Review of Simple ForecastUsing Slope-Origin

O = r x I

Ted Mitchell

Forecasting with a single Performance 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 advertising• 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

Tabular Representation of a Pie Selling Machine

Performance 1

Input: Advertising Dollars, A

A1 = $2,000

Output: Sales of Pies, Q

Q1 = 12,000 pies

Tabular Representation of a Pie Selling MachineCalculate the conversion rate

Performance 1

Input: Advertising Dollars, A

A1 = $2,000

Calculate the conversion ratePies per dollar of advertising, r = Q/A

Q/A= r1= 12,000/$2,000 =6 pies per dollar of advertising

Output: Sales of Pies, Q

Q1 = 12,000 pies

Tabular Representation of a Pie Selling MachineUsing the calculated conversion rate to forecast

Performance 1 Forecasted performance

Input: Advertising Dollars, A

A1 = $2,000 Proposed InputA2 = $2,800

Calculate the conversion ratePies per dollar of advertising, r = Q/A

Q/A= r1= 12,000/$2,000 =6 pies per dollar of advertising

Use the calculated conversion rate6 pies per dollar

Output: Sales of Pies, Q

Q1 = 12,000 pies Forecasted outputQ = 6 pies per dollar x $2,800 = 16,800 pies

Slope-Origin Forecast Calibrated From Single Observation

Calibrate Conversion rate

r = 12,000/$2,000 = 6 pies per dollar

Perfrmance #1 ($2,000, 12,000)

Input FactorAdvertising

Output Pies Sold

0, 0 $2,000

16,800 pies

X12,000 pies

$2,800

13,200 pies

XWeek#2 predicted Point ($2,800. 16,800)

Actual Pie Sales in Performance 2

Performance 1 Forecasted performance

Actual Period 2

Input: Advertising Dollars, A

A1 = $2,000 Proposed InputA2 = $2,800

A2 = $2,800

Calculate the conversion ratePies per dollar of advertising, r = Q/A

Q/A= r1= 12,000/$2,000 =6 pies per dollar of advertising

Use the calculated conversion rate6 pies per dollar

Output: Sales of Pies, Q

Q1 = 12,000 pies Forecasted outputQ = 6 pies per dollar x $2,800 = 16,800 pies

Actual SalesQ2 = 13,200 pies

Calculate the actual conversion rate, r, in period 2 = Q2/A2

Performance 1 Forecasted performance

Actual Period 2

Input: Advertising Dollars, A

A1 = $2,000 Proposed InputA2 = $2,800

A2 = $2,800

Calculate the conversion ratePies per dollar of advertising, r = Q/A

Q/A= r1= 12,000/$2,000 =6 pies per dollar of advertising

Use the calculated conversion rate6 pies per dollar

Calculate the actual conversion rate, r2 = 13,200/$2,800= 4.7 pies per dollar

Output: Sales of Pies, Q

Q1 = 12,000 pies Forecasted outputQ = 6 pies per dollar x $2,800 = 16,800 pies

Actual SalesQ2 = 13,200 pies

Two Performance Observations

Week #1 ($2,000, 12,000)

Input FactorAdvertising

Output Pies Sold

0, 0 $2,000

16,800 pies

X12,000 pies

$2,800

13,200 pies

XWeek#2 Forecasted Point ($2,800. 16,800)

X

Actual Week #2 ($2,800, 13,200)

Average 0f Two Performance Observations

Week #1 ($2,000, 12,000)

Input FactorAdvertising

Output Pies Sold

0, 0 $2,000

16,800 pies

X12,000 pies

$2,800

13,200 pies X

Actual Week #2 ($2,800, 13,200)

Average of Two performance