What is the r-value of the following data, to three decimal places?xy4 25 98 109 1213 23

To calculate the r-value, also known as the correlation coefficient, we first need to understand the formula for it. The formula is:

r = n(Σxy) - (Σx)(Σy) / sqrt([nΣx^2 - (Σx)^2][nΣy^2 - (Σy)^2])

Where:

• n is the number of pairs of scores
• Σ is the sum of
• x and y are the scores of individual pairs

Given the data:

x: 4, 5, 9, 13 y: 2, 10, 10, 23

We can calculate the following:

Σx = 4 + 5 + 9 + 13 = 31 Σy = 2 + 10 + 10 + 23 = 45 Σxy = 42 + 510 + 910 + 1323 = 8 + 50 + 90 + 299 = 447 Σx^2 = 4^2 + 5^2 + 9^2 + 13^2 = 16 + 25 + 81 + 169 = 291 Σy^2 = 2^2 + 10^2 + 10^2 + 23^2 = 4 + 100 + 100 + 529 = 733 n = 4 (the number of pairs)

Substitute these values into the formula:

r = 4(447) - (31)(45) / sqrt([4291 - (31)^2][4733 - (45)^2]) r = 1788 - 1395 / sqrt([1164 - 961][2932 - 2025]) r = 393 / sqrt([203][907]) r = 393 / sqrt(184021) r = 393 / 429.093

Finally, we get:

r = 0.915

So, the r-value of the given data to three decimal places is 0.915.

To calculate the r-value, also known as the correlation coefficient, we first need to calculate several different values: the sum of all x-values (Σx), the sum of all y-values (Σy), the sum of all squared x-values (Σx²), the sum of all squared y-values (Σy²), and the sum of the product of each x/y pair (Σxy).

Given the data:

x: 4, 5, 9, 13 y: 2, 10, 10, 23

We can calculate the following:

Σx = 4 + 5 + 9 + 13 = 31 Σy = 2 + 10 + 10 + 23 = 45 Σx² = 4² + 5² + 9² + 13² = 16 + 25 + 81 + 169 = 291 Σy² = 2² + 10² + 10² + 23² = 4 + 100 + 100 + 529 = 733 Σxy = 42 + 510 + 910 + 1323 = 8 + 50 + 90 + 299 = 447

Then we can use these values in the formula for r:

r = (nΣxy - ΣxΣy) / sqrt([nΣx² - (Σx)²] * [nΣy² - (Σy)²])

Where n is the number of pairs, which is 4 in this case.

So,

r = (4447 - 3145) / sqrt([4291 - 31²] * [4733 - 45²])

Calculating this gives us the r-value. Please note that you'll need a calculator to compute these values.