# Single Regression: Approaches to Forecasting : A Tutorial

Published on: Jan, 25, 2011

## 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

- 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

### 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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