Bivariate data: Average Rainfall and Average Temperature for European Countries

1. Bivariate data: Average Rainfall
and Average Temperature for
European countries
By:
-Laura Sandoval Belando
-Marta Ibáñez Díaz-Peco

2. Europe:
Europe is a continent that comprises the westernmost part of Eurasia. It’s
bordered by the Arctic Ocean to the north, the Atlantic Ocean to the west, and
the Mediterranean Sea to the south.
Europe is situated mainly in the temperate climate
zones, being subjected to prevailing westerlies.

3. And now, with this presentation, we’re going to compare two
weather characteristics, such as rainfall and temperature. So let’s
see if there is any relation between them.

4. First, we have collected the average rainfall and the average temperature for
20 European countries:
Collecting data:

5. Sources:
We have collected the Precipitation data from:
http://data.worldbank.org/indicator/AG.LND.PRCP.MM
And the Rainfall data from:
https://www.currentresults.com/Weather/Europe/Cities/temperature-
annual-average.php

6. After that, we have calculated the marginal means and variances, the
covariance and the coefficient of correlation:
Relations between the averages:

7. How can we interprate it?
We see that the covariance is negative, so there is an inverse or
negative dependence between the data.
This means that the higher the temperature is, the lower the rainfall will be.
We also see that this relation serves to guide us a bit about how will the
results be with other countries, but it isn’t very reliable, because the
correlation coefficient is not very close to 1 or -1.

8. Regression line:
The regression line allows the estimation of an unknown value of the Y
variable depending on a value of the X variable, and vice versa, with a
simple formula:
So, if we would like to find the ecuation of the regression line of Rainfall
over Temperature, will be:
And the regression line of Temperature over Rainfall, will be:
y=-0.0045x+19.17
x=-37.82y+1451.9

9. Knowing this equation, if we know the temperature of an European
country, we could get an idea of its rainfall.
We’re going to apply that to Turkey, whose average
temperature is 18º per year, and the result says that
this country’s average rainfall would be:
As we have said before, this relation isn’t very reliable, because its
currently result is an average rainfall of 593 mm per year.
x = -37.82*18+1451.9 = 771.14 mm per year

10. Knowing this equation, if we know the temperature of an European
country, we could get an idea of its rainfall.
We’re going to apply that to Turkey, whose average
temperature is 18º per year, and the result says that
this country’s average rainfall would be:
As we have said before, this relation isn’t very reliable, because its
currently result is an average rainfall of 593 mm per year.
x = -37.82*18+1451.9 = 771.14 mm per year