Question

Each month, the owner of a restaurant records y=monthly sales receipts and x=amount spent that month on advertising, both in thousands of dollars. For the first four months of operation, the observations are as shown in the table.
Advertising Sales
0 4
1 7
3 9
5 11
a.Find the mean and standard deviation for each variable.
b.Find the values for a and b in the regression line.
c. Find the correlation coefficient. Interpret the relationship between two variables using correlation coefficient.

Answer 1

	n=	4.0000
	X̅=ΣX/n	2.250
	Y̅=ΣY/n	7.750
	sx=(√(Σx2-(Σx)2/n)/(n-1))=	2.2174
	sy=(√(Σy2-(Σy)2/n)/(n-1))=	2.9861
	Cov=sxy=(ΣXY-(ΣXΣY)/n)/(n-1)=	6.4167
	r=Cov/(Sx*Sy)=	0.9691

a)

mean of advertisement =2.25

standard deviation of advertisement =2.2174

mean of Sales =7.75

standard deviation of Sales =2.9861

b)

slope= b  =		r*Sy/Sx=1.3051
intercept= a     =		(Σy-β1Σx)/n=4.8136

c)

correlation coefficient r=0.9691

since correlation coefficient is positive and near 1 , there apears a strong positive linear relation between advertisement and sales