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 PersonHour 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 n2 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 PersonHour 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 PersonHour 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 PersonHour 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 
Canada
Correlation between the Production in Manufacturing Industry(x) and Output per PersonHour 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 PersonHour 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 PersonHour 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 PersonHour 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 