Question

Examine the computation formula for r, the sample correlation coefficient.

(a) In the formula for r, if we exchange the symbols x and y, do we get a different result or do we get the same (equivalent) result? Explain your answer.

The result is different because the formula is dependent on the symbols.The result is the same because the formula is dependent on the symbols.     The result is the same because the formula is not dependent on the symbols.The result is different because the formula is not dependent on the symbols.

(b) If we have a set of x and y data values and we exchange corresponding x and y values to get a new data set, should the sample correlation coefficient be the same for both sets of data? Explain your answer.

The result is different because the formula is dependent on which values are the x values and which values are the y values.The result is the same because the formula is dependent on which values are the x values and which values are the y values.     The result is the same because the formula is not dependent on which values are the x values and which values are the y values.The result is different because the formula is not dependent on which values are the x values and which values are the y values.

(c) Compute the sample correlation coefficient r for each of the following data sets and show that r is the same for both. (Use 3 decimal places.)

(i)	x	6	5	9
	y	2	4	5

(ii)	x	2	4	5
	y	6	5	9

	r
(i)
(ii)

Answer 1

a)  The result is the same because the formula is not dependent on the symbols.

b)   The result is the same because the formula is not dependent on which values are the x values and which values are the y values

c)

i)

S.No	X	Y	(x-x̅)2	(y-y̅)2	(x-x̅)(y-y̅)
1	6	2	0.4444	2.7778	1.1111
2	5	4	2.7778	0.1111	-0.5556
3	9	5	5.4444	1.7778	3.1111
Total	20	11	8.6667	4.6667	3.6667
Mean	6.667	3.667	SSX	SSY	SXY

correlation coefficient r=

Sxy/(√Sxx*Syy)               =

0.577

ii)

correlation coefficient r=

Sxy/(√Sxx*Syy)               =

0.577