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# L5 - Meaning of r 2 Worked Example Example x = explanatory...

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Unformatted text preview: Meaning of r 2- Worked Example Example x = explanatory variable = temperature (degrees Celsius) y = response variable = yield (kg) x y 18 76.1 19 77.9 20 78.1 21 78.2 22 78.8 23 79.7 24 79.9 25 81.1 26 81.2 27 81.8 28 82.8 29 83.5 1 First check that a regression line makes sense! Plot. Looks great .. 2 Computations ¯ x = 23 . 5 ¯ y = 79 . 85 s x = 3 . 606 s y = 2 . 302 r = 0 . 9944 Recall ˆ β = r s y s x = 0 . 635 ˆ α = ¯ y- ˆ β ¯ x = 64 . 928 Regression line ˆ y = 64 . 928 + 0 . 635 x Predictions x = 32 ˆ y = 64 . 928 + 0 . 635(32) = 85 . 25 kg 3 Suppose only had values y . Compute means, standard deviations, histogram. .. Summary statistics mean yield = ¯ y = 79 . 85 standard deviation = s y = 2.302 4 Total variation in y data SST 0 = n X i =1 ( y i- ¯ y ) 2 = 58 . 29 Now include temperature to explain variability in yields. Predicted yields ˆ y i = a + bx i replace ¯ y ....
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L5 - Meaning of r 2 Worked Example Example x = explanatory...

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