**1. **Causal Forecasting by Gordon Lloyd

**2. **What will be covered? What is forecasting?
Methods of forecasting
What is Causal Forecasting?
When is Causal Forecasting Used?
Methods of Causal Forecasting
Example of Causal Forecasting

**3. **What is Forecasting?
Forecasting is a process of estimating the unknown
There are many uses for forecasting. Every industry has a need to predict the ?unknown? whether it be in production, manufacturing, retail, or service industry. Forecasting helps management plan for the future, whether it be in the short- range plans or long-range. Forecasting is NOT 100% accurate and can never be assumed to pinpoint There are many uses for forecasting. Every industry has a need to predict the ?unknown? whether it be in production, manufacturing, retail, or service industry. Forecasting helps management plan for the future, whether it be in the short- range plans or long-range. Forecasting is NOT 100% accurate and can never be assumed to pinpoint

**4. **Business Applications Basis for most planning decisions
Scheduling
Inventory
Production
Facility Layout
Workforce
Distribution
Purchasing
Sales
There are many other applications for forecasting. Use examples from your industry or business.There are many other applications for forecasting. Use examples from your industry or business.

**5. **Methods of Forecasting Time Series Methods
Causal Forecasting Methods
Qualitative Methods Times Series Methods - methods that use historical data over a given period of time to estimate future demand.
Examples ? moving average, weighted moving average, exponential smoothing, and adjusted exponential smoothing
Regressions or Causal Forecasting Methods - A model in which the variable of interest (the dependent variable) is related to various explanatory variables (or causal variables) based on a specified theory.
Examples ? regression, econometric models, input-output Models, and simulation Modeling
Qualitative Methods ? forecasting based on managements judgment, expertise, and opinion.Times Series Methods - methods that use historical data over a given period of time to estimate future demand.
Examples ? moving average, weighted moving average, exponential smoothing, and adjusted exponential smoothing
Regressions or Causal Forecasting Methods - A model in which the variable of interest (the dependent variable) is related to various explanatory variables (or causal variables) based on a specified theory.
Examples ? regression, econometric models, input-output Models, and simulation Modeling
Qualitative Methods ? forecasting based on managements judgment, expertise, and opinion.

**6. **What is Causal Forecasting?
Causal forecasting methods are based on the relationship between the variable to be forecasted and an independent variable.?

**7. **When Is Causal Forecasting Used? Know or believe something caused demand to act a certain way
Demand or sales patterns that vary drastically with planned or unplanned events
Examples of a variable that causes demand to act a certain way:
Sales of ice cream increase when temperature is high
New home starts increase when interest rates are low
Number of employees increase when demand increases
Demand for lumber increases when new home starts are up
An planned event could be a sale or and advertising promotion.
An unplanned event could be a snow storm or severe weather, strike, or materials shortages.Examples of a variable that causes demand to act a certain way:
Sales of ice cream increase when temperature is high
New home starts increase when interest rates are low
Number of employees increase when demand increases
Demand for lumber increases when new home starts are up
An planned event could be a sale or and advertising promotion.
An unplanned event could be a snow storm or severe weather, strike, or materials shortages.

**8. **Types of Causal Forecasting
Regression
Econometric models
Input-Output Models:
Regression ? a mathematical equation relates a dependent variable to one or more independent variables that are believed to influence the dependent variable
Econometric models - system of interdependent regression equations that describe some sector of economic activity
Input-Output Models - describes the flows from one sector of the economy to another, and so predicts the inputs required to produce outputs in another sector Regression ? a mathematical equation relates a dependent variable to one or more independent variables that are believed to influence the dependent variable
Econometric models - system of interdependent regression equations that describe some sector of economic activity
Input-Output Models - describes the flows from one sector of the economy to another, and so predicts the inputs required to produce outputs in another sector

**9. **Regression Analysis Modeling Pros
Increased accuracies
Reliability
Look at multiple factors of demand
Cons
Difficult to interpret
Complicated math
These are just a few of the pros and cons of regression analysis. Because you are using multiple variable to determine the forecasted demand the results tend to be more accurate and reliable. This of course depends on how strong the relationship is that you are comparing. Once again no model will forecast demand 100%.
Some of the cons involved with regression analysis are the math involved and the interpretation of the results. With the example that will follow we will see that by using excel we can quickly and without using any math, create a model for forecasting. As for the interpretation of the data, the level of interpretation will depend on what information we are trying to use. For our example today we will look at interpreting the data in the most simplistic way possible.These are just a few of the pros and cons of regression analysis. Because you are using multiple variable to determine the forecasted demand the results tend to be more accurate and reliable. This of course depends on how strong the relationship is that you are comparing. Once again no model will forecast demand 100%.
Some of the cons involved with regression analysis are the math involved and the interpretation of the results. With the example that will follow we will see that by using excel we can quickly and without using any math, create a model for forecasting. As for the interpretation of the data, the level of interpretation will depend on what information we are trying to use. For our example today we will look at interpreting the data in the most simplistic way possible.

**10. **Linear RegressionLine Formula
y = a + bx
y = the dependent variable
a = the intercept
b = the slope of the line
x = the independent variable
This is a simple algebraic formula. It simply defines the shape of a line. When used with regression analysis the y or dependent variable represents the demand. This is the number we are trying to forecast. The x or independent variable represents the item that directly influences the shape of the line.This is a simple algebraic formula. It simply defines the shape of a line. When used with regression analysis the y or dependent variable represents the demand. This is the number we are trying to forecast. The x or independent variable represents the item that directly influences the shape of the line.

**11. **Linear Regression Formulas
a = Y ? bX
b = ?xy ? nXY
?x? - nX?
a = intercept
b = slope of the line
X = ?x = mean of x
n the x data
Y = ?y = mean of y
n the y data
n = number of periods Once again the y or dependent variable represent the demand, the number we are trying forecast. The x is the independent variable or the item that directly influences the shape of the line. A gives us the point at which the line crosses the x-axis. B tells who steep or flat the line is.Once again the y or dependent variable represent the demand, the number we are trying forecast. The x is the independent variable or the item that directly influences the shape of the line. A gives us the point at which the line crosses the x-axis. B tells who steep or flat the line is.

**12. **Correlation Measures the strength of the relationship between the dependent and independent variable
Once a model has been developed and tested, the effectiveness of the model needs to be determined. Correlation is used to determine how strong the relationship between the dependent and independent variables are.Once a model has been developed and tested, the effectiveness of the model needs to be determined. Correlation is used to determine how strong the relationship between the dependent and independent variables are.

**13. **Correlation Coefficient Formula
r = ______n?xy - ?x?y______
v[n?x? - (?x)?][n?y? - (?y)?]
______________________________________
r = correlation coefficient
n = number of periods
x = the independent variable
y = the dependent variable

**14. **Coefficient of Determination Another measure of the relationship between the dependant and independent variable
Measures the percentage of variation in the dependent (y) variable that is attributed to the independent (x) variable
r = r? The coefficient of determination is another way in which we can determine the effectiveness of the regression model. The coefficient of determination measures what percentage of the dependent variable (y) is attributed to the independent variable (x). The coefficient is figured by squaring r from the correlation formula.The coefficient of determination is another way in which we can determine the effectiveness of the regression model. The coefficient of determination measures what percentage of the dependent variable (y) is attributed to the independent variable (x). The coefficient is figured by squaring r from the correlation formula.

**15. **Example Concrete Company
Forecasting Concrete Usage
How many yards will poured during the week
Forecasting Inventory
Cement
Aggregate
Additives
Forecasting Work Schedule A local concrete company (XYZ Concrete) has determined that there is a direct correlation between housing starts and the amount of inventory it carries and the number of drivers it schedules. Each week the number of housing starts are published in the local newspaper. XYZ knows that approximately two weeks after the numbers are published work will begin on the houses. XYZ wants to develop a forecasting model to help it determine the amount of inventory it will need to have on hand and the number of drivers it needs to schedule.A local concrete company (XYZ Concrete) has determined that there is a direct correlation between housing starts and the amount of inventory it carries and the number of drivers it schedules. Each week the number of housing starts are published in the local newspaper. XYZ knows that approximately two weeks after the numbers are published work will begin on the houses. XYZ wants to develop a forecasting model to help it determine the amount of inventory it will need to have on hand and the number of drivers it needs to schedule.

**16. **Example of Linear Regression # of Yards of
Week Housing starts Concrete Ordered
x y xy x? y?
1 11 225 2475 121 50625
2 15 250 3750 225 62500
3 22 336 7392 484 112896
4 19 310 5890 361 96100
5 17 325 5525 289 105625
6 26 463 12038 676 214369
7 18 249 4482 324 62001
8 18 267 4806 324 71289
9 29 379 10991 841 143641
10 16 300 4800 256 90000
Total 191 3104 62149 3901 1009046
This data represent data accumulated from the past 10 weeks. X represent the number of housing starts and y represent the yards of concrete poured during that week. In the next column we multiplied x times y. This number is required as part of the linear regression formula. The last two columns show that the x value and the y value are squared, this will also be needed as part of the regression formula.This data represent data accumulated from the past 10 weeks. X represent the number of housing starts and y represent the yards of concrete poured during that week. In the next column we multiplied x times y. This number is required as part of the linear regression formula. The last two columns show that the x value and the y value are squared, this will also be needed as part of the regression formula.

**17. **Example of Linear Regression X = 191/10 = 19.10
Y = 3104/10 = 310.40
b = ?xy ? nxy = (62149) ? (10)(19.10)(310.40)
?x? -nx? (3901) ? (10)(19.10)?
b = 11.3191
a = Y - bX = 310.40 ? 11.3191(19.10)
a = 94.2052
This slide shows the numbers from the previous slide being plugged into the formula.This slide shows the numbers from the previous slide being plugged into the formula.

**18. **Example of Linear Regression Regression Equation
y = a + bx
y = 94.2052 + 11.3191(x)
Concrete ordered for 25 new housing starts
y = 94.2052 + 11.3191(25)
y = 377 yards
Once a and b are determined, those number are put into the regression formula. In order to finish the example lets say that the published number of housing start will be 25, the x value. Put the 25 into the formula and do the calculations. The demand (y) is 377 yards. Once you know what your estimated demand is going to be you can order inventory and prepare the drivers schedule.Once a and b are determined, those number are put into the regression formula. In order to finish the example lets say that the published number of housing start will be 25, the x value. Put the 25 into the formula and do the calculations. The demand (y) is 377 yards. Once you know what your estimated demand is going to be you can order inventory and prepare the drivers schedule.

**19. **Correlation Coefficient Formula
r = ______n?xy - ?x?y______
v[n?x? - (?x)?][n?y? - (?y)?]
______________________________________
r = correlation coefficient
n = number of periods
x = the independent variable
y = the dependent variable Once we have finished the calculations for the regression model we need to determine the strength of the model. In order to do this we will use the correlation coefficient formula. All numbers needed will come from the data table at the beginning of the example.
Once we have finished the calculations for the regression model we need to determine the strength of the model. In order to do this we will use the correlation coefficient formula. All numbers needed will come from the data table at the beginning of the example.

**20. **Correlation Coefficient r = ______n?xy - ?x?y______
v[n?x? - (?x)?][n?y? - (?y)?]
r = 10(62149) ? (191)(3104)
v[10(3901)-(3901)?][10(1009046)-(1009046)?]
r = .8433
The numbers used in the formula are taken directly from the data table at the start of the problem and put into the formula where required. The numbers used in the formula are taken directly from the data table at the start of the problem and put into the formula where required.

**21. **Coefficient of Determination r = .8433
r? = (.8433)?
r? = .7111

**22. **Excel Regression Example Now we will use the data analysis function in excel to come up with the same numbers. The data will need to be imputed into a excel spreadsheet. The only data required is the housing starts and the yards of concrete ordered columns.
Step 1 ? Click on tools in the menu bar.
Step 2 ? Click on data analysis
Step 3 ? Go through the list until you come to regression. Highlight regression and click ok.
Step 4 ? This brings you to a regression wizard. The first field asks for the y data. This is the dependent data or in this case the yardage ordered. Left click in the first entered field and hold the button down as you drag the mouse to the bottom of the data. Once this is done go to the field asking for the x data and repeat the process just completed for the y data.
Step 5 ? All other field can be left alone. Click ok and a regression analysis table will be shown.
The following slide shows the table.Now we will use the data analysis function in excel to come up with the same numbers. The data will need to be imputed into a excel spreadsheet. The only data required is the housing starts and the yards of concrete ordered columns.
Step 1 ? Click on tools in the menu bar.
Step 2 ? Click on data analysis
Step 3 ? Go through the list until you come to regression. Highlight regression and click ok.
Step 4 ? This brings you to a regression wizard. The first field asks for the y data. This is the dependent data or in this case the yardage ordered. Left click in the first entered field and hold the button down as you drag the mouse to the bottom of the data. Once this is done go to the field asking for the x data and repeat the process just completed for the y data.
Step 5 ? All other field can be left alone. Click ok and a regression analysis table will be shown.
The following slide shows the table.

**23. **Excel Regression Example This is an example of what the regression table looks like. For our purposes we will be looking at just a few of the fields in this table. The following slide isolated these fields.This is an example of what the regression table looks like. For our purposes we will be looking at just a few of the fields in this table. The following slide isolated these fields.

**24. **Excel Regression Example To finish the linear regression formula we need to look at the last two rows under the heading coefficients. The intercept value represents the (a) value. Put this value into the regression equation. The x variable value, from the table, represents the (b) value. Insert this value into the regression equation. Once again the x value that needs to be determined from the published reports.
To finish the linear regression formula we need to look at the last two rows under the heading coefficients. The intercept value represents the (a) value. Put this value into the regression equation. The x variable value, from the table, represents the (b) value. Insert this value into the regression equation. Once again the x value that needs to be determined from the published reports.

**25. **Compare Excel to Manual Regression Manual Results
a = 94.2052
b = 11.3191
y = 94.2052 + 11.3191(25)
y = 377 Excel Results
a = 94.2052
b = 11.3191
y = 94.2052 + 11.3191(25)
y = 377 If we compare the manual results to the excel results we can see that they are the same. There may be some variance in between the numbers but should be insignificant.If we compare the manual results to the excel results we can see that they are the same. There may be some variance in between the numbers but should be insignificant.

**26. **Excel Correlation and Coefficient of Determination Multiple R represents r from the correlation coefficient formula.
R Square represents the r being squared.Multiple R represents r from the correlation coefficient formula.
R Square represents the r being squared.

**27. **Compare Excel to Manual Regression Manual Results
r = .8344
r? = .7111 Excel Results
r = .8344
r? = .7111 If we compare the manual results to the excel results we can see that they are the same. There may be some variance in between the numbers but should be insignificant.
If we compare the manual results to the excel results we can see that they are the same. There may be some variance in between the numbers but should be insignificant.

**28. **Conclusion Causal forecasting is accurate and efficient
When strong correlation exists the model is very effective
No forecasting method is 100% effective
Though some may perceive causal forecasting to be hard and difficult, it is accurate and efficient. When strong correlation exists between the variables, the regression model is very effective in determining demand. It should be noted that no forecasting method is going to be 100% effective. In fact, forecasting will never accurately predict demand. It does however give a prediction that may closely resemble actual results. Though some may perceive causal forecasting to be hard and difficult, it is accurate and efficient. When strong correlation exists between the variables, the regression model is very effective in determining demand. It should be noted that no forecasting method is going to be 100% effective. In fact, forecasting will never accurately predict demand. It does however give a prediction that may closely resemble actual results.

**29. **Reading List Lapide, Larry, New Developments in Business Forecasting, Journal of Business Forecasting Methods & Systems, Summer 99, Vol. 18, Issue 2
http://morris.wharton.upenn.edu/forecast, Principles of Forecasting, A Handbook for Researchers and Practitioners, Edited by J. Scott Armstrong, University of Pennsylvania
www.uoguelph.ca/~dsparlin/forecast.htm,
Forecasting