Lecture 07 forecasting  causal forecasting models regression analysis
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    Lecture 07 forecasting  causal forecasting models regression analysis Lecture 07 forecasting causal forecasting models regression analysis Document Transcript

    • Unit 2 Management of Conversion System Chapter 3: ForecastingLesson 7:- Causal Forecasting Models: Regression AnalysisLearning ObjectivesAfter reading this lesson you will understand Causal forecasting models Linear regression analysis Multiple regression analysis Monitoring and controlling forecastsGood Morning students, today we are going to introduce the concept of what isknown as the Causal Forecasting Models. Friends, by now we have progressedmuch in the journey of learning forecasting. Before coming end to this journey weneed to learn about causal forecasting, linear and multiple regression analysis, andhow to monitor and control forecasted values.But I’m getting carried away.First thing first.Let us first start with causal forecasting model.Causal forecasting modelsCausal forecasting models usually consider several variables that are related to thevariable being predicted. It utilizes time series related to the variable being forecast in aneffort to better explain the cause of a time series behaviour. For example, sales of aproduct depend on various factors.Some of these are listed below: Firm’s advertisement budget The price charged Competitor’s prices Promotional strategies
    • Regression analysis is the tool most often used in developing these causal models.The complete discussion of regression analysis is beyond the scope of this class. We willdiscuss a few underlying concepts to get insight about how this technique is used. First ofall, according to the logic and methodology of regression analysis, the time series valuethat we want to forecast is referred to as the dependent variable. The variables that we tryto relate to the dependent variable are referred to as independent variables, and thefunction that is developed to relate the dependent variable to the independent variables iscalled the estimated regression function. Thus if we can identify a good set ofindependent or predictor variables, we may be able to develop an estimated regressionfunction for predicting or forecasting the time series.Linear regression analysisThe most common quantitative causal forecasting model is linear regression analysis. Bylinear, we mean an equation of degree 1.The equation given below fulfills this criterion: ^ Y = a + bxWhere, ^ Y = value of the dependent variable a = y – axis intercept b = slope of the regression line x = independent variableMultiple Regression AnalysisThis is the next step in regression analysis and is considered to be an improvement overthe linear regression method discussed above.The equation in this case can be represented as: ^ Y = a + b1x1 + b2x2
    • The construction of regression line will be clearer by taking an example.ExampleSymphony is a construction company that builds offices in Delhi. Over time, thecompany has found that its rupee volume of renovation work is dependent on the Delhiarea payroll. The following table lists Symphony’s revenues and the amount of moneyearned by wage earners in Delhi during the years 1991 – 1996.Symphony’s sales (Rs in thousands), y Local payroll (Rs in lakhs), x2.0 13.0 32.5 42.0 22.0 13.5 7Symphony’s management wants to establish a mathematical relationship that will help itpredict sales. First, they need to determine whether there is a straight-line (linear)relationship between area payroll and sales, so they plot the known data on a scatterdiagram. Fig. 3.3 Scatter diagramIt appears from the six data points that a slight positive relationship exists between theindependent variable, payroll, and the dependent variable, sales. As payroll increases,
    • Symphony’s sales tend to be higher. We can find a mathematical equation by using theleast squares regression approach.Sales Payroll x2 xyy x2.0 1 1 2.03.0 3 9 9.02.5 4 16 10.02.0 2 4 4.02.0 1 1 2.03.5 7 49 24.5∑y = 15.0 ∑x = 18 ∑x2 = 80 ∑xy = 51.5−X= ∑X =3 n−Y= ∑Y = 2.5 nb = .25a = 1.75The estimated regression equation, therefore, is: Y = 1.75 + .25xOr Sales = 1.75 + .25 payrollIf the prediction is that Delhi area payroll will be Rs600 lakhs next year, we can estimatesales for Symphony with the regression equation: Sales (in thousands) = 1.75 + .25(6) = 3.25i.e. Sales = Rs3250
    • The final part of this example illustrates a central weakness of causal forecasting likeregression. Even though we have computed a regression equation, it is necessary toprovide a forecast of the independent variable x – in this case, payroll – before estimatingthe dependent variable y for the next time period.To measure the accuracy of the regression estimates we need to compute the standarderror of the estimate, Sy,x. This is called the standard deviation of the regression. It isexpressed as ∑(y − y ) 2 c Sy,x = n−2Where y = y-value of each data point yc = the computed value of the dependent variable, from the regression equation n = the number of data pointsThe next issue in today’s agenda, coming up now:-Monitoring and controlling forecastsThe monitoring and controlling forecasts determine the extent of success of businessforecasting. It helps the manager to focus on the adequacy or redundancy (as the casemay be) of the forecasting estimates and hence makes remedial/corrective measurespossibleTracking signalA tracking signal assumes great significance in this regard. It is a measurement of howwell the forecast is predicting actual values.The tracking signal is computed as the running sum of the forecast errors (RSFE) dividedby the mean absolute deviation (MAD). Tracking signal = RSFE / MAD = ∑(Actual demand in period I – Forecast demand in period I) / MAD
    • where MAD = ∑ |Forecast errors| / nPositive tracking signals indicate that demand is greater than forecast. Negative signalsmean that demand is less than forecast. A good tracking signal, that is, one with a lowRSFE, has about as much positive bias as it has negative bias. In other words, smallbiases are okay, but the positive and negative ones should balance one another so thetracking signal centers closely on zero bias. + Upper control limit 0 MADs Acceptable range - Lower control limit Time Tracking signal(If tracking signal lies within +6 and –6 the forecast could be considered to beacceptable)To make it clear we take an exampleExample Quarterly sales are given. Calculate tracking signal
    • Quarter Forecast Actual Error RSFE |FE| MAD Tracking Sales sales signal 1 100 90 -10 -10 10 10.0 -1 2 100 95 -5 -15 5 7.5 -2 3 100 115 +15 0 15 10.0 0 4 110 100 -10 -10 10 10.0 -1 5 110 125 +15 +5 15 11.0 +.5 6 110 140 +30 +35 30 14.2 +2.5 MAD = ∑ |Forecast Errors|/n = 85/6 = 14.2 Tracking signal = RSFE/ MAD = 35/14.2 = 2.46Having discussed quite a few concepts, now let us apply these in actual practice.POM in practice - A short range forecasting system*The company considered in this case was a producer of residential and light commercialair-conditioners and heating units. With the recession of 1974 – 75, the sudden decline inhousing starts caused current forecasts to be very optimistic. The company had lost faithin their computer approach and was relying mostly on judgment. The old system used a12-month moving average adjusted by an appropriate seasonal factor that was obtainedfrom the previous 3 years’ data. Four-month forecasts were necessary to accommodatemanufacturer’s lead times.Analysis of this existing system showed that its major problems were an inability torespond quickly to sudden changes in demand and total lack of any forward-lookingprocedure. Consequently, a new system was proposed. This was composed of twoindependent segments: an objective forecasting system based on historical data and
    • projections of certain economic variables and a subjective forecast generated byjudgments of regional field managers. Theses were combined into a final forecast asshown I the figureForward-lookingObjective forecastUsing regression Objective ForecastBackward-lookingObjective forecastUsing adaptiveSmoothing Final forecastSubjectiveField forecastsFig Proposed forecasting system
    • In order to adapt to sudden changes in demand, an adaptive smoothing technique wasused. The adaptive smoothing method provided the basis for a backward-looking forecastrelying purely on historical data for the heating and air-conditioning company.The forward-looking objective forecast was based on regression analysis. From a list ofpotentially influential economic indicators, the following list was selected usingstatistical analysis: 1. Heating units Private housing starts. Private investment-residential structures. Private, nonfarm, single-family housing starts. 2. Cooling units Total gross private domestic investment (PDIC). Private housing starts (HST). Government purchases of goods and services (GVTC).A typical regression equation that resulted wasDeseasonalised cooling units = -57,725.5 + 292.058 (PDIC) + 7822.676 (HST) + 216.535 (GVTC)Five regional managers for their respective districts generated subjective forecasts. Thesewere combined with the two objective forecasts in order to obtain the final forecast.Comparisons of actual orders versus the regional forecasts were made to track theperformance of the system and to provide feedback to the regional managers. The new method, developed with close cooperation of the company’s personnel,resulted in more accurate forecasts than were previously generated, and plans for usingthis method on a regular basis were instituted.With that, we have come to the end of today’s discussions. I hope it has been anenriching and satisfying experience. See you around in the next lecture. Take care.Bye.