Question

#4.    The following data represent the daily supply (y in thousands of units) and the unit price (x in dollars) for a product.

Daily Supply (y)	Unit Price (x)
5	2
7	4
9	8
12	5
10	7
13	8
16	16
16	6

4a). Compute and interpret the sample correlation coefficient. use formula ( rxy= Sxy/SxSy )

4b). A student has to take 9 more courses before he can graduate. If none of the courses are prerequisite to others, how many groups of four courses can he select for the next semester?

Answer 1

a)

S.No	x	y	X12	Y12	XY
1	2	5	4.0000	25.0000	10.00
2	4	7	16.0000	49.0000	28.00
3	8	9	64.0000	81.0000	72.00
4	5	12	25.0000	144.0000	60.00
5	7	10	49.0000	100.0000	70.00
6	8	13	64.0000	169.0000	104.00
7	16	16	256.0000	256.0000	256.00
8	6	16	36.0000	256.0000	96.00
	ΣX	ΣY	ΣX2	ΣY2	ΣXY
total	56.0000	88.0000	514.0000	1080.0000	696.0000

	n=	8.0000
	X̅=ΣX/n	7.000
	Y̅=ΣY/n	11.000
	sx=(√(Σx2-(Σx)2/n)/(n-1))=	4.175
	sy=(√(Σy2-(Σy)2/n)/(n-1))=	4.000
	Cov=Sxy=(ΣXY-(ΣXΣY)/n)/(n-1)=	11.4286
	r=Sxy/(Sx*Sy)=	0.6844

above indicate that there is a positive correlation between x and y. if x increases then y tend to increase or if x decrease y tend to decrease,.

b)

number of group of 4 course for next semester from 9 =(9C4)=9!/(4!*5!) =126