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Calculation of Correlation Co-efficient X Values - Statistics Assignment Help
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Assignment Task:
Task:
Answer 1.
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Region code |
Sales (INR 000s) |
Advertising (TV spots per month) (in INR, 000s) |
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X |
Y |
XY |
XX |
YY |
X - Mx |
Y - My |
(X - Mx)2 |
(Y - My)2 |
(X - Mx)(Y - My) |
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|
1 |
260.3 |
5 |
1301.5 |
67756.09 |
25 |
-138.195 |
-5.4 |
19097.85803 |
29.16 |
746.253 |
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2 |
286.1 |
7 |
2002.7 |
81853.21 |
49 |
-112.395 |
-3.4 |
12632.63603 |
11.56 |
382.143 |
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3 |
279.4 |
6 |
1676.4 |
78064.36 |
36 |
-119.095 |
-4.4 |
14183.61903 |
19.36 |
524.018 |
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4 |
410.8 |
9 |
3697.2 |
168756.64 |
81 |
12.305 |
-1.4 |
151.413025 |
1.96 |
-17.227 |
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5 |
438.2 |
12 |
5258.4 |
192019.24 |
144 |
39.705 |
1.6 |
1576.487025 |
2.56 |
63.528 |
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6 |
315.3 |
8 |
2522.4 |
99414.09 |
64 |
-83.195 |
-2.4 |
6921.408025 |
5.76 |
199.668 |
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7 |
565.1 |
11 |
6216.1 |
319338.01 |
121 |
166.605 |
0.6 |
27757.22603 |
0.36 |
99.963 |
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8 |
570 |
16 |
9120 |
324900 |
256 |
171.505 |
5.6 |
29413.96503 |
31.36 |
960.428 |
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9 |
426.1 |
13 |
5539.3 |
181561.21 |
169 |
27.605 |
2.6 |
762.036025 |
6.76 |
71.773 |
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10 |
315 |
7 |
2205 |
99225 |
49 |
-83.495 |
-3.4 |
6971.415025 |
11.56 |
283.883 |
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11 |
403.6 |
10 |
4036 |
162892.96 |
100 |
5.105 |
-0.4 |
26.061025 |
0.16 |
-2.042 |
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12 |
220.5 |
4 |
882 |
48620.25 |
16 |
-177.995 |
-6.4 |
31682.22003 |
40.96 |
1139.168 |
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13 |
343.6 |
9 |
3092.4 |
118060.96 |
81 |
-54.895 |
-1.4 |
3013.461025 |
1.96 |
76.853 |
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14 |
644.6 |
17 |
10958.2 |
415509.16 |
289 |
246.105 |
6.6 |
60567.67103 |
43.56 |
1624.293 |
X: X Values Y: Y Values
Mx: Mean of X Values My: Mean of Y Values
X - Mx & Y - My: Deviation scores
(X - Mx)2 & (Y - My)2: Deviation Squared
(X - Mx)(Y - My): Product of Deviation Scores
Calculation of Correlation Co-efficient X Values
∑ = 7969.9
Mean = 398.495
∑(X - Mx)2 = SSx = 241429.93
Y Values
∑ = 208
Mean = 10.4
∑(Y - My)2 = SSy = 308.8
X and Y Combined N = 20
∑(X - Mx)(Y - My) = 7665.74
R Calculation
r = ∑((X - My)(Y - Mx)) / √((SSx)(SSy))
r = 7665.74 / √((241429.93)(308.8)) = 0.8878 r = 0.8878
The value of R is 0.8878.
This is a strong positive correlation, which means that high X variable scores go with high Y variable scores (and vice versa).
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SUMMARY OUTPUT |
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Regression Statistics |
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Multiple R |
0.876960439 |
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R Square |
0.769059612 |
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Adjusted R Square |
0.755474883 |
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Standard Error |
1.943703825 |
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Observations |
19 |
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ANOVA |
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df |
SS |
MS |
F |
Significance F |
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Regression |
1 |
213.8795256 |
213.8795256 |
56.61206981 |
0.00 |
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Residual |
17 |
64.22573752 |
3.77798456 |
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Total |
18 |
278.1052632 |
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Coefficients |
Standard Error |
t Stat |
P-value |
Lower 95% |
Upper 95% |
Lower 95.0% |
Upper 95.0% |
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Intercept |
-1.929583352 |
1.734743141 |
-1.112316461 |
0.281484889 |
-5.58957142 |
1.730404717 |
-5.58957142 |
1.730404717 |
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260.3 |
0.031086189 |
0.00413155 |
7.524099269 |
8.32653E-07 |
0.022369382 |
0.039802997 |
0.022369382 |
0.039802997 |
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