Chapter Regression

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CHAPTER 4

CAUSAL FORECASTING WITH REGRESSION

TIME SERIES METHODS

SIMPLE LINEAR REGRESSION

We wish to forecast a dependent variable. The value

of dependent variable is related to an observable

value of one or more independent variables.

We call this process causal forecasting, because the

value of the dependent variable is often caused by,

or at least highly correlated with, the value of the

independent variable.


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we minimize the sum of the squared differencesbetween the actual sales and the sales indicated by

the model. The difference is the error of the

forecast.



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Example

Example


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Example

Example


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Example

If there are 23 housing starts in January of 1996,

we would expect to sell about

24.17 +1.83 23 66 fixtures in February.

Coefficient of determination


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Comments on Regression Regression models are very useful for forecasting when

there is a strong relationship and a time lag between the

dependent variable and the iindependent variable.

If there is no time lag between dependent and

independent variables, i.e., they occur in the same time

period, we cannot forecast future values of the dependent

value unless we use a forecast of the independent

variable, which may introduce additional error in theforecast of the dependent variable.

If causal relationships do not exist, regression is not the

best forecasting method.

Time Series Methods

For short-term forecasting, time series methods are favored.

A time series is simply a time-ordered list of historical data, theunderlying assumption which is that history is a reasonable predictor ofthe future.

There are several time series models and methods to choose from,including a constant, trend, or seasonal model, depending on thehistorical data and our understanding of the underlying process. Constant process

Moving Average

Simple Exponential Smoothing

Trend process

Double Exponential Smoothing

Double Moving Average (Regression)

Seasonal process

Winters Method


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Constant Process-Last Data Point (LPD)

Constant Process- Average all past data

Given T periods ofdata, the average at time T is


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Example

Example


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Constant Process- Moving Average

Rather than take an average of all data points, we might choose

to average only some of the more recent data. This method,

called a moving average, is a compromise between the last data

point and average methods. It averages recent data to reduce

the effect of random fluctuations.

Constant Process- Moving Average


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Constant Process-Simple Exponential Smoothing



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Trend Process-Double Exponential Smoothing


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Solution:

First, compute the averages of the months 1 to 12, and

13 to 24.




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Trend Process- Other Method

Regression, with time as the independent variable,

can be used. Let dt be the demand in period t.

T=1,2,..T.

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Seasonal Process-Winters Method

Many processes naturally have some number of seasons in a year.

If the time periods are weeks, the year would have 52 seasons.

Periods of months and quarters have 12 and 4 seasons in a year,

respectively.

A good model must consider the constant portion of demand, the

trend and seasonality.



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Chapter Regression