The following data shows the score of 12 students for Accoun

The following data shows the score of 12 students for Accounting and Statistics  

         examinations.

a)Calculate a simple correlation coefficient

b)Fit a regression equation of Statistics on Accounting using least square estimates.

c)Predict the score of Statistics if the score of accounting is 85.

                                                                                                                                                                         

Accounting
X

Statistics
Y

1

74.00

81.00

2

93.00

86.00

3

55.00

67.00

4

41.00

35.00

5

23.00

30.00

6

92.00

100.00

7

64.00

55.00

8

40.00

52.00

9

71.00

76.00

10

33.00

24.00

11

30.00

48.00

12

71.00

87.00

	Accounting X	Statistics Y
1	74.00	81.00
2	93.00	86.00
3	55.00	67.00
4	41.00	35.00
5	23.00	30.00
6	92.00	100.00
7	64.00	55.00
8	40.00	52.00
9	71.00	76.00
10	33.00	24.00
11	30.00	48.00
12	71.00	87.00

Solution

correlation coefficient:

Step 1: Find X?Y , X2 and Y2 as it was done in the table below.

Step 2: Find the sum of every column to get:

?X=687 , ?Y=741 , ?X?Y=48407 , ?X2=45591 , ?Y2=52525

Step 3: Use the following formula to work out the correlation coefficient.

r r = n??XY??X??Y[n?X2?(?X)2]?[n?Y2?(?Y)2]??????????????????????????????????= 12?48407?687?741[12?45591?6872]?[12?52525?7412]?????????????????????????????????0.9194

r = 0.9194

Regression equation is y = 7.019 + 0.956?x

x=85

y = 7.019+88.279

X	Y	X?Y	X?X	Y?Y
74	81	5994	5476	6561
93	86	7998	8649	7396
55	67	3685	3025	4489
41	35	1435	1681	1225
23	30	690	529	900
92	100	9200	8464	10000
64	55	3520	4096	3025
40	52	2080	1600	2704
71	76	5396	5041	5776
33	24	792	1089	576
30	48	1440	900	2304
71	87	6177	5041	7569