1. Identify variables that ou think might explain what you are trying to forecast-initial regression model

2. Collect the data (observations)

3.Check for problematic data points

4. Build regression model and test

5. Use model to forecast

a. linear relationship exists between the independent variables and the dependent variables

b. independent variables are not highly correlated

c. residuals (errors) exhibit a constant variable

d. independent residuals

e. normally distributed residuals

Two ways to check

Scatter Plots: a plot should suggest straight line relationship

Residual Plots: a plot should exhibit a random pattern

The independent variables must not be highly correlated. The accepted rule of thumb is that the absolute value of the correlation, r, does not exceed .90

Excessive correlations among two (collinearity) or more (multicollinearity) independent variables creates several adverse effects

-unstable regression coefficients

-inflated standard errors which leads to type II error

Heteroscedasticity: the condition where the variance of the residuals is not constant

Homoscedasticity: the condition where the variance of teh residuals is constant

To check:

scatterplot: plot should exhibit a random pattern with a relatively uniform variance

The residuals must be independent of each other.

To check:

first, order the data in time sequence from oldest to most recent

Scatter plot: plot should not exhibit a trend or any special pattern

The residuals must be normally distributed, although regression analysis is fairly robust with regard to violation of this condition.

To check:

Histogram: should exhibit a bell shaped curve about zero

• A P-Value represents the probablility of obtaining a value of the test statistic equal to or more extreme than the value obtained for the sample if the null hypothesis is true
• If null hypothesis is rejected it is significant
• If null hypothesis is not rejected it is not significant
• A statistical decision is made by comparing the p-value and the significance level (alpha)
• P value < a then reject Ho
• P value > then fail to reject Ho

Regression Model

• the significance of the overal regression model is determined using Excel by the "Significance F"
• The null hypothesis (Ho) is that the set of independent variables cannot be used to predict the dependent variables (the model is not significant)
• The alternative hypothesis (Ha) is that one, or more of the independent variables can be used to predict the dependent variable (the model is significant)

Independent Variables

• The significance of a specific independent variable (xi) is determined using Excel by the "p-value" associated with the variable
• The null hypothesis (Ho) is that this independent variable cannot be used to predict the dependent variable (this variable is not significant)
• The alternatve hypothesis (Ha) is that this independent variable can be used to predict the dependent variable (this variable is significant)

The coefficiant of determination,R², is used to assess how well the regression model fits the data.

The coefficient of determination represents the percentage of the variation in the dependent variable that is explained, or accounted for, by the regression model

• R² varies between 0 (no fit) to 1 (perfect fit)
• adjusted R² is a refinement of R² which considers the relative values of the sample size (n) and the number of independent variables (k)

Require historical data

-forecasts extrapolate past data into the future

Some of the most commonly used methods

-simple moving average

-weighted moving average

-exponential smoothing

Time series forecasts have been shown to typically yield more accurate short-term forecasts

1.Identify time series data components
2.Choose appropriate time series methods
3.Evaluate different methods

-calculate forecasts using historical data

-evaluate forecasting errors for each method

-choose method which performs best

4.Implement method of choice

5. Monitor forecast performance

The naive forecast for the next period equals the demand for the current period.

F_{t + 1}= A_t

Period 1 demand =15

Period 2 Forecast = 15

• Simple moving average places the same weight on each time period
• Method works well when the demnad is fairly stable over time
• Method does not do a good job of forecasting when a trend is present
• The forecast lags the actual demand because of averaging effect.
• Decreasing the number of periods in forecast, creates a more responsive forecast
  

F_t+1= A_t + A_t-1/2

Period 1 Demand = 15

Period 2 Demand =28

Period 3 Forecast = 21.5

• The larger n, the smoother the forecast and the less responsive it is to changes in demand.
• The smaller n, the forecasts is more responsive to changes in demand

• Weighted moving average allows different emphasis to be placed on different time periods
• Method works well when the demand is fairly stable over time
• Method does not do a good job of forecasting when a trend is present
• The forecast lags the actual demand because of averaging effect
• Weights tend to be based on the forecaster's experience
• Decreasing the number of periods in forecast and/or increasing the size of the weights for more recent demand creates a more responsive forecast

F_t+1= 3A_t + 2A_t-1/3+2

Period 1 Demand= 15

Period 2 Demand= 28

Period 3 Forecast = 22.8

• Exponential smoothing is suitable for data without a trend.
• Exponential smoothing forecasting is a sophisticated weighterd moving average forecasting.
• This forecast lags the actual demand because of averaging effect.

F_t+1= F_t + 0.3 (A_t-F_t)

Period 1 Demand=15

Period 1 Forecast= 15

Period 2 Demand = 28

Period 2 Forecast= 15

Smoothing parameter = 0.3

Period 3 Forecast=18.9

The exponential smoothing parameter equation places exponetially larger weights on more recent data

• A larger smoothing parameter emphasizes recent demand and yields a forecast which is more responsive to changes in actual demand
• A smaller smoothing parameter places more uniform empahsis on demand and yields a forecast which is more stable and less responsive to changes in actual demand.

• The ultimate goal of any forecasting endeavor is to have an accurate and unbiased forecast.
• The cost associated with prediction error can be substanial and include the cost of lost sales, safety stock, unsatisfied customers, and loss of goodwill.

Forecast Error, which is the difference between actual demand and the forecast, is used to evaluate the accuracy of a forecasting model.

Error (E_t)= Actual_t-Forecast_t

For all measures of forecast accuracy, the closer the measure is to 0, the better the forecast.

1. Actual measures of forecast accuracy

-These measures are expressed in the same unit of measurement as the data.

Relative measures of forecast accuracy

-These measures provide a perspective of the magnitude of the forecast error relative to actual demand

Common absolute measures to evaluate forecast accuracy are:

1. Running Sum of Forecast Error (RSFE)

-Mean Forecast Error (MFE)

2. Mean Absolute Deviation (MAD)

3. Mean Squared Error (MSE)

RSFE=Σ (A_t-F_t)= Σ E_t

MFE= Σ E_t/n= RSFE/n

-Measures the average magnitude or size of the forecast errors (central tendency) or bias.

-Bias represents the tendency of a forecast to be consistently higher or lower than the actual demand.

• A positive RSFE (and MFE) indicates that the forecasts generally are low-the forecasts underestimate demand and stock outs may occur.
• A negative RSFE (and MFE) indicates that the forecasts generally are high- the forecasts overestimate demand resulting in higher inventory carrying costs.
• A zero RSFE (and MFE) indicates that the forecast is unbiased. This does not imply that the forecast was necessarily accurate.

MAD = Σ lE_tl /n

-Measures the average magnitude of the forecast errors without regard to direction of error.

• The MAD is a widely used indicator of forecast accuracy. It provides a simple way to compare different forecast methods.
• A MAD value greater than zero indicates the forecast either overestimates or underestimates demand.
• A zero MAD indicates that the forecast exactly predicted demand over the entire evaluation period.

MSE = Σ E_t²/n

-It is sensitive to large errors.

-In general, models that yield forecasts with many small errors and a few very large ones are not desirable.

MAPE= (Σ lE_t/A_tl) (100/n)

-Measures the average relative magnitude of the forecast errors, expressed as a percentage.

Tracking Signal = RSFE / MAD

• Used to monitor the performance of a forecast over time.
• Tracks forecast bias relative to the average magnitude of the forecast error.
• The tracking signal is updated after every period.

• A "control chart" is often used to monitor the tracking signal.
• If the tracking signal falls outside present control limits, there is a bias problem with the forecast method and reevaluation of the forecast method is warranted.

Some inventory experts suggest using tracking signal control limits of ±4 for high-volume items and ±8 for low-volume items

Note: As higher limits are instituted, there is a greater probability of finding exceptions that require no action, but this also means catching changes in demand sooner.