Respuesta :
Answer:
r=0.933
Step-by-step 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 [tex]\sum x[/tex] [tex]\sum y[/tex] [tex]\sum x^2[/tex] [tex]\sum y^2[/tex] [tex]\sum xy[/tex]
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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
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On this case n=17, [tex]\sum x = 511.5[/tex] [tex]\sum y=267.1[/tex] [tex]\sum x^2 =16628.65[/tex] [tex]\sum y^2 =4549.43[/tex] [tex]\sum xy =8653.45[/tex]
And we can use the following formula to calculate the correlation coefficient:
[tex]r=\frac{n(\sum xy)-(\sum x)(\sum y)}{\sqrt{[n\sum x^2-(\sum x)^2][n\sum y^2-(\sum y)^2]}}[/tex]
And replacing we have:
[tex]r=\frac{17(8653.45)-(511.5)(267.1)}{\sqrt{[17(16628.65)-(511.5)^2][17(4549.43)-(267.1)^2]}}=0.933[/tex]
