Question

An energy economist studying the growth and decay of both the coal and natural gas industries wanted to leverage data collected by environmental scientists. Particularly, the economist wanted to study the link between the total yearly carbon emissions from both energy sources. They looked at 30 years of total yearly carbon emissions for a particular nation (measured in million metric tons of carbon dioxide) for both forms of energy. The data is provided below. Use Excel to calculate the correlation coefficient r between the two data sets. Round your answer to two decimal places.

MMTons CO2 Natural Gas   MMTons CO2 from Coal
144.975   1552.524
173.578   1519.755
168.448   1517.232
183.205   1537.343
178.596   1528.600
190.391   1658.477
212.140   1708.757
222.428   1626.367
210.728   1810.590
219.543   1733.430
257.485   1773.156
256.113   1828.702
274.249   1991.943
292.051   1807.748
316.249   1849.436
272.586   1948.157
310.474   1874.673
313.879   1923.322
340.916   1999.025
356.621   2057.241
368.335   1959.583
362.115   1805.112
399.512   1809.525
392.326   1745.279
468.730   1570.326
434.550   1513.523
456.864   1512.334
503.702   1369.385
561.474   1245.502
490.599   1258.338

Answer 1

Correlation Coefficient b/w MMTons CO2 Natural Gas & MMTons CO2 from Coal:

We use the formula:

=CORREL(array1, array2)

which is equivalent to:

r =

Where:

• r – the correlation coefficient of the linear relationship between the variables x and y
• x_i – the values of the x-variable in a sample
• x̅ – the mean of the values of the x-variable
• y_i – the values of the y-variable in a sample
• ȳ – the mean of the values of the y-variable

and x and y will correspond to data of MMTons CO2 from Natural Gas and MMTons CO2 from Coal respectively or vice-versa.

Where,

array1 = column/row of MMTons CO2 from Natural Gas

array2 = column/row of MMTons CO2 from Coal

Thus

r = -0.26

This shows a weak negative b/w two variables. (As r lies b/w -0.3 - 0.3)

Please upvote if you have liked my answer, would be of great help. Thank you.