Single Regression
Advanced techniques can be used when there is trend or seasonality, or when other factors (such as price discounts) must be considered.
h2.
 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.
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 asis, or as a starting point for more qualitative analysis.
h2.
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
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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