Question

A company is investigating the relationship between sales and advertising revenue. Data has been collected on these two variables and is shown below (all figures are in £000s):

month	jan	feb	mar	april	may	june	july	aug	sept	oct	nov	dec
sales	60	60	58	45	41	33	31	25	24	23	23	23
adv	6.0	6.0	6.0	5.8	4.5	4.1	3.3	3.1	2.5	2.4	2.3	2.3

(a) Plot a scatter diagram of the data given in the table above. Comment on the strength of the association between the two variables.

(b) Obtain the least squares regression line and comment on how well it fits the data.

(c) What would the expected sales be, given an advertising expenditure of £5000?

Answer 1

(a)the scatter plot shows the strong association between the two variable

(b) the regression line y=a+bx=-0.235+9.292x

b=cov(x,y)/var(x)=21.204/2.282

a=mean(y)-b*mean(x)=37.167-9.292*4.025=-0.235

(c) the expected sales=46.225

for x=5 thousand,  y=a+bx=-0.235+9.292*5=46.225

following information has been generated using ms-excel

month	adv(x)	sales(y)
jan	6	60
feb	6	60
mar	6	58
april	5.8	45
may	4.5	41
june	4.1	33
july	3.3	31
aug	3.1	25
sept	2.5	24
oct	2.4	23
nov	2.3	23
dec	2.3	23
mean=	4.025	37.167
cov(x,y)=	21.204
var=	2.282	210.972
b=	9.292
a=	-0.235