STAT3613 Tutorial 01

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The University of Hong Kong *

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3613

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Nov 24, 2024

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THE UNIVERSITY OF HONG KONG DEPARTMENT OF STATISTICS AND ACTUARIAL SCIENCE STAT2313/3613 Marketing Engineering Tutorial 1 Market Response Model Review Marketing engineering • Use of decision models for making marketing decisions. • Apply computer models to help transform objective and subjective data about the marketing envi- ronment into insights, decisions and implementation of decisions. Data are facts, beliefs or observations used in making decision • Dependent or output variables are those determined by a set of independent variables • Products sales (dependent variable) are driven by the level of advertising spending (independent variable 1) and the quality of the product (independent variable 2) Mathematical models • Specify the relationships embodied in a model in the form of equations Inputs • Independent variables • the marketing actions that the marketer can control Outputs • Dependent variables • Measurable outputs of concern to the firm • Customers awareness levels, product perceptions, sales levels, and profits Response model • The linkage from those inputs to the outputs • Relationship, specification, mathematical form • equations or sets of equations that relate dependent variables to independent variables in a model 1

Least Square Errors • y i is the observed value and ˆ y i is the predicted value under the model • Define sum of squared error ( SSE ) as SSE = n X i =1 ( y i - ˆ y i ) 2 • Define total sum of squares ( SST ) as SST = n X i =1 ( y i - ¯ y i ) 2 , ¯ Y = 1 n n X i =1 y i • SSE is the amount of the variation not explained by the model. • R 2 , R-square, defined as 1 - ratio of variation not explained by the model to the total variation R 2 = 1 - SSE SST • In general, the higher the R 2 , the better is the model. • R 2 = 0 , only as good as the average of y ; R 2 = 1 for the perfect model Type of Models Model Function Range of parameters Remarks Linear Y = a + bX a ≥ 0 linear relationship Power series Y = a + bX + cX 2 + dX 3 + . . . a ≥ 0 takes many shapes Fractional root Y = a + bX c c = 1 2 ⇒ square root model c = - 1 ⇒ reciprocal model Semilog Y = a + b ln X X > 0 threshold model Exponential Y = ae bX a > 0 , X > 0 Modified exponential Y = a (1 - e - bX ) + c a ≥ 0 Logistic Y = a 1+ e - ( b + cX ) + d Gompertz Y = ab c x + d a > 0 , 0 < b < 1 , c > 1 ADBUDG Y = a + b X c X c + d Phenomena a) Linear: Linear, power series and fractional root models b) Concave (decreasing returns): Power series, fractional root, semilog, modified exponential and ADBUDG models c) Saturation: Fractional root, modified exponential, logistic, Gompertz and ADBUDG models d) Convex (increasing returns): Power series, fractional root, semilog and exponential model e) S-shape: Power series, logistic, Gompertz and ADBUDG models f) Threshold: Semilog model g) Super saturation: Power series and ADBUDG models Example A company develops promotional response model tools to help it decide the level and allocation of promotional spending using response modeling and optimization with SAS. The managers constructed a response model, relating promotional spending with sales. They explored the promotional spending response analysis using the following information: 2

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