To calculate Pearson's correlation coefficient (r), we first need to complete the table with x2, y2, and xy…

Question

To calculate Pearson's correlation coefficient (r), we first need to complete the table with x2, y2, and xy values for each data point, and then find the sums of all columns.

ScanSolve AI Tutor · Accepted Answer

To calculate Pearson's correlation coefficient ( $r$ ), we first need to complete the table with $x^2$ , $y^2$ , and $xy$ values for each data point, and then find the sums of all columns.

The formula for Pearson's correlation coefficient is:

r = \frac{n(\sum xy) - (\sum x)(\sum y)}{\sqrt{[n(\sum x^2) - (\sum x)^2][n(\sum y^2) - (\sum y)^2]}}

where $n$ is the number of data points. In this case, $n=5$ .

Complete the table with $x^2$ , $y^2$ , and $xy$ values.

$x$	$y$	$x^2$	$y^2$	$xy$
62	71	$62^2 = 3844$	$71^2 = 5041$	$62 \times 71 = 4402$
75	84	$75^2 = 5625$	$84^2 = 7056$	$75 \times 84 = 6300$
41	56	$41^2 = 1681$	$56^2 = 3136$	$41 \times 56 = 2296$
69	73	$69^2 = 4761$	$73^2 = 5329$	$69 \times 73 = 5037$
82	90	$82^2 = 6724$	$90^2 = 8100$	$82 \times 90 = 7380$

Calculate the sums for each column.
$\sum x = 62 + 75 + 41 + 69 + 82 = 329$ $\sum y = 71 + 84 + 56 + 73 + 90 = 374$ $\sum x^2 = 3844 + 5625 + 1681 + 4761 + 6724 = 22635$ $\sum y^2 = 5041 + 7056 + 3136 + 5329 + 8100 = 28662$ $\sum xy = 4402 + 6300 + 2296 + 5037 + 7380 = 25415$
Substitute these sums and $n=5$ into the Pearson's correlation coefficient formula.
Calculate the numerator:
$n(\sum xy) - (\sum x)(\sum y) = 5(25415) - (329)(374)$ $= 127075 - 123046$ $= 4029$
Calculate the first part of the denominator under the square root:
$n(\sum x^2) - (\sum x)^2 = 5(22635) - (329)^2$ $= 113175 - 108241$ $= 4934$
Calculate the second part of the denominator under the square root:
$n(\sum y^2) - (\sum y)^2 = 5(28662) - (374)^2$ $= 143310 - 139876$ $= 3434$
Calculate the full denominator and then $r$ .
$\text{Denominator} = \sqrt{(4934)(3434)}$ $\text{Denominator} = \sqrt{16948356}$ $\text{Denominator} \approx 4116.8383$
Now, calculate $r$ :
$r = \frac{4029}{4116.8383}$ $r \approx 0.97866$
Round the result to three decimal places.
$r \approx 0.979$
This value matches option A.

The final answer is $\text{A. 0.979}$ .

To calculate Pearson's correlation coefficient (r), we first need to complete the table with x2, y2, and xy values for each data point, and then find the sums of all columns.

Answer

Step-by-step solution

Complete the table with $x^2$ , $y^2$ , and $xy$ values.

Calculate the sums for each column.

Substitute these sums and $n=5$ into the Pearson's correlation coefficient formula.

Calculate the full denominator and then $r$ .

Round the result to three decimal places.

Try one yourself

Still stuck on this one?

More Mathematics Questions

To calculate Pearson's correlation coefficient (r), we first need to complete the table with x2, y2, and xy values for each data point, and then find the sums of all columns.

Answer

Step-by-step solution

Complete the table with x2x^2x2, y2y^2y2, and xyxyxy values.

Calculate the sums for each column.

Substitute these sums and n=5n=5n=5 into the Pearson's correlation coefficient formula.

Calculate the full denominator and then rrr.

Round the result to three decimal places.

Try one yourself

Still stuck on this one?

More Mathematics Questions

Complete the table with $x^2$ , $y^2$ , and $xy$ values.

Substitute these sums and $n=5$ into the Pearson's correlation coefficient formula.

Calculate the full denominator and then $r$ .