Ch04 forecasting
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This document discusses various forecasting techniques used to predict future events and trends. It describes short, medium, and long-range forecasts used for production planning, budgeting, and new product development. Both qualitative methods like executive opinion and surveys, and quantitative methods like time series analysis, moving averages, and regression are covered. The key factors influencing forecasts like product life cycles and demand trends are also explained.
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Ch04 forecasting
- 1. 4-1 What is Forecasting?What is Forecasting? ♦ Process of predicting a future event ♦ Underlying basis of all business decisions ♦ Production ♦ Inventory ♦ Personnel ♦ Facilities Sales will be $200 Million!
- 2. 4-2 ♦Short-range forecast ♦ Up to 1 year; usually less than 3 months ♦ Job scheduling, worker assignments ♦Medium-range forecast ♦ 3 months to 3 years ♦ Sales & production planning, budgeting ♦Long-range forecast ♦ 5-10 years ♦ New product planning, facility location Types of Forecasts by TimeTypes of Forecasts by Time HorizonHorizon
- 3. 4-3 Short-term vs. Longer-term ForecastingShort-term vs. Longer-term Forecasting ♦Medium/long range forecasts deal with more comprehensive issues and support management decisions regarding planning and products, plants and processes. ♦Short-term forecasting usually employs different methodologies than longer-term forecasting ♦Short-term forecasts tend to be more accurate than longer-term forecasts.
- 4. 4-4 Influence of Product Life CycleInfluence of Product Life Cycle ♦Stages of introduction and growth require longer forecasts than maturity and decline ♦Forecasts useful in projecting ♦ staffing levels, ♦ inventory levels, and ♦ factory capacity as product passes through life cycle stages
- 5. 4-5 Strategy and Issues During aStrategy and Issues During a Product’s LifeProduct’s Life Introduction Growth Maturity Decline Standardization Less rapid product changes - more minor changes Optimum capacity Increasing stability of process Long production runs Product improvement and cost cutting Little product differentiation Cost minimization Over capacity in the industry Prune line to eliminate items not returning good margin Reduce capacity Forecasting critical Product and process reliability Competitive product improvements and options Increase capacity Shift toward product focused Enhance distribution Product design and development critical Frequent product and process design changes Short production runs High production costs Limited models Attention to quality Best period to increase market share R&D product engineering critical Practical to change price or quality image Strengthen niche Cost control critical Poor time to change image, price, or quality Competitive costs become critical Defend market position OMStrategy/IssuesCompanyStrategy/Issues HDTV CD-ROM Color copiers Drive-thru restaurants Fax machines Station wagons Sales 3 1/2” Floppy disks Internet
- 6. 4-6 Types of ForecastsTypes of Forecasts ♦Economic forecasts ♦ Address business cycle, e.g., inflation rate, money supply etc. ♦Technological forecasts ♦ Predict technological change ♦ Predict new product sales ♦Demand forecasts ♦ Predict existing product sales
- 7. 4-7 Seven Steps in ForecastingSeven Steps in Forecasting ♦Determine the use of the forecast ♦Select the items to be forecast ♦Determine the time horizon of the forecast ♦Select the forecasting model(s) ♦Gather the data ♦Make the forecast ♦Validate and implement results
- 8. 4-8 Product Demand Charted over 4Product Demand Charted over 4 Years with Trend and SeasonalityYears with Trend and Seasonality Year 1 Year 2 Year 3 Year 4 Seasonal peaks Trend component Actual demand line Average demand over four years Demandforproductorservice Random variation
- 9. 4-9 Actual Demand, Moving Average,Actual Demand, Moving Average, Weighted Moving AverageWeighted Moving Average 0 5 10 15 20 25 30 35 Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Month SalesDemand Actual sales Moving average Weighted moving average
- 10. 4-10 Realities of ForecastingRealities of Forecasting ♦Forecasts are seldom perfect ♦Most forecasting methods assume that there is some underlying stability in the system ♦Both product family and aggregated product forecasts are more accurate than individual product forecasts
- 11. 4-11 Forecasting ApproachesForecasting Approaches ♦ Used when situation is ‘stable’ & historical data exist ♦ Existing products ♦ Current technology ♦ Involves mathematical techniques ♦ e.g., forecasting sales of color televisions Quantitative Methods ♦ Used when situation is vague & little data exist ♦ New products ♦ New technology ♦ Involves intuition, experience ♦ e.g., forecasting sales on Internet Qualitative Methods
- 12. 4-12 Overview of Qualitative MethodsOverview of Qualitative Methods ♦Jury of executive opinion ♦ Pool opinions of high-level executives, sometimes augment by statistical models ♦Sales force composite ♦ Estimates from individual salespersons are reviewed for reasonableness, then aggregated ♦Delphi method ♦ Panel of experts, queried iteratively ♦Consumer Market Survey ♦ Ask the customer
- 13. 4-13 ♦ Involves small group of high-level managers ♦ Group estimates demand by working together ♦ Combines managerial experience with statistical models ♦ Relatively quick ♦ ‘Group-think’ disadvantage © 1995 Corel Corp. Jury of Executive OpinionJury of Executive Opinion
- 14. 4-14 Sales Force CompositeSales Force Composite ♦ Each salesperson projects their sales ♦ Combined at district & national levels ♦ Sales rep’s know customers’ wants ♦ Tends to be overly optimistic SalesSales © 1995 Corel Corp.
- 15. 4-15 Delphi MethodDelphi Method ♦Iterative group process ♦3 types of people ♦ Decision makers ♦ Staff ♦ Respondents ♦Reduces ‘group- think’ RespondentsRespondents StaffStaff Decision MakersDecision Makers (Sales?) (What will sales be? survey) (Sales will be 45, 50, 55) (Sales will be 50!)
- 16. 4-16 Consumer Market SurveyConsumer Market Survey ♦ Ask customers about purchasing plans ♦ What consumers say, and what they actually do are often different ♦ Sometimes difficult to answer How many hours will you use the Internet next week? How many hours will you use the Internet next week? © 1995 Corel Corp.
- 17. 4-17 Overview of Quantitative ApproachesOverview of Quantitative Approaches ♦Naïve approach ♦Moving averages ♦Exponential smoothing ♦Trend projection ♦Linear regression Time-series Models Associative models
- 18. 4-18 Quantitative Forecasting MethodsQuantitative Forecasting Methods (Non-Naive)(Non-Naive) Quantitative Forecasting Linear Regression Associative Models Exponential Smoothing Moving Average Time Series Models Trend Projection
- 19. 4-19 ♦ Set of evenly spaced numerical data ♦ Obtained by observing response variable at regular time periods ♦ Forecast based only on past values ♦ Assumes that factors influencing past and present will continue influence in future ♦ Example Year: 1993 1994 1995 1996 1997 Sales: 78.7 63.5 89.7 93.2 92.1 What is a Time Series?What is a Time Series?
- 20. 4-20 TrendTrend SeasonalSeasonal CyclicalCyclical RandomRandom Time Series ComponentsTime Series Components
- 21. 4-21 ♦Persistent, overall upward or downward pattern ♦Due to population, technology etc. ♦Several years duration Mo., Qtr., Yr. Response © 1984-1994 T/Maker Co. Trend ComponentTrend Component
- 22. 4-22 ♦Regular pattern of up & down fluctuations ♦Due to weather, customs etc. ♦Occurs within 1 year Mo., Qtr. Response Summer © 1984-1994 T/Maker Co. Seasonal ComponentSeasonal Component
- 23. 4-23 ♦Repeating up & down movements ♦Due to interactions of factors influencing economy ♦Usually 2-10 years duration Mo., Qtr., Yr.Mo., Qtr., Yr. ResponseResponse Cycle Cyclical ComponentCyclical Component
- 24. 4-24 ♦Erratic, unsystematic, ‘residual’ fluctuations ♦Due to random variation or unforeseen events ♦ Union strike ♦ Lockouts ♦Short duration & nonrepeating © 1984-1994 T/Maker Co. Random ComponentRandom Component
- 25. 4-25 ♦Any observed value in a time series is the product (or sum) of time series components ♦Multiplicative model ♦ Yi = Ti · Si · Ci · Ri (if quarterly or monthly data) ♦Additive model ♦ Yi = Ti + Si + Ci + Ri (if quarterly or mo. data) General Time Series ModelsGeneral Time Series Models
- 26. 4-26 Naive ApproachNaive Approach ♦ Assumes demand in next period is the same as demand in most recent period ♦ e.g., If May sales were 48, then June sales will be 48 ♦ Sometimes cost effective & efficient © 1995 Corel Corp.
- 27. ♦ Another method of this type is the ‘free-hand projection method’. This includes the plotting of the data series on a graph paper and fitting a free-hand curve to it. This curve is extended into the future for deriving the forecasts. The ‘semi-average projection method’ is another naive method. Here, the time-series is divided into two equal halves, averages calculated for both, and a line drawn connecting the two semi averages. This line is projected into the future and the forecasts are developed. 4-27
- 28. 4-28 ♦ The forecasted demand for 1991, using the last period method = actual sales in 1990 = 117 units. ♦ The forecasted demand for 1991, using the free-hand projection method = 119 units. (Please check the results using a graph papers!) ♦ The semi-averages for this problem will be calculated for the periods 1983-86 and 1987-90. The resultant semi-averages are 103.75 and 112.75. A straight line joining these points would lead to a forecast for the year 1991. The value of this forecast will be = 120 units
- 29. 4-29 ♦ MA is a series of arithmetic means ♦ Used if little or no trend ♦ Used often for smoothing ♦ Provides overall impression of data over time ♦ Equation MAMA nn nn == ∑∑ Demand inDemand in PreviousPrevious PeriodsPeriods Moving Average MethodMoving Average Method
- 30. 4-30 You’re manager of a museum store that sells historical replicas. You want to forecast sales (000) for 1998 using a 3-period moving average. 1993 4 1994 6 1995 5 1996 3 1997 7 © 1995 Corel Corp. Moving Average ExampleMoving Average Example
- 31. 4-31 Moving Average SolutionMoving Average Solution Time Response Yi Moving Total (n=3) Moving Average (n=3) 1995 4 NA NA 1996 6 NA NA 1997 5 NA NA 1998 3 4+6+5=15 15/3 = 5 1999 7 2000 NA
- 32. 4-32 Moving Average SolutionMoving Average Solution Time Response Yi Moving Total (n=3) Moving Average (n=3) 1995 4 NA NA 1996 6 NA NA 1997 5 NA NA 1998 3 4+6+5=15 15/3 = 5 1999 7 6+5+3=14 14/3=4 2/3 2000 NA
- 33. 4-33 Moving Average SolutionMoving Average Solution Time Response Yi Moving Total (n=3) Moving Average (n=3) 1995 4 NA NA 1996 6 NA NA 1997 5 NA NA 1998 3 4+6+5=15 15/3=5.0 1999 7 6+5+3=14 14/3=4.7 2000 NA 5+3+7=15 15/3=5.0
- 34. 4-34 95 96 97 98 99 00 Year Sales 2 4 6 8 Actual Forecast Moving Average GraphMoving Average Graph
- 35. 4-35
- 36. 4-36
- 37. 4-37 ♦Used when trend is present ♦ Older data usually less important & recent past periods should be given more weights or importance ♦Weights based on intuition ♦ Often lay between 0 & 1, & sum to 1.0 ♦Equation WMA =WMA = ΣΣ(Weight for period(Weight for period nn) (Demand in period) (Demand in period nn)) ΣΣ WeightsWeights Weighted Moving Average MethodWeighted Moving Average Method
- 38. ExampleExample ♦ For example, a department store may find that in a four-month period, the best forecast is derived by using 40 percent of the actual sales for the most recent month, 30 percent of two months ago, 20 percent of three months ago, and 10 percent of four months ago. If actual sales experience was ♦ Month 1 Month 2Month 3Month 4Month5 ♦ 100 90 105 95 ? the forecast for month 5 would be F5 = 0.40(95) + 0.30(105) + 0.20(90) + 0.10(100) = 38 + 31.5+ 18+ 10 = 97.5 4-38
- 39. 4-39 Actual Demand, Moving Average,Actual Demand, Moving Average, Weighted Moving AverageWeighted Moving Average 0 5 10 15 20 25 30 35 Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Month SalesDemand Actual sales Moving average Weighted moving average
- 40. 4-40 ♦Increasing n makes forecast less sensitive to changes ♦Do not forecast trend well ♦Require much historical data © 1984-1994 T/Maker Co. Disadvantages ofDisadvantages of Moving Average MethodsMoving Average Methods
- 41. 4-41 ♦Form of weighted moving average ♦ Weights decline exponentially ♦ Most recent data weighted most ♦Requires smoothing constant (α) ♦ Ranges from 0 to 1 ♦ Subjectively chosen ♦Involves little record keeping of past data Exponential Smoothing MethodExponential Smoothing Method
- 42. 4-42 ♦ Ft = αAt-1+ α(1-α)At-2 + α(1- α)2 ·At-3 + α(1- α)3 At-4 + ... + α(1- α)t-1 ·A0 ♦ Ft = Forecast value ♦ At = Actual value ♦ α = Smoothing constant ♦ Ft = Ft-1 + α(At-1 - Ft-1) forecast error ♦ Use for computing forecast Exponential Smoothing EquationsExponential Smoothing Equations
- 43. 4-43 You’re organizing a Kwanza meeting. You want to forecast attendance for 2000(yr) using exponential smoothing (α = .10). The1995 forecast was 175. 1995 180 1996 168 1997 159 1996 175 1999 190 © 1995 Corel Corp. Exponential Smoothing ExampleExponential Smoothing Example
- 44. 4-44 Ft = Ft-1 + ·(At-1 - Ft-1) TimeTime Actual Forecast, Ft (αα == .10.10)) 19951995 180 175.00 (Given) 19961996 168168 19971997 159159 19981998 175175 19991999 190190 20002000 NANA 175.00 +175.00 + Exponential Smoothing SolutionExponential Smoothing Solution
- 45. 4-45 Ft = Ft-1 + ·(At-1 - Ft-1) TimeTime ActualActual Forecast,Forecast, FFtt (( αα == .10.10)) 19951995 180180 175.00 (Given)175.00 (Given) 19961996 168168 175.00 +175.00 + .10.10(180(180 - 175.00- 175.00)) = 175.50= 175.50 19971997 159159 19981998 175175 19991999 190190 20002000 NANA Exponential Smoothing SolutionExponential Smoothing Solution
- 46. 4-46 Ft = Ft-1 + ·(At-1 - Ft-1) Time Actual Forecast, Ft (α = .10) 19951995 180180 175.00 (Given)175.00 (Given) 19961996 168168 175.00 + .10(180 - 175.00) = 175.50175.00 + .10(180 - 175.00) = 175.50 19971997 159159 175.50 + .10(168 - 175.50) = 174.75175.50 + .10(168 - 175.50) = 174.75 19981998 175175 174.75 + .10(159 - 174.75) = 173.18174.75 + .10(159 - 174.75) = 173.18 19991999 190190 173.18 + .10(175 - 173.18) = 173.36173.18 + .10(175 - 173.18) = 173.36 20002000 NANA 173.36173.36 ++ .10.10(190(190 - 173.36- 173.36) = 175.02) = 175.02 Exponential Smoothing SolutionExponential Smoothing Solution
- 47. 4-47 Year Sales 140 150 160 170 180 190 93 94 95 96 97 98 Actual Forecast Exponential Smoothing GraphExponential Smoothing Graph
- 48. 4-48 Y Xi i= ┼a b ♦Shows linear relationship between dependent & explanatory variables ♦ Example: Sales & advertising (not time) Dependent (response) variable Independent (explanatory) variable SlopeY-intercept ^ Linear Regression ModelLinear Regression Model
- 49. 4-50 ♦Slope (b) ♦ Estimated Y changes by b for each 1 unit increase in X ♦ If b = 2, then sales (Y) is expected to increase by 2 for each 1 unit increase in advertising (X) ♦Y-intercept (a) ♦ Average value of Y when X = 0 ♦ If a = 4, then average sales (Y) is expected to be 4 when advertising (X) is 0 Interpretation of CoefficientsInterpretation of Coefficients
- 50. 4-51 ♦Variation of actual Y from predicted Y ♦Measured by standard error of estimate ♦ Sample standard deviation of errors ♦ Denoted SY,X ♦Affects several factors ♦ Parameter significance ♦ Prediction accuracy Random Error VariationRandom Error Variation
- 51. 4-52 Least Squares AssumptionsLeast Squares Assumptions ♦Relationship is assumed to be linear. Plot the data first - if curve appears to be present, use curvilinear analysis. ♦Relationship is assumed to hold only within or slightly outside data range. Do not attempt to predict time periods far beyond the range of the data base. ♦Deviations around least squares line are assumed to be random.
- 52. 4-53 Text uses symbol Yc Standard Error of the EstimateStandard Error of the Estimate ( ) 2− −− = 2− − = ∑ ∑∑ ∑ 1= 1=1= 2 1= 2 n yxbyay n yˆy S n i n i iii n i i n i ii x,y
- 53. 4-54 ♦Answers: ‘how strong is the linear relationship between the variables?’ ♦Coefficient of correlation Sample correlation coefficient denoted r ♦ Values range from -1 to +1 ♦ Measures degree of association ♦Used mainly for understanding CorrelationCorrelation
- 54. 4-55 Sample Coefficient of CorrelationSample Coefficient of Correlation − − − = ∑ ∑∑ ∑ ∑ ∑ ∑ 1= 2 1= 2 1= 2 1= 2 1= 1= 1= n i n i ii n i n i ii n i n i n i iiii yynxxn yxyxn r
- 55. 4-57 ♦You want to achieve: ♦ No pattern or direction in forecast error ♦ Error = (Yi - Yi) = (Actual - Forecast) ♦ Seen in plots of errors over time ♦ Smallest forecast error ♦ Mean square error (MSE) ♦ Mean absolute deviation (MAD) Guidelines for SelectingGuidelines for Selecting Forecasting ModelForecasting Model ^
- 56. 4-58 Time (Years) Error 0 Desired Pattern Time (Years) Error 0 Trend Not Fully Accounted for Pattern of Forecast ErrorPattern of Forecast Error
- 57. © Wiley 201059 Measuring Forecast ErrorMeasuring Forecast Error ♦ Forecasts are never perfect ♦ Need to know how much we should rely on our chosen forecasting method ♦ Measuring forecast error: ♦ Note that over-forecasts = negative errors and under-forecasts = positive errors ttt FAE −=
- 58. © Wiley 2010 60 Measuring Forecasting AccuracyMeasuring Forecasting Accuracy ♦ Mean Absolute Deviation (MAD) ♦ measures the total error in a forecast without regard to sign ♦ Cumulative Forecast Error (CFE) ♦ Measures any bias in the forecast ♦ Mean Square Error (MSE) ♦ Penalizes larger errors ♦ Tracking Signal ♦ Measures if your model is working ( ) n forecast-actual MSE 2 ∑= MAD CFE TS = n forecastactual MAD ∑ − = ( )∑ −= forecastactualCFE
- 59. © Wiley 2010 61 Accuracy & Tracking Signal Problem: A company is comparing the accuracy of twoAccuracy & Tracking Signal Problem: A company is comparing the accuracy of two forecasting methods. Forecasts using both methods are shown below along with theforecasting methods. Forecasts using both methods are shown below along with the actual values for January through May. The company also uses a tracking signal withactual values for January through May. The company also uses a tracking signal with ±4 limits to decide when a forecast should be reviewed. Which forecasting method is±4 limits to decide when a forecast should be reviewed. Which forecasting method is best?best? Month Actual sales Method A Method B F’cast Error Cum. Error Tracking Signal F’cast Error Cum. Error Tracking Signal Jan. 30 28 2 2 2 27 2 2 1 Feb. 26 25 1 3 3 25 1 3 1.5 March 32 32 0 3 3 29 3 6 3 April 29 30 -1 2 2 27 2 8 4 May 31 30 1 3 3 29 2 10 5 MAD 1 2 MSE 1.4 4.4
Editor's Notes
- At this point, it may be useful to point out the “time horizons” considered by different industries. For example, some colleges and universities look 30 to fifty years ahead, industries engaged in long distance transportation (steam ship, railroad) or provision of basic power (electrical and gas utilities, etc.) also look far ahead (20 to 100 years). Ask them to give examples of industries having much shorter long-range horizons.
- At this point it may be helpful to discuss the actual variables one might wish to forecast in the various time periods.
- This slide introduces the impact of product life cycle on forecasting The following slide, reproduced from chapter 2, summarizes the changing issues over the product’s lifetime for those faculty who wish to treat the issue in greater depth.
- One can use an example based upon one’s college or university. Students can be asked why each of these forecast types is important to the college. Once they begin to appreciate the importance, one can then begin to discuss the problems. For example, is predicting “demand” merely as simple as predicting the number of students who will graduate from high school next year (i.e., a simple counting exercise)?
- A point to be made here is that one requires a forecasting “plan,” not merely the selection of a particular forecasting methodology.
- This slide illustrates a typical demand curve. You might ask students why it is important to know more than simply the actual demand over time. Why, for example, would one wish to be able to break out a “seasonality” factor?
- This slide illustrates one of the simplest forecasting techniques - the moving average. It may be useful to point out the lag introduced by exponential smoothing - and ask how one can actually make use of the forecast.
- This slide provides a framework for discussing some of the inherent difficulties in developing reliable forecasts. You may wish to include in this discussion the difficulties posed by attempting forecast in a continuously, and rapidly changing environment where product life-times are measured less often in years and more often in months than ever before. One might wish to emphasize the inherent difficulties in developing reliable forecasts.
- This slide distinguishes between Quantitative and Qualitative forecasting. If you accept the argument that the future is one of perpetual, and perhaps significant change, you may wish to ask students to consider whether quantitative forecasting will ever be sufficient in the future - or will we always need to employ qualitative forecasting also. (Consider Tupperware’s ‘jury of executive opinion.’)
- This slide outlines several qualitative methods of forecasting. Ask students to give examples of occasions when each might be appropriate. The next several slides elaborate on these qualitative methods.
- Ask your students to consider other potential disadvantages. (Politics?)
- You might ask your students to consider what problems might occur when trying to use this method to predict sales of a potential new product.
- You might ask your students to consider whether there are special examples where this technique is required. ( Questions of technology transfer or assessment, for example; or other questions where information from many different disciplines is required.)
- You might discuss some of the difficulties with this technique. Certainly there is the issue that what consumers say is often not what they do. There are other problems such as that consumers sometime wish to please the surveyor; and for unusual, future, products, consumers may have a very imperfect frame of reference within which to consider the question.
- A point you may wish to make here is that only in the case of linear regression are we assuming that we know “why” something happened. General time-series models are based exclusively on “what” happened in the past; not at all on “why.” Does operating in a time of drastic change imply limitations on our ability to use time series models?
- This and subsequent slide frame a discussion on time series - and introduce the various components.
- This slide introduces two general forms of time series model. You might provide examples of when one or the other is most appropriate.
- This slide introduces the naïve approach. Subsequent slides introduce other methodologies.
- At this point, you might discuss the impact of the number of periods included in the calculation. The more periods you include, the closer you come to the overall average; the fewer, the closer you come to the value in the previous period. What is the tradeoff?
- This slide shows the resulting forecast. Students might be asked to comment on the useful ness of this forecast.
- This slide introduces the “weighted moving average” method. It is probably most important to discuss choice of the weights.
- This slide illustrates one of the simplest forecasting techniques - the moving average. It may be useful to point out the lag introduced by exponential smoothing - and ask how one can actually make use of the forecast.
- These points should have been brought out in the example, but can be summarized here.
- This slide introduces the exponential smoothing method of time series forecasting. The following slide contains the equations, and an example follows.
- You may wish to discuss several points: - this is just a moving average wherein every point in included in the forecast, but the weights of the points continuously decrease as they extend further back in time. - the equation actually used to calculate the forecast is convenient for programming on the computer since it requires as data only the actual and forecast values from the previous time point. - we need a formal process and criteria for choosing the “best” smoothing constant.
- This slide begins an exponential smoothing example.
- This slide illustrates the result of the steps used to make the forecast desired in the example. In the PowerPoint presentation, there are additional slides to illustrate the individual steps.
- This slide illustrates graphically the results of the example forecast.
- This slide introduces the linear regression model. This can be approached as simply a generalization of the linear trend model where the variable is something other than time and the values do not necessarily occur a t equal intervals.
- This slide probably merits discussion - additional to that for the linear trend model. You might make the point here that the dependent and independent variable are not necessarily of the same nature - they need not both be dollars, for example. You might also wish to note that setting x = 0 may not have a useful physical interpretation.
- Here you may wish to at least begin the discussion of the distinction between explainable and unexplainable, and random and non-random error variation. There are also slides which come later in the presentation that will refer to this topic.
- This slide raises several points: - What does it mean to be “linear”? How does one tell if something is linear or not? Or perhaps, how does one tell if something is sufficiently linear that a linear regression model is appropriate? - If the relationship is assumed to hold only within or slightly outside the data range, how do we use this model to make projections into the future (for which we don’t have data)? - What does it mean for data to be random? How can we tell? You might discuss making scatter plots not only of the original data, but also of the resulting deviations. (Obviously there are more rigorous methods of determining if the deviations are random, but a scatter plot is a good start.)
- Again, it is probably useful to point out which elements in the equations represent the actual data values and which the averages of these values.
- This slide can frame the start of a discussion of correlation.. You should probably expect to add to this a discussion of cause and effect, emphasizing in particular that correlation does not imply a cause and effect relationship. Ask student to suggest examples of significant correlation of unrelated phenomenon.
- Here again an explanation of each variable is probably useful.
- While this slide introduces the implications of negative and positive correlation, it is probably also a good point to re-emphasis the difference between correlation and cause and effect.
- This slide introduces overall guideline for selecting a forecasting model. You may also wish to re-emphasize the role of scatter plots, and discuss the role of “understanding what is going on” (especially in limiting one’s choice of model).
- This slide illustrates both possible patterns in forecast error, and the merit of making a scatter plot of forecast error.