Without actual data it is hard to answer the question but I guess you are looking for something like this:

Top15['Citable docs per Capita'].corr(Top15['Energy Supply per Capita'])

That calculates the correlation between your two columns 'Citable docs per Capita' and 'Energy Supply per Capita'.

To give an example:

import pandas as pd

df = pd.DataFrame({'A': range(4), 'B': [2*i for i in range(4)]})

   A  B
0  0  0
1  1  2
2  2  4
3  3  6

Then

df['A'].corr(df['B'])

gives 1 as expected.

Now, if you change a value, e.g.

df.loc[2, 'B'] = 4.5

   A    B
0  0  0.0
1  1  2.0
2  2  4.5
3  3  6.0

the command

df['A'].corr(df['B'])

returns

0.99586

which is still close to 1, as expected.

If you apply .corr directly to your dataframe, it will return all pairwise correlations between your columns; that's why you then observe 1s at the diagonal of your matrix (each column is perfectly correlated with itself).

df.corr()

will therefore return

          A         B
A  1.000000  0.995862
B  0.995862  1.000000

In the graphic you show, only the upper left corner of the correlation matrix is represented (I assume).

There can be cases, where you get NaNs in your solution - check this post for an example.

If you want to filter entries above/below a certain threshold, you can check this question. If you want to plot a heatmap of the correlation coefficients, you can check this answer and if you then run into the issue with overlapping axis-labels check the following post.

I ran into the same issue. It appeared Citable Documents per Person was a float, and python skips it somehow by default. All the other columns of my dataframe were in numpy-formats, so I solved it by converting the columnt to np.float64

Top15['Citable Documents per Person']=np.float64(Top15['Citable Documents per Person'])

Remember it's exactly the column you calculated yourself

My solution would be after converting data to numerical type:

Top15[['Citable docs per Capita','Energy Supply per Capita']].corr()