# 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.

• 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

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.
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

For Winter quarter

[ -18.57 + 108.57*Period ] * .83

Or more generally:

[ -18.57 + 108.57*Period ] * Seasonal Index ### 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.