Single Regression: Approaches to Forecasting : A Tutorial

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.