast) for Winter quarters:
• Winter ‘04: (80 / 90) = 0.89
• Winter ‘05: (400 / 524.3) = 0.76
• Average of these two = .83
• Interpretation:

• For Winter quarters, actual demand has been, on average, 83% of the unadjusted forecast

Seasonally adjusted forecast model

For Winter quarter

[ -18.57 + 108.57*Period ] * .83

Or more generally:

[ -18.57 + 108.57*Period ] * Seasonal Index

Seasonally adjusted forecasts

Comparison of adjusted regression model to historical demand

Single regression and causal forecast models

• Time series assume that demand is a function of time. This is not always true.
• Examples:
  • Demand as a function of advertising dollars spent
  • Demand as a function of population
• Demand as a function of other factors (ex. – flu outbreak)

• Regression analysis can be used in these situations as well; We simply need to identify the x and y values

EXAMPLE: Causal Modeling

Month	Price per unit	Demand
1	$1.50	7,135
2	$1.50	6,945
3	$1.25	7,535
4	$1.40	7,260
5	$1.65	6,895
6	$1.65	7,105
7	$1.75	6,730
8	$1.80	6,650
9	$1.60	6,975
10	$1.60	6,800

Two possible x variables: Month or Price

Which would be a better predictor of demand?

Demand seems to be trending down over time, but the relationship is weak. There may be a better model . . .

… Demand shows a strong negative relationship to price. Using Excel to develop a regression model results in the following:

• Demand = 9328 – 1481 * (Price)

• Interpretation: For every dollar the price increases, we would expect demand to fall 1481 units.