Question 1
a) i) -0.722 implies a relatively strong negative correlation, which means that as GDP increases, 72.2% of the
time, infant mortality decreases. Therefore, this is an unreasonable correlation from which to conclude
that there is almost no association between GDP and Infant Mortality Rate.
ii) A correlation of .44 between GDP and Continent is reasonable as GDP would be more closely
associated with countries rather than continents.
iii) The correlation of 1.22 between Life Expectancy and GDP is unreasonable because correlation
coefficients must be between -1 and +1.
iv) This is a reasonable correlation.
b) This is an appropriate summary because as E-commerce increases through the years, the number of
sales made on the Internet should increase with it, which implies a correlation of close to 1 (a strong
positive correlation).
c) i)
12
Group 1
10
8
6
Y
4
2
0
0 1 2 X3 4 5 6
X and Y are negatively correlated, as shown by the negative direction of the least squares line.
ii)
Group 2
20
15
Y 10
5
0
0 2 4 6 8 10 12
X Again, X and Y are negatively correlated, as shows by the negative direction of the least squares line.
The correlation coefficient is very close to -1, which indicates a very strong negative correlation and
the line fits the data points almost perfectly.
iii)
Group 1 & 2
20
15
Y 10
5
0
0 2 4 6 8 10 12
X
iv) Creating a single scatterplot containing all of the observations makes it clear that this is an example of
Simpson’s Paradox. When the data is grouped separately as shown in the above individual scatterplots,
both groups have a very strong negative correlation, however, when grouped together, the correlation
coefficient is positive and signifying a weaker relationship between the data.
a) i) The relationship between Total Mortgages and Interest Rate is a relatively strong negative correlation,
which means that as Interest Rate increases, 84% of the time, Total Mortgages decreases.
ii) The correlation coefficient would remain unchanged.
iii) The correlation coeffic

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