Answer:
0.997
Step-by-step explanation:
You want the correlation coefficient between X and Y, where ...
X = {3, 4, 5, 6, 7, 8}
Y = {12.35, 15.9, 17.75, 21.9, 24.65, 27.1}
Calculator
A statistics calculator or spreadsheet has built-in functions for computing the correlation coefficient. The attachment shows the value is about 0.997.
The correlation coefficient is about 0.997.
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Additional comment
If you want to calculate it "by hand", you can compute it as the ratio of the covariance of X and Y to the root of the product of the variances of X and Y. For either of these calculations, you have ...
var(A, B) = ∑(AB)/n -(∑A/n)(∑B/n)
Where var(A) = var(A, A) = ∑A²/n -(∑A/n)²
In short, you need the sums of X, Y, X², Y², and XY, and the number of numbers in each sum. For the given data set, these are ...
- ∑X = 33
- ∑Y = 119.65
- ∑X² = 199
- ∑Y² = 2542.0375
- ∑XY = 710.15
- n = 6
Then the correlation coefficient is ...
[tex]r=\dfrac{var(X,Y)}{\sqrt{var(X)var(Y)}}=\dfrac{710.15/6 -(33/6)(119.65/6)}{\sqrt{(199/6-(33/6)^2)(2542.0375/6-(119.65/6)^2)}}\\\\\\r=\dfrac{6(710.15)-33(119.65)}{\sqrt{(6(199)-33^2)(6(2542.0375)-119.65^2)}}=\dfrac{312.45}{\sqrt{105(936.1025)}}\\\\\\r\approx0.99660756[/tex]
