The term marketing mix refers to the different components that can be controlled in a marketing strategy to increase sales or profit. The name comes from a cooking-mix analogy used by Neil Borden in his 1953 presidential address to the American Marketing Association. In 1960, E. Jerome McCarthy proposed the “four Ps” of marketing—product, price, place (or distribution), and promotion—as the most basic components of the marketing mix. Variables related to the four Ps are called marketing mix variables. A market researcher for a major manufacturer of computer printers is constructing a multiple regression model to predict monthly sales of printers using various marketing mix variables. The model uses historical data for various printer models and will be used to forecast sales for a newly introduced printer. The dependent variable for the model is: y = sales in a given month (in thousands of dollars) The predictor variables for the model are chosen from the following marketing mix variables: x11 = product feature index for the printer (a score based on its quantity and quality of features) x22 = average sale price (in dollars) x33 = number of retail stores selling the printer x44 = advertising spending for the given month (in thousands of dollars) x55 = amount of coupon rebate (in dollars) The market researcher decides to predict sales using only the product feature index for the printer, the advertising spending for the given month, and the amount of the coupon rebate. The multiple regression model has the following form: y = β00 + β11x11 + β33x33 + β55x55 y = β00 + β11x11 + β44x44 + β55x55 + ε y = β00 + β11x11 + β44x44 + β55x55 y = β00 + β11x11 + β33x33 + β55x55 + ε According to the specified multiple regression model, the expected value of the dependent variable, given the values of the predictor variables, has the following form: E(y) = β00 + β11x11 + β33x33 + β55x55 + ε E(y) = β00 + β11x11 + β44x44 + β55x55 + ε E(y) = β00 + β11x11 + β44x44 + β55x55 E(y) = β00 + β11x11 + β33x33 + β55x55 The estimated multiple regression equation has the following form: ŷ = b00 + b11x11 + b33x33 + b55x55 ŷ = b00 + b11x11 + b44x44 + b55x55 + ε ŷ = b00 + b11x11 + b44x44 + b55x55 ŷ = b00 + b11x11 + b33x33 + b55x55 + ε The least-squares estimates of the parameters β00, β11, β44, and β55 in the multiple regression equation can be obtained by minimizing: Σii(yii – b00 – b11x1i1i – b33x3i3i – b55x5i5i)22 Σii(yii – ŷii) Σii(yii – b00 – b11x1i1i – b44x4i4i – b55x5i5i) Σii(yii – b00 – b11x1i1i – b44x4i4i – b55x5i5i)22 Σii(yii – b00 – b11x1i1i – b33x3i3i – b55x5i5i) Using the least-squares criterion, the researcher obtained the following estimated multiple regression equation: ŷ = 1,179 + 87x11 + 65x44 + 18x55 The coefficient 87 in the estimated multiple regression equation just given is an estimate of the change in average printer sales in a given month (in thousands of dollars) corresponding to a change in index score when of the other predictor variables are held constant. If the index score increases by 12 units under this condition, you expect printer sales to increase on average by an estimated amount of

The term marketing mix refers to the different components that can be controlled in a marketing strategy to increase sales or profit. The name comes from a cooking-mix analogy used by Neil Borden in his 1953 presidential address to the American Marketing Association. In 1960, E. Jerome McCarthy proposed the “four Ps” of marketing—product, price, place (or distribution), and promotion—as the most basic components of the marketing mix. Variables related to the four Ps are called marketing mix variables. A market researcher for a major manufacturer of computer printers is constructing a multiple regression model to predict monthly sales of printers using various marketing mix variables. The model uses historical data for various printer models and will be used to forecast sales for a newly introduced printer. The dependent variable for the model is: y = sales in a given month (in thousands of dollars) The predictor variables for the model are chosen from the following marketing mix variables: x11 = product feature index for the printer (a score based on its quantity and quality of features) x22 = average sale price (in dollars) x33 = number of retail stores selling the printer x44 = advertising spending for the given month (in thousands of dollars) x55 = amount of coupon rebate (in dollars) The market researcher decides to predict sales using only the product feature index for the printer, the advertising spending for the given month, and the amount of the coupon rebate. The multiple regression model has the following form: y = β00 + β11x11 + β33x33 + β55x55 y = β00 + β11x11 + β44x44 + β55x55 + ε y = β00 + β11x11 + β44x44 + β55x55 y = β00 + β11x11 + β33x33 + β55x55 + ε According to the specified multiple regression model, the expected value of the dependent variable, given the values of the predictor variables, has the following form: E(y) = β00 + β11x11 + β33x33 + β55x55 + ε E(y) = β00 + β11x11 + β44x44 + β55x55 + ε E(y) = β00 + β11x11 + β44x44 + β55x55 E(y) = β00 + β11x11 + β33x33 + β55x55 The estimated multiple regression equation has the following form: ŷ = b00 + b11x11 + b33x33 + b55x55 ŷ = b00 + b11x11 + b44x44 + b55x55 + ε ŷ = b00 + b11x11 + b44x44 + b55x55 ŷ = b00 + b11x11 + b33x33 + b55x55 + ε The least-squares estimates of the parameters β00, β11, β44, and β55 in the multiple regression equation can be obtained by minimizing: Σii(yii – b00 – b11x1i1i – b33x3i3i – b55x5i5i)22 Σii(yii – ŷii) Σii(yii – b00 – b11x1i1i – b44x4i4i – b55x5i5i) Σii(yii – b00 – b11x1i1i – b44x4i4i – b55x5i5i)22 Σii(yii – b00 – b11x1i1i – b33x3i3i – b55x5i5i) Using the least-squares criterion, the researcher obtained the following estimated multiple regression equation: ŷ = 1,179 + 87x11 + 65x44 + 18x55 The coefficient 87 in the estimated multiple regression equation just given is an estimate of the change in average printer sales in a given month (in thousands of dollars) corresponding to a change in index score when of the other predictor variables are held constant. If the index score increases by 12 units under this condition, you expect printer sales to increase on average by an estimated amount of

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Question

In 1960, E. Jerome McCarthy proposed the “four Ps” of marketing—product, price, place (or distribution), and promotion—as the most basic components of the marketing mix. Variables related to the four Ps are called marketing mix variables.

A market researcher for a major manufacturer of computer printers is constructing a multiple regression model to predict monthly sales of printers using various marketing mix variables. The model uses historical data for various printer models and will be used to forecast sales for a newly introduced printer.

The dependent variable for the model is:

y = sales in a given month (in thousands of dollars)

The predictor variables for the model are chosen from the following marketing mix variables:

x11 = product feature index for the printer (a score based on its quantity and quality of features)

x22 = average sale price (in dollars)

x33 = number of retail stores selling the printer

x44 = advertising spending for the given month (in thousands of dollars)

x55 = amount of coupon rebate (in dollars)

The market researcher decides to predict sales using only the product feature index for the printer, the advertising spending for the given month, and the amount of the coupon rebate.

The multiple regression model has the following form:

y = β00 + β11x11 + β33x33 + β55x55

y = β00 + β11x11 + β44x44 + β55x55 + ε

y = β00 + β11x11 + β44x44 + β55x55

y = β00 + β11x11 + β33x33 + β55x55 + ε

According to the specified multiple regression model, the expected value of the dependent variable, given the values of the predictor variables, has the following form:

E(y) = β00 + β11x11 + β33x33 + β55x55 + ε

E(y) = β00 + β11x11 + β44x44 + β55x55 + ε

E(y) = β00 + β11x11 + β44x44 + β55x55

E(y) = β00 + β11x11 + β33x33 + β55x55

The estimated multiple regression equation has the following form:

ŷ = b00 + b11x11 + b33x33 + b55x55

ŷ = b00 + b11x11 + b44x44 + b55x55 + ε

ŷ = b00 + b11x11 + b44x44 + b55x55

ŷ = b00 + b11x11 + b33x33 + b55x55 + ε

The least-squares estimates of the parameters β00, β11, β44, and β55 in the multiple regression equation can be obtained by minimizing:

Σii(yii – b00 – b11x1i1i – b33x3i3i – b55x5i5i)22

Σii(yii – ŷii)

Σii(yii – b00 – b11x1i1i – b44x4i4i – b55x5i5i)

Σii(yii – b00 – b11x1i1i – b44x4i4i – b55x5i5i)22

Σii(yii – b00 – b11x1i1i – b33x3i3i – b55x5i5i)

Using the least-squares criterion, the researcher obtained the following estimated multiple regression equation:

ŷ = 1,179 + 87x11 + 65x44 + 18x55

The coefficient 87 in the estimated multiple regression equation just given is an estimate of the change in average printer sales in a given month (in thousands of dollars) corresponding to a change in index score when of the other predictor variables are held constant. If the index score increases by 12 units under this condition, you expect printer sales to increase on average by an estimated amount of

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