Question

- How might squaring a correlation coefficient be useful to understanding the relationship between two variables?
- Why is it important to remember “association, not causation” when discussing correlations? Please provide an example.

Answer #1

Suppose the correlation coefficient between X and Y is -0.9 and
that between X and Z is 0.3. It is difficult to compare the
correlation between X, Y and X, Z. Now if we look into the square
of correlation coefficient ie r^{2}. We see that for X and
Y, r^{2} = 0.81 and for X, Z, r^{2} takes value
0.09. Now it is possible to see which relationship is much
stronger.

Suppose we find that the correlation coefficient between "marks obtained by girls" and "marks obtained by boys" in a particular subject is 0.9. We can say that the association between two variable is high enough. But we cannot tell that the marks obtained by girls is highly affected by the marks obtained by boys because both boys and girls studied and had given exams independently of each other. So if we interpret the correlation coefficient as a causation then the interpretation becomes meaningless.

How might squaring a correlation coefficient be useful to
understanding the relationship between two variables?

Provided a detailed summary of what the squaring of a
correlation coefficient be useful to understanding the relationship
between two variables
Only partially provided a summary of what the squaring of a
correlation coefficient be useful to understanding the relationship
between two variables

Why is it important to remember “association, not causation”
when discussing correlations? Please provide an example.

A Correlation Coefficient is a measurement of
the relationship between two variables. A positive correlation
means that as one variable increases, the second variable increases
too. A negative correlation means that as one variable increases,
the second variable decreases, or as one variable decreases, the
second variable increases. Positive and negative correlations
exists in nature, science, business, as well as a variety of other
fields. Please watch the following video for a graphical
explanation of the correlation coefficient:
For Discussion...

One of the major misconceptions about correlation is that a
relationship between two variables means causation; that is, one
variable causes changes in the other variable. There is a
particular tendency to make this causal error, when the two
variables seem to be related to each other.
What is one instance where you have seen correlation
misinterpreted as causation? Please describe
Can you help me understand how to answer this question

Describe the relationship between two variables when the
correlation coefficient r is near 0.

Discussion 1: Searching for Causes
This week examines how
to use correlation and simple linear regression to test the
relationship of two variables. In both of these tests you can use
the data points in a scatterplot to draw a line of best fit; the
closer to the line the points are the stronger the association
between variables. It is important to recognize, however, that even
the strongest correlation cannot prove causation.
For this Discussion,
review this week’s Learning Resources...

a brief explanation of when an observed correlation might
represent a true relationship between variables and why. Be
specific and provide examples. must relate to public health.

A coefficient of correlation of -0.9 indicates the relationship
between the two variables is
(a) weak and negative
(b) strong and positive
(c) strong and negative

Suppose the correlation coefficient between two variables is
found to be 0.83. Which of the following statements are true?
small values of one variable are associated with large values of
the other variable
the relationship between the variables is weak
a scatter plot of the points would show an upward trend
low values of one variable tend to be paired with low values of
the other variable
there is a strong positive curvilinear relationship between the
variables
there is a...

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