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
1.35	2.583	0.7371

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

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

++

xx

b. Interpret the value of the slope as it relates to this problem.

For every $1 increase in advertising spending, there is a $1.213 increase in profit.

For every $100 increase in advertising spending, there is a $1,213 increase in profit.

For every $100 increase in advertising spending, there is a $121.3 increase in profit.

For every $1,000 increase in advertising spending, there is a $121.3 increase in profit.

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 $2,300.

Round to the nearest cent

e. If the expected profit in a particular month is $55,233, about how much should be set aside for advertising that month?

Round to the nearest cent

h(i,x)=

{10if  program i halts on input x,otherwise.{1if  program i halts on input x,0otherwise.

Answer 1

we have

slope	yy-intercept	rr
1.35	2.583	0.7371

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

a. State the least-squares regression line for the data.
ŷ =2.583 +1.35x

For every $100 increase in advertising spending, there is a $258.3 increase in profit.

c. Compute and interpret the coefficient of determination.
R²=0.5433

d. Predict the monthly profit for a month when advertising is $2,300.

ŷ =2.583 +1.35*23 = 33.63~$34