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I am first going to do the estimates for the UK. Latter on exactly the same tests are applied to different countries.
Correlation between the Production in Manufacturing Industry (x) and Output per Person-Hour in Manufacturing(y) can be expressed in the form:
y = 1.5795x - 63.13
The estimated R2 = 0.2808 for that data, that indicates some correlation, but not much.
Now I am going to test whether the coeficient in front of x is significantly different from 0 at 95% level. If it is not then clearly we cannot be sure that x causes y. I call the coeficient b, ie b=1.5795
I define the standard error of b to be q=0.538. n is the number of observations, in this case it is 24. n=24
H0:b=0
H1:b>0
Test rule: b/q is distributed by t distribution with n-2 degrees of freedom. In this case the critical value for 1 tail 5% for t=2.068654794
Test value = 2.93
Reject H0, b is signifficantly different from 0 at 5% level.
Following table summarises the statistics and should be used as a template for further correlations.
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Correlation between the Production in Manufacturing Industry(x) and Output per Person-Hour in Manufacturing(y) |
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y = 1.5795x - 63.13 |
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No of observations |
24 |
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tangent of the line |
1.57946907 |
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The standard error of the x coeficient is |
0.538986083 |
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R2 |
0.280752127 |
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t value of 5% 1 tail (critical value) |
2.068654794 |
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Test value |
2.930444997 |
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Reject H0: |
YES |
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Correlation between the Growth rate of real GDP at l990 market prices: annual % changes and Growth rate of real per capita GDP: annual % changes |
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No of observations |
25 |
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tangent of the line |
0.987058153 |
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The standard error of the x coeficient is |
0.016910368 |
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R2 |
0.993294572 |
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t value of 5% 1 tail (critical value) |
2.063898137 |
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Test value |
58.36999908 |
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Reject H0: |
YES |
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France
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Correlation between the Production in Manufacturing Industry(x) and Output per Person-Hour in Manufacturing(y) |
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No of observations |
25 |
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tangent of the line |
1.944510093 |
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The standard error of the x coeficient is |
0.213058898 |
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R2 |
0.783621881 |
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t value of 5% 1 tail (critical value) |
2.063898137 |
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Test value |
9.126631687 |
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Reject H0: |
YES |
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Correlation between the Growth rate of real GDP at l990 market prices: annual % changes and Growth rate of real per capita GDP: annual % changes |
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No of observations |
25 |
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tangent of the line |
0.950692371 |
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The standard error of the x coeficient is |
0.015843614 |
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R2 |
0.993652672 |
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t value of 5% 1 tail (critical value) |
2.063898137 |
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Test value |
60.00476691 |
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Reject H0: |
YES |
|
USA
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Correlation between the Production in Manufacturing Industry(x) and Output per Person-Hour in Manufacturing(y) |
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No of observations |
25 |
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tangent of the line |
1.030296057 |
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The standard error of the x coeficient is |
0.036324523 |
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R2 |
0.972205326 |
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t value of 5% 1 tail (critical value) |
2.063898137 |
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Test value |
28.36365029 |
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Reject H0: |
YES |
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|
Correlation between the Growth rate of real GDP at l990 market prices: annual % changes and Growth rate of real per capita GDP: annual % changes |
||
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No of observations |
25 |
|
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tangent of the line |
0.996699507 |
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The standard error of the x coeficient is |
0.0100735 |
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R2 |
0.99765609 |
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t value of 5% 1 tail (critical value) |
2.063898137 |
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Test value |
98.94271998 |
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Reject H0: |
YES |
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Canada
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Correlation between the Production in Manufacturing Industry(x) and Output per Person-Hour in Manufacturing(y) |
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No of observations |
25 |
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tangent of the line |
1.194454939 |
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The standard error of the x coeficient is |
0.103991143 |
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R2 |
0.851546812 |
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t value of 5% 1 tail (critical value) |
2.063898137 |
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Test value |
11.4861218 |
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Reject H0: |
YES |
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|
Correlation between the Growth rate of real GDP at l990 market prices: annual % changes and Growth rate of real per capita GDP: annual % changes |
||
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No of observations |
25 |
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tangent of the line |
0.620953473 |
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The standard error of the x coeficient is |
0.125091118 |
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R2 |
0.517226493 |
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t value of 5% 1 tail (critical value) |
2.063898137 |
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Test value |
4.964009278 |
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Reject H0: |
YES |
|
West Germany
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Correlation between the Production in Manufacturing Industry(x) and Output per Person-Hour in Manufacturing(y) |
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No of observations |
25 |
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tangent of the line |
1.433577576 |
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The standard error of the x coeficient is |
0.12525675 |
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R2 |
0.850640231 |
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t value of 5% 1 tail (critical value) |
2.063898137 |
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Test value |
11.44511237 |
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Reject H0: |
YES |
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Correlation between the Growth rate of real GDP at l990 market prices: annual % changes and Growth rate of real per capita GDP: annual % changes |
||
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No of observations |
25 |
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tangent of the line |
0.944991684 |
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The standard error of the x coeficient is |
0.055698854 |
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R2 |
0.926008892 |
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t value of 5% 1 tail (critical value) |
2.063898137 |
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Test value |
16.96608857 |
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Reject H0: |
YES |
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Italy
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Correlation between the Production in Manufacturing Industry(x) and Output per Person-Hour in Manufacturing(y) |
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No of observations |
25 |
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tangent of the line |
1.32165322 |
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The standard error of the x coeficient is |
0.063858685 |
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R2 |
0.949041355 |
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t value of 5% 1 tail (critical value) |
2.063898137 |
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Test value |
20.69653055 |
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Reject H0: |
YES |
|
|
Correlation between the Growth rate of real GDP at l990 market prices: annual % changes and Growth rate of real per capita GDP: annual % changes |
||
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No of observations |
25 |
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|
tangent of the line |
0.718612141 |
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The standard error of the x coeficient is |
0.127691965 |
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R2 |
0.579301744 |
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t value of 5% 1 tail (critical value) |
2.063898137 |
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Test value |
5.627700549 |
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Reject H0: |
YES |
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Japan:
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Correlation between the Production in Manufacturing Industry(x) and Output per Person-Hour in Manufacturing(y) |
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No of observations |
25 |
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tangent of the line |
1.030208598 |
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The standard error of the x coeficient is |
0.036061454 |
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R2 |
0.972590938 |
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t value of 5% 1 tail (critical value) |
2.063898137 |
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Test value |
28.56813818 |
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Reject H0: |
YES |
|
|
Correlation between the Growth rate of real GDP at l990 market prices: annual % changes and Growth rate of real per capita GDP: annual % changes |
||
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No of observations |
25 |
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|
tangent of the line |
0.840627843 |
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The standard error of the x coeficient is |
0.060340755 |
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R2 |
0.894049428 |
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t value of 5% 1 tail (critical value) |
2.063898137 |
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Test value |
13.93134441 |
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Reject H0: |
YES |
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OECD
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Correlation between the Growth rate of real GDP at l990 market prices: annual % changes and Growth rate of real per capita GDP: annual % changes |
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No of observations |
25 |
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tangent of the line |
0.899951611 |
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The standard error of the x coeficient is |
0.046695189 |
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R2 |
0.941690163 |
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t value of 5% 1 tail (critical value) |
2.063898137 |
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Test value |
19.27289789 |
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Reject H0: |
YES |
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