https://training-course-material.com/index.php?action=history&feed=atom&title=Properties_of_Pearson%27s_rProperties of Pearson's r - Revision history2026-05-22T23:43:22ZRevision history for this page on the wikiMediaWiki 1.45.1https://training-course-material.com/index.php?title=Properties_of_Pearson%27s_r&diff=84448&oldid=prevIvasiletc: /* Quiz */2021-11-25T08:21:49Z<p><span class="autocomment">Quiz</span></p>
<p><b>New page</b></p><div>{{Cat|Describing Bivariate Data| 03}}<br />
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=Range=<br />
A basic property of Pearson's r is that its possible range is from -1 to 1. <br />
* A correlation of -1 means a perfect negative linear relationship, <br />
* a correlation of 0 means no linear relationship, and <br />
* a correlation of 1 means a perfect positive linear relationship.<br />
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=Symmetry=<br />
Pearson's correlation is symmetric in the sense that the correlation of X with Y is the same as the correlation of Y with X. <br />
* For example, the correlation of Weight with Height is the same as the correlation of Height with Weight.<br />
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=Linear transformations=<br />
A critical property of Pearson's r is that it is unaffected by linear transformations. <br />
* This means that multiplying a variable by a constant and/or adding a constant does not change the correlation of that variable with other variables. <br />
* For instance, the correlation of Weight and Height does not depend on whether Height is measured in inches, feet, or even miles. <br />
* Similarly, adding five points to every student's test score would not change the correlation of the test score with other variables such as GPA.<br />
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=Quiz=<br />
==Quiz==<br />
<quiz display=simple ><br />
{ The correlation between temperature and number of ice cream cones bought is the same whether the temperature is measured in Celsius or Fahrenheit. <br />
<br />
|type="()"}<br />
+True<br />
-False<br />
<br />
{<br />
{{Show Answer|<br />
True<br />
<br />
It will be the same because that is a linear transformation.<br />
}}<br />
}<br />
<br />
{The correlation between two sets of numbers is the same as the correlation between the log of those two sets of numbers. <br />
<br />
|type="()"}<br />
-True<br />
+False<br />
<br />
{<br />
{{Show Answer|<br />
False<br />
<br />
It won't be the same because a log transformation is not a linear transformation.<br />
}}<br />
}<br />
<br />
{Which of the following is not a possible value for Pearson's correlation? <br />
<br />
|type="()"}<br />
+-1.5<br />
--1<br />
-0.0<br />
-0.99<br />
<br />
{<br />
{{Show Answer|<br />
-1.5<br />
<br />
Pearson's correlation can be any value between -1 and 1 inclusive. <br />
}}<br />
}<br />
<br />
{Which is higher, the correlation between height and weight or the correlation between weight and height? <br />
<br />
|type="()"}<br />
-weight and height<br />
-They are about the same<br />
+They are exactly the same<br />
-height and weight<br />
<br />
{<br />
{{Show Answer|<br />
They are exactly the same.<br />
Correlations are symmetric so they are exactly the same.<br />
}}<br />
}<br />
</quiz></div>Ivasiletc