Term
Causal Modeling Using Regression Analysis 

Definition
1. Identify variables that ou think might explain what you are trying to forecastinitial regression model
2. Collect the data (observations)
3.Check for problematic data points
4. Build regression model and test
5. Use model to forecast 


Term
Necessary Conditions for Regression Analysis 

Definition
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 


Term

Definition
Two ways to check
Scatter Plots: a plot should suggest straight line relationship
Residual Plots: a plot should exhibit a random pattern 


Term
Correlation Among Independent Variables 

Definition
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 


Term

Definition
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 


Term

Definition
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 


Term
Normally Distributed Residuals 

Definition
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 


Term

Definition
 A PValue 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 pvalue and the significance level (alpha)
 P value < a then reject Ho
 P value > then fail to reject Ho



Term
Hypothesis Testing: The Model 

Definition
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)



Term
Hypothesis Model: The Variables 

Definition
Independent Variables
 The significance of a specific independent variable (xi) is determined using Excel by the "pvalue" 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)



Term
Coefficient of Determination 

Definition
The coefficiant of determination,R^{2}, 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
 R^{2} varies between 0 (no fit) to 1 (perfect fit)
 adjusted R^{2} is a refinement of R^{2} which considers the relative values of the sample size (n) and the number of independent variables (k)



Term
Time Series Forecasting Models 

Definition
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 shortterm forecasts 


Term
Developing a Time Series Forecast 

Definition
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 


Term

Definition
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 


Term

Definition
 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



Term

Definition
F_{t+1}= A_{t} + A_{t1}/2
Period 1 Demand = 15
Period 2 Demand =28
Period 3 Forecast = 21.5 


Term
Simple Moving Average: Choosing n 

Definition
 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



Term

Definition
 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



Term

Definition
F_{t+1}= 3A_{t} + 2A_{t1}/3+2
Period 1 Demand= 15
Period 2 Demand= 28
Period 3 Forecast = 22.8 


Term
Weighted Moving Average: Choosing n 

Definition
The smaller the eights w_{i} for more recent demand and the more weights (larger n), the smoother the forecast and less responsive it is to changes in demand. 


Term

Definition
 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.



Term
Exponential Smoothing Example 

Definition
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



Term
Choosing the Smoothing Parameter 

Definition
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.



Term
Linear Regression Formula 

Definition


Term

Definition
 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.



Term

Definition
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.



Term
Measures of Forecast Accuracy 

Definition
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 


Term
Absolute Measures of Forecast Accuracy 

Definition
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) 


Term
Running Sum of Forecast Error and Mean Forecast Error Formulas 

Definition
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. 


Term

Definition
 A positive RSFE (and MFE) indicates that the forecasts generally are lowthe 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.



Term
Mean Absolute Deviation Formula 

Definition
MAD = Σ lE_{t}l /n
Measures the average magnitude of the forecast errors without regard to direction of error. 


Term

Definition
 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.



Term

Definition
MSE = Σ E_{t}^{2}/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. 


Term
Mean Absolute Percent Error 

Definition
MAPE= (Σ lE_{t}/A_{t}l) (100/n)
Measures the average relative magnitude of the forecast errors, expressed as a percentage. 


Term

Definition
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.



Term
Monitoring Forecast Errors 

Definition
 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.



Term
Tracking Signal Guidelines 

Definition
Some inventory experts suggest using tracking signal control limits of ±4 for highvolume items and ±8 for lowvolume 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. 

