The following data shows the score of 12 students for Accounting and Statistics
ID: 3436233 • Letter: T
Question
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
Explanation / Answer
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 7569Related Questions
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