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Sample Test 3 (linear regression) calcs

# Sample Test 3 (linear regression) calcs - rainfall x wheat...

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df8b18b8757d6cf679efd5baf977aa2a63e98409.xls data rainfall, x wheat, y (in/yr) (bushel/acre) 12.9 62.5 7.2 28.7 11.3 52.2 19.6 80.6 8.8 41.6 10.3 44.5 15.9 73.3 13.1 54.4 5 10 15 20 25 0 10 20 30 40 50 60 70 80 90 wheat, y rainfall (in/yr) wheat yield (bu/a)

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df8b18b8757d6cf679efd5baf977aa2a63e98409.xls calculations rainfall, x wheat, y x^2 xy y^2 (in/yr) (bushel/acre) 12.9 62.5 166.41 806.25 3906.25 7.2 28.7 51.84 206.64 823.69 11.3 52.2 127.69 589.86 2724.84 19.6 80.6 384.16 1579.76 6496.36 8.8 41.6 77.44 366.08 1730.56 10.3 44.5 106.09 458.35 1980.25 15.9 73.3 252.81 1165.47 5372.89 13.1 54.4 171.61 712.64 2959.36 sums 99.10 437.80 1338.050 5885.050 25994.200 means 12.39 54.73 b1 num = 461.8 b1 den = 110.45 b1 = 4.1811 bushels/inch of rainfall b0 = 2.9310 bushels Equation of the best fitting straight line (the regression line): Y = 4.1811x + 2.9310 where: x is the annual rainfall in inches Y is the fitted wheat yield per acre in bushels r num = 461.8025 = b1 num (line 16) r den x term = 110.4488 = b1 den (line 17) r den y term = 2035.6 r den x*y = 224828.9233 r den sqrt = 474.1613 r num/r den sqrt= 0.9739 = r r = 0.9739 R^2 = r * r = 0.9486 for x = 6, Y = 28.02 bushels for y = 90, x = 20.82 inches of rain A B C D E F 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43
df8b18b8757d6cf679efd5baf977aa2a63e98409.xls

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