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Ted M itchell

Chapter 3 Forecasting: Two Observations Construct: Slope-Intercept Equation of The Meta-Marketing Machine. Ted M itchell. Chapter Goals. 1) Start aggregating inputs into dollars 2) Improve Forecasting With Meta-marketing Machine Using Two-Observations

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Ted M itchell

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  1. Chapter 3Forecasting: Two ObservationsConstruct: Slope-Intercept Equation of The Meta-Marketing Machine Ted Mitchell

  2. Chapter Goals • 1) Start aggregating inputs into dollars • 2) Improve Forecasting With Meta-marketing Machine Using Two-Observations • 3) Learn the 7 steps for constructing a Slope-Intercept Equation of Meta-Marketing Machine

  3. Goal #4 Typology of Demand Producing Marketing Machines

  4. To build the Typology we need • 1) Simplify The types of Input into Positive and Negative elements of the 4P marketing mix • 2) Meta-Machine for Forecasting Demand, Q, from Positive Inputs of Marketing Mix • 3) Meta-machine for Forecasting Demand, Q, from Negative Input of Selling Price Tag

  5. Aggregating Inputs into Dollars • Inputs as numbers of hours, servers, coffee quality, radio spots • Cups per hour, per server, per radio spot, shelf facing • Combining various promotion efforts, into dollars of budget expenditure • Cups per $ of promotion, product expense, channel expense

  6. Forecasting with a single point for calibration • You observe • An output Q = 12,000 pies sold • An input Advertising Budget, A = $2,000 • You set the Two-Factor Machine as • 12,000 pies = (conversion rate, r) x $2,000 • Calibrate the conversion rate • r = Q/A = 12,000/$2,000 = 6 pies per dollar • You forecast using the calibrated Two-Factor machine with a proposed input of $2,800 and the conversion rate of 6 pies per advertising dollar • Forecasted pies, Q* = (6 pies per dollar) x $2,800 • Forecasted pies, Q* = 16,800 pies

  7. Slope-Proposed Point Forecast Calibrated From Single Observation Calibrate Conversion rate r = 12,000/$2,000 = 6 pies per dollar Output Pies Sold 16,800 pies X Week#2 predicted Point ($2,800. 16,800) 13,200 pies X 12,000 pies 0, 0 $2,000 $2,800 Input Factor Advertising Week #1 ($2,000, 12,000)

  8. Two Points of Observation Output Pies Sold 16,800 pies X Week#2 predicted Point ($2,800. 16,800) 13,200 pies X X 12,000 pies Actual Week #2 ($2,800, 13,200) 0, 0 $2,000 $2,800 Input Factor Advertising Week #1 ($2,000, 12,000)

  9. Two Points of Observation Output Pies Sold Actual Linear Relationship between advertising and pies sold 16,800 pies X Week#2 predicted Point ($2,800. 16,800) 13,200 pies X X 12,000 pies Actual Week #2 ($2,800, 13,200) 0, 0 $2,000 $2,800 Input Factor Advertising Week #1 ($2,000, 12,000)

  10. Meta-Machine Conversion Rate, m Actual Week #2 ($2,800, 13,200) Actual Linear Relationship between advertising and pies sold Output Pies Sold 16,800 pies X 13,200 pies ∆ Pies = Run Meta-Conversion Rate m = ∆Pies/∆Adv m = 1.5 X 12,000 pies ∆ Advertising = Run 0, 0 $2,000 $2,800 Input Factor Advertising Week #1 ($2,000, 12,000)

  11. Meta-Marketing Machine Calibration point (∆π, ∆ø) Output, ∆ø Slope-Point Equation for Two-Factor Meta-machine ∆ø X Meta-Conversion rate m = rise/run m = ∆ø/∆π Rise 0, 0 ∆π Input Factor, ∆π Run

  12. Two-Factor Meta-Marketing Machine • Uses the ∆input and the ∆output • To construct a single point Meta-Marketing Machine Forecast • Awkward to Use • Input the change in hours, servers, change in dollar expenditures • Output is the change in cups sold, change in pies sold, change in Q

  13. Step 1 Forecasting With Single Point Meta-Machine Calibrate m

  14. Step 2 Forecasting With Single Point Meta-Machine Calculate ∆input

  15. Step 3 Forecasting With Single Point Meta-Machine Calculate ∆output

  16. Step 4 Forecasting With Single Point Meta-Machine Calculate New Q

  17. Forecasting along the line of the Meta-Marketing Machine Forecast ∆ø from a proposed ∆π (∆π, ∆ø) Output, ∆ø Slope-Point Equation for Two-Factor Meta-Machine ∆ø X Meta-Conversion rate m = rise/run m = ∆ø/∆π Rise 0, 0 ∆π Input Factor, ∆π Run

  18. Wanted the Slope-Intercept Equation of the Meta-Marketing Machine Actual Week #2 ($2,800, 13,200) Q* = m(π*) + a Q* = 1.5(π*) + 9,000 Output Pies Sold 16,800 pies X 13,200 pies ∆ Pies = Run Meta-Conversion Rate m = ∆Pies/∆Adv m = 1.5 12,000 pies X 9,000 pies ∆ Advertising = Run 0, 0 $2,000 $2,800 Input Factor Advertising Week #1 ($2,000, 12,000)

  19. Using Slope-Intercept Equation • Forecasted, Q* = a + m(π*) • From the calibration process we know • Y-intercept, a = 9,000 pies • Meta-Conversion rate, m = 1.5 pies changed per dollar of advertising expenditure changed • Proposed level of advertising, π* = $2,500 • Forecasted, Q* = 9,000 pies + (1.5 pie∆/$∆)($2,500) • Forecasted Q* = 9,000 pies + 3,750 pies • Forecasted Q* = 12,750 pies

  20. Calibrate the Slope-Intercept Equation of the Meta-Marketing Machine • A minimum of two observations of the machine’s performances and 7 Steps in the Calibration Process • Step 1) Observe and record the differences between the two observed inputs, ∆π = π2-π1, at two different levels of observation, P1= (π1, ø1) and P2 = (π2, ø2) • Step 2) Observe and record the differences between the two observed outputs, ∆ø = ø2-ø2, at the two different levels of operation • Step 3) Define the Two-Factor model of the meta-marketing machine in terms of the meta-output, ∆ø, meta-input, ∆π, and meta-conversion rate, m.∆ø = m x ∆π • m = ∆ø/∆π

  21. Steps 4 & 5 • Step 4) Determine the value of the meta-conversion rate, m, by using the size of the changes in input, ∆π, as a measurement of meta-input, the size of the changes in output, ∆ø, as a measure of meta-output and calculating the ratio of the meta-output over the meta-input using the Rise-Over-Run equation, such that • Meta-Conversion Rate, m = ∆ø/∆π. • Step 5) Define the Calibrated Slope-Proposed Point equation of the meta-marketing machine as the meta-conversion rate, m, and one of the observed points (π2. ø2) • (ø – ø2)/(π-π2) = m • where the proposed point of operation (π, ø) is to be where the input is set at π=0 and the output is the value of the y-intercept, ø=a.

  22. Steps 6 and 7 • Step 6) With the observed values of ø2 =y, π2=x, and the calculated value of conversion rate, m = b, then the value of the output, ø=a, at the y-intercept is calculated as • (a-y)/(0-x) = b • a = b(-x) + y • Step 7) Define the Calibrated Slope-Intercept equation of the meta-marketing model with the calculated value of the meta-conversion rate, m=b, and the calculated value of the y-intercept, a. • Output, O = a + b x (Input, I)

  23. Example: Step 1, 2, 3 • Step 1: Two Observations (π, ø) • P1=($2,000, 12,000 pies)P2= ($2,800, 13,200 pies) • Step 2: Two differences∆π = ($2,800 -$2,000) = $800∆ø = (13,200 – 12,000) = 1,200 pies • Step 3: Set the meta-machine equation∆ø = meta-conversion rate, m) x ∆π

  24. Example Steps 4 & 5 • Step 4: Calibrate the meta-conversion rate, m • m = ∆ø/∆π = 1,200 Pies∆/$800∆ • m = 1.5 pies per $∆ • Step 5: Set the calibrated meta-machine • ∆ø = (1.5 pies per $∆) x ∆π

  25. Example steps 6 & 7 • Step 6: Choose the proposed point to be the y-intercept, π3 = $0, ø3 = a, solve for a • (ø3-ø2) = (1.5 pies per $) x π3-π2 • (a – 13,200)pies = (1.5 pies per $) x ($0 - $2,800) • (a – 13,200)pies = -4,200 pies • a = 13,200 pies – 4,200 pies = 9,000 pies • Step 7: set the calibrated slope-intercept equation of the meta-marketing machine • Forecasted Output, O* = a + m x (proposed Input, I*) • ø* = 9,000 pies +(1.5 pies∆ per $∆) x π*

  26. Q = kπa Quantity, Q Q = a + bπ Q = kπa x x x x x x x x x x x x x x x x x x x x Linear Meta-Machine is a secant that approximates the Quantity sold as a function of advertising π = Advertising Budget

  27. Demand Generating Meta-Machine Using Selling Price, P, as Input • The slope-intercept equation has the form • Output, O = a + m(Price Tag, P) • However, the meta-conversion rate is invariably negative so the value of the slope is normally illustrated as m = -b and the output is invariably the quantity sold, Q • Quantity Sold, Q = a –b(Price, P)

  28. LowerPrice Sells More Units Quantity Sold Demand Equation Q = a - bP 2,200 2,000 Revenue = 2,000 x $4.00Revenue = $8,000 Price per Cup $3.90 $4.00 TJM

  29. You may have to Calibrate the Revenue Producing Meta-π Machine • Using the basic 7 steps for calibrating the • Slope-Intercept Equation • of the Meta-Marketing Machine • Output = a – m(Input) • Where a = calibrated value of the y-interceptm = calibrated value of the slope. ∆ø/∆I

  30. Typology of Demand Producing Marketing Machines

  31. Two-Basic Types of Demand Machines • 1) The Simple Two-Factor Model using a single point of observation for the calibration of its conversion rate, r = O/I • 2) The Two-Factor Meta-Model using a minimum of two observations for calibration of its conversion rate, m = ∆O/∆I

  32. Two Basic Types of Input, I • 1) Positive Elements of the marketing mix, π, that increase value to customer:Promotion, Place, Product quality • 2) Revenue generating element of the price tag, P, to the customer, that reduces value to the customer

  33. Two Basic Uses of Marketing Machine Models • 1) Diagnostic PurposesSimple Two-Factor models are useful here • 2) Forecasting PurposesMeta-Machines are useful hereSlope-Intercept equations are very useful here

  34. Any Questions?

  35. Review the 7 Calibration Steps • 1) Observe two inputs to the machine, ∆π = π2-π1. • 2) Observe two outputs of the machine, ∆ø = ø2-ø2. • 3) Establish the Meta-Machine, ∆ø = m x ∆π • 4) Determine the meta-conversion rate, m = b = ∆ø/∆π. • 5) Set Slope-Proposed Point Equation, (ø – ø2)/(π-π2) = m where the input is set at π=0 and the output is the y-intercept, ø=a. • 6) Use observed values of ø2 =y, π2=x, and the calculated value of conversion rate, m = b, to calculate the value of the y-intercept, ø=a, (a-y)/(0-x) = ba = b(-x) + y • 7) Establish the Slope-Intercept equation of the meta-marketing model asOutput = a + b(Input)

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