A set of n = 5 pairs of X and Y values has SSX = 4, SSY = 16 and SP = 8. For these data, what is the Pearson correlation?
Well, it looks like we're dealing with some scatterplot shenanigans here! To find the Pearson correlation, we can use the formula r = SP / √(SSX * SSY).
So in this case, we have SSX = 4, SSY = 16, and SP = 8. Plugging those into the formula, we get r = 8 / √(4 * 16).
Now, let's do some clown math to find the answer! √(4 * 16) = √64 = 8. So we have r = 8 / 8, which simplifies to r = 1.
Ta-da! The Pearson correlation for these data is 1. It's as strong as a clown juggling routine – tight and perfectly coordinated!
To find the Pearson correlation, we can use the formula:
r = SP / √(SSX * SSY)
Given that SSX = 4, SSY = 16, and SP = 8, we can substitute the values into the formula:
r = 8 / √(4 * 16)
Next, we can calculate the values inside the square root:
r = 8 / √64
Simplifying further:
r = 8 / 8
Finally, we find that:
r = 1
Therefore, the Pearson correlation for these data is 1.
To find the Pearson correlation coefficient (r) for a set of paired data, you need to use the following formula:
r = (SP) / sqrt(SSX * SSY)
Where:
- SP is the Sum of Products of the differences between each X value and the mean of X, and each Y value and the mean of Y.
- SSX is the Sum of Squares of the differences between each X value and the mean of X.
- SSY is the Sum of Squares of the differences between each Y value and the mean of Y.
In this case, you are given:
- SSX = 4
- SSY = 16
- SP = 8
Now, let's calculate the Pearson correlation coefficient using these values:
r = (SP) / sqrt(SSX * SSY)
= 8 / sqrt(4 * 16)
= 8 / sqrt(64)
= 8 / 8
= 1
Therefore, the Pearson correlation coefficient (r) for the given data is 1.