Question

The owners of an e-business have been successful in selling fashion products but are now venturing into another domain. Knowing that the impact of advertising on profit cannot be overemphasized, they are interested in determining the right amount to allocate to advertising for the new business. Based on a monthly report from the fashion e-business, a regression analysis of monthly profit (in thousands of dollars) on advertising spending (in hundreds of dollars) produced the following results:

slope	yy-intercept	rr
1.26	2.435	0.7379

where yy = profit (in $1000s)
           xx = advertising spending (in $100s)

a. State the least-squares regression line for the data.
ŷ = ŷ =

++

xx

c. Compute and interpret the coefficient of determination.
R2=R2=

Round to 4 decimal places

d. Predict the monthly profit for a month when advertising is $2,100.

Round to the nearest cent

e. If the expected profit in a particular month is $41,495, about how much should be set aside for advertising that month?

Round to the nearest cent

Answer 1

Given:

Based on a monthly report from the fashion e-business, a regression analysis of monthly profit (in thousands of dollars) on advertising spending (in hundreds of dollars) produced the following results:

slope	y-intercept	r
1.26	2.435	0.7379

where y = profit (in $1000s)
x = advertising spending (in $100s)

a) The least-squares regression line for the data.

ŷ = Intercept + slop* x

ŷ = 2.435 + 1.26x

c) The coefficient of determination:

R² = (r) ^2 = ( 0.7379) ^2 = 0.5445

Interpretation :

54.45% of the variation in the response variable ( i.e expected profit) is explained by the linear regression model.

d) Predict the monthly profit for a month when advertising is $2,300. so in model x = advertising spending (in $100s)

so x = 2100/100

x= 21

y = 2.435 + 1.26 * 21

y = 2.435 + 26.46

y = $28.895

Since y = profit (in $1000s) = 28.895 * 1000 = $28895

So $ 28895 monthly profit for a month when advertising is $2,100.

e) y = 41495 ,

y = profit (in $1000s) = 41495 / 1000 = 41.495

y = 1.26 x + 2.435

41.495 = 1.26x + 2.435

41.495 - 2.435 = 1.26x

39.06 =1.26x

x = 39.06/ 1.26

x = 31

So x = advertising spending (in $100s) = 31*100 = $3100

expected profit in a particular month is $43,448, about $ 3100 should be set aside for advertising that month.