Question 1196570
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I don't know how the tutor @ewatrrr is getting  r = 0.284846442	 as that isn't correct.


The correct r value is approximately r = 0.703903176239897
which when rounded to four decimal places is roughly r = 0.7039


You can use any correlation coefficient calculator you like to confirm this.


Here is one such online calculator
<a href = "http://www.alcula.com/calculators/statistics/correlation-coefficient/">http://www.alcula.com/calculators/statistics/correlation-coefficient/</a>


Refer to this page to see an example how the r value is calculated
<a href = "https://www.algebra.com/algebra/homework/word/evaluation/Evaluation_Word_Problems.faq.question.1196643.html">https://www.algebra.com/algebra/homework/word/evaluation/Evaluation_Word_Problems.faq.question.1196643.html</a>


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However, @ewatrrr is correct in stating that the r value doesn't change when you scale the data sets consistently across the board.


Consider this example set A = {1,2,3,4}
The mean is 2.5 which is found by adding up the values and dividing by the sample size n = 4
Now multiply each item by 5 to get B = {5,10,15,20} and the mean of this is 12.5; this is a jump of "times 5" since 2.5*5 = 12.5
Therefore, the mean has scaled exactly the same way as the other values.
The standard deviation will also scale up by 5 through more complicated steps.


Apply that type of logic to this current data set and you'll find the mean and standard deviation are scaled the same amount. 


If for instance we multiplied everything in the x data set by 5 then the old Zx = (x-xbar)/sigma will turn into the new Zx = (5x - 5*xbar)/(5*sigma), in which the 5's cancel
The 5 isn't that special and you can use any constant you like. The multiplier will cancel out anyway.
The Zx for the original x data set, and the Zx for the scaled x data set, are the same.
The Zx value doesn't change as long as we apply the same multiplier to each x.


Similar reasoning shows Zy doesn't change either. You don't have to use the same multiplier as you did with the x data set.


Hence the value 
r = Sum(ZxZy)/(n-1)
will remain the same. 


This fact is mentioned in the article here
<a href = "https://en.wikipedia.org/wiki/Pearson_correlation_coefficient">https://en.wikipedia.org/wiki/Pearson_correlation_coefficient</a>
Quote: "A key mathematical property of the Pearson correlation coefficient is that it is invariant under separate changes in location and scale in the two variables. That is, we may transform X to a + bX and transform Y to c + dY, where a, b, c, and d are constants with b, d > 0, without changing the correlation coefficient."


Also, this article mentions it as well
<a href = "https://online.stat.psu.edu/stat509/lesson/18/18.1">https://online.stat.psu.edu/stat509/lesson/18/18.1</a>
scroll down to the portion that reads "The Pearson correlation coefficient is invariant to location and scale transformations"
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