Question

asked Jul 7, 2020 20.1k views

1 Answer

Van Kichline · Answer 1 · 2020-07-10T14:47:03+0000

Answer:

r=0.933

Explanation:

X = the water content of snow on April 1

Y = the yield from April to July (in inches) on the Snake River watershed in Wyoming for 1919 to 1935.

x: 23.1 32.8 31.8 32.0 30.4 24.0 39.5 24.2 52.5 37.9 30.5 25.1 12.4 35.1 31.5 21.1 27.6

y: 10.5 16.7 18.2 17.0 16.3 10.5 23.1 12.4 24.9 22.8 14.1 12.9 8.8 17.4 14.9 10.5 16.1

We can construct the following table

n
$\sum x$
$\sum y$
$\sum x^2$
$\sum y^2$
$\sum xy$

______________________________________________

1 23.1 10.5 533.61 110.25 242.55

2 32.8 16.7 1075.84 278.89 547.76

3 31.8 18.2 1011.24 331.24 578.76

4 32.0 17.0 1024 289 544

5 30.4 16.3 924.16 265.69 495.52

6 24.0 10.5 600.25 110.25 252

7 39.5 23.1 1560.25 533.61 912.45

8 24.2 12.4 585.64 153.76 300.48

9 52.5 24.9 2756.25 620.01 1307.25

10 37.9 22.8 1436.41 519.84 864.12

11 30.5 14.1 930.25 198.81 430.05

12 25.1 12.9 630.01 166.41 323.79

13 12.4 8.8 153.76 77.44 109.12

14 35.1 17.4 1232.01 302.76 610.74

15 31.5 14.9 992.25 222.01 469.35

16 21.1 10.5 445.21 110.25 221.55

17 27.6 16.1 761.76 259.21 444.36

____________________________________________

On this case n=17,
$\sum x = 511.5$
$\sum y=267.1$
$\sum x^2 =16628.65$
$\sum y^2 =4549.43$
$\sum xy =8653.45$

And we can use the following formula to calculate the correlation coefficient:

$r=(n(\sum xy)-(\sum x)(\sum y))/(√([n\sum x^2-(\sum x)^2][n\sum y^2-(\sum y)^2]))$

And replacing we have:

r=(17(8653.45)-(511.5)(267.1))/(√([17(16628.65)-(511.5)^2][17(4549.43)-(267.1)^2]))=0.933

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