Question 1131770
month |Advertising expense ($ million) }|Sales revenue ($ million)

july |...........................{{{2 }}}...........................|............{{{7}}}
August| ......................{{{1}}} ...........................|............{{{3}}}
Sept|............................ {{{3}}}..........................| ..............{{{8}}}
Oct|............................. {{{4}}} ..........................|.............{{{10}}} 

Sum of {{{X = 10}}}
Sum of {{{Y = 28}}}
Mean {{{X = 2.5}}}
Mean {{{Y = 7}}}

a) determine the regression of equation

{{{X - M[x]}}}| {{{Y - M[y]}}}|{{{(X - M[x])^2}}}| {{{(X - M[x])(Y - M[y])}}}

{{{-0.5}}}      |..{{{0 }}}.....      |{{{0.25}}}.....       |{{{0}}}
{{{-1.5}}}       |..{{{-4}}}.....       |{{{2.25}}}.....       |{{{6}}}
{{{0.5 }}}      |..{{{1}}}.....       |{{{0.25}}}.....       |{{{0.5}}}
{{{1.5}}}       |..{{{3}}}.....       |{{{2.25 }}}.....      |{{{4.5}}}


Sum of squares{{{ (SSX) = 5}}}
Sum of products {{{(SP) = 11}}}

Regression Equation = ŷ  ={{{ bX + a}}}


b) interpret the values of {{{a}}} and {{{b}}}

{{{b = SP/SSX = 11/5 = 2.2}}}

{{{a = MY - bMX = 7 - (2.2*2.5) = 1.5}}}

ŷ = {{{2.2X + 1.5}}}

For your data, the regression equation for Y is:

ŷ = {{{2.2X + 1.5}}}

c) estimate sales when ${{{3}}} million is spent on advertising. 

ŷ = {{{2.2*3 + 1.5}}}
ŷ = {{{8.1}}} million