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The correlation between height and weight for a certain breed of plant is found to be 0.75. What percentage of the variability in plant weight is NOT explained by height? 1-0.75 = 0.25 or 25% (b) 1-(.75)^2 = 0.5625 or 56.25% (c) 1-(.75)^2 = 0.4375 or 43.75% (d) (1 - 0.75)^2 = 0.0625 or 6.25%

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okpalawalter8

Answer:

The percentage of the variability in plant weight is NOT explained by height is  

      [tex]p = 43.75[/tex]%

Step-by-step explanation:

From the question we are told that

      The correlation between height and weight is  [tex]r = 0.75[/tex]

Generally the R-Squared  between height and weight is mathematically represented as

        [tex]R - square = r^2[/tex]

substituting values

         [tex]R - square = 0.75^2[/tex]

         [tex]R - square = 0.563[/tex]

This R-Squared tells us the percentage of plant weight is accounted by height

and from the calculation we see that it is  56.3%

Now the percentage of plant weight that is not accounted by height is

          [tex]p = 100 - 56.3[/tex]

          [tex]p = 43.75[/tex]%

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