Question

A shoe store developed the following estimated regression equation relating sales to inventory investment and advertising expenditures.

ŷ = 27 + 12x₁ + 8x₂

where

x1	=	inventory investment ($1,000s)
x2	=	advertising expenditures ($1,000s)
y	=	sales ($1,000s).

(a)

Predict the sales (in dollars) resulting from a $15,000 investment in inventory and an advertising budget of $11,000.

$ _________________?

(b)

Interpret b₁ and b₂ in this estimated regression equation.

Sales can be expected to increase by $___________ for every dollar increase in inventory investment when advertising expenditure is held constant. Sales can be expected to increase by $_________ for every dollar increase in advertising expenditure when inventory investment is held constant.

Answer 1

The given regression equation is

ŷ = 27 + 12x1 + 8x2

a) the sales (in 1000 dollars) resulting from a $15,000 investment in inventory and an advertising budget of $11,000 is predicted (in 1000$) as

= 27 + 12*15 + 8*11 = 295

Therefore the predicted sales value is $2,95,000

b) the regression coefficients b1 and b2 are respectively 12 and 8, hence:

Sales can be expected to increase by $12 for every dollar increase in inventory investment when advertising expenditure is held constant. Sales can be expected to increase by $8 for every dollar increase in advertising expenditure when inventory investment is held constant.