Question

During an advertising campaign, the number of commercials and the sales level were recorded for each of six different intervals: Commercials Sales 27 32 41 52 39 51 4 5 6 Compute the covariance and the coefficient of correlation to measure how the number of commercials (X) and sales level (Y) are related to one another. First, in the following table, check the box to the left of each quantity if you need to compute that quantity in order to find the coefficient of correlation. Then type in the correct value of each quantity that you will need. If you will not need the quantity, leave the value blank. Quantity Needed? Value 5% Cov - What are these numbers telling you? There is a linear relationship between the number of commercials shown and level of sales. When there are more commercials, sales levels tend to be

Answer 1

S.No XY 729.0000 27 1.0000 27.00 32 4 16.0000 1024.0000 128.00 41 25.0000 1681.0000 205.00 52 4 25.0000 2704.0000 260.00 39 4.0000 1521.0000 78.00 2601.0000 51 36.0000 306.00 zy Izx ΣΧ zY ΣΧΥ 10260.0000 total 23.0000 242.0000 107.0000 1004.0000

	n=	6.0000
	X̅=ΣX/n	3.830
	Y̅=ΣY/n	40.330
	sx=(√(Σx2-(Σx)2/n)/(n-1))=	1.940
	sy=(√(Σy2-(Σy)2/n)/(n-1))=	9.990
	Cov=sxy=(ΣXY-(ΣXΣY)/n)/(n-1)=	15.2667
	r=Cov/(Sx*Sy)=	0.7877

from above:

Quantity Needed? Value ΣΧ 23 107 ΣΧ2 ΣΧΥ2 ΣΧΥ 1004 242 ΣΥ ΣΥ2 10260

Cov=15.2667

r =0.7877

positive There is a linear relationship between the number of commercials shown and level of sales. When there are more commercials, sales levels tend to be higher (more)