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SCRC Article Library: Single Regression: Approaches to Forecasting : A Tutorial

Single Regression: Approaches to Forecasting : A Tutorial

Published on: Jan, 25, 2011

by: Cecil Bozarth, PhD

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.

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