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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.

 Correlation between the Production in Manufacturing Industry(x) and Output per Person-Hour in Manufacturing(y) y = 1.5795x - 63.13 No of observations 24 tangent of the line 1.57946907 The standard error of the x coeficient is 0.538986083 R2 0.280752127 t  value of 5% 1 tail (critical value) 2.068654794 Test value 2.930444997 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 No of observations 25 tangent of the line 0.987058153 The standard error of the x coeficient is 0.016910368 R2 0.993294572 t  value of 5% 1 tail (critical value) 2.063898137 Test value 58.36999908 Reject H0: YES

France

 Correlation between the Production in Manufacturing Industry(x) and Output per Person-Hour in Manufacturing(y) No of observations 25 tangent of the line 1.944510093 The standard error of the x coeficient is 0.213058898 R2 0.783621881 t  value of 5% 1 tail (critical value) 2.063898137 Test value 9.126631687 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 No of observations 25 tangent of the line 0.950692371 The standard error of the x coeficient is 0.015843614 R2 0.993652672 t  value of 5% 1 tail (critical value) 2.063898137 Test value 60.00476691 Reject H0: YES

USA

 Correlation between the Production in Manufacturing Industry(x) and Output per Person-Hour in Manufacturing(y) No of observations 25 tangent of the line 1.030296057 The standard error of the x coeficient is 0.036324523 R2 0.972205326 t  value of 5% 1 tail (critical value) 2.063898137 Test value 28.36365029 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 No of observations 25 tangent of the line 0.996699507 The standard error of the x coeficient is 0.0100735 R2 0.99765609 t  value of 5% 1 tail (critical value) 2.063898137 Test value 98.94271998 Reject H0: YES

 Correlation between the Production in Manufacturing Industry(x) and Output per Person-Hour in Manufacturing(y) No of observations 25 tangent of the line 1.194454939 The standard error of the x coeficient is 0.103991143 R2 0.851546812 t  value of 5% 1 tail (critical value) 2.063898137 Test value 11.4861218 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 No of observations 25 tangent of the line 0.620953473 The standard error of the x coeficient is 0.125091118 R2 0.517226493 t  value of 5% 1 tail (critical value) 2.063898137 Test value 4.964009278 Reject H0: YES

West Germany

 Correlation between the Production in Manufacturing Industry(x) and Output per Person-Hour in Manufacturing(y) No of observations 25 tangent of the line 1.433577576 The standard error of the x coeficient is 0.12525675 R2 0.850640231 t  value of 5% 1 tail (critical value) 2.063898137 Test value 11.44511237 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 No of observations 25 tangent of the line 0.944991684 The standard error of the x coeficient is 0.055698854 R2 0.926008892 t  value of 5% 1 tail (critical value) 2.063898137 Test value 16.96608857 Reject H0: YES

Italy

 Correlation between the Production in Manufacturing Industry(x) and Output per Person-Hour in Manufacturing(y) No of observations 25 tangent of the line 1.32165322 The standard error of the x coeficient is 0.063858685 R2 0.949041355 t  value of 5% 1 tail (critical value) 2.063898137 Test value 20.69653055 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 No of observations 25 tangent of the line 0.718612141 The standard error of the x coeficient is 0.127691965 R2 0.579301744 t  value of 5% 1 tail (critical value) 2.063898137 Test value 5.627700549 Reject H0: YES

Japan:

 Correlation between the Production in Manufacturing Industry(x) and Output per Person-Hour in Manufacturing(y) No of observations 25 tangent of the line 1.030208598 The standard error of the x coeficient is 0.036061454 R2 0.972590938 t  value of 5% 1 tail (critical value) 2.063898137 Test value 28.56813818 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 No of observations 25 tangent of the line 0.840627843 The standard error of the x coeficient is 0.060340755 R2 0.894049428 t  value of 5% 1 tail (critical value) 2.063898137 Test value 13.93134441 Reject H0: YES

OECD

 Correlation between the Growth rate of real GDP at l990 market prices: annual % changes and Growth rate of real per capita GDP: annual % changes No of observations 25 tangent of the line 0.899951611 The standard error of the x coeficient is 0.046695189 R2 0.941690163 t  value of 5% 1 tail (critical value) 2.063898137 Test value 19.27289789 Reject H0: YES