Answer:
The correlation between height and weight for a certain breed of plant is found to be 0.75. the percentage of the variability in plant weight is not explained by height is 43.75%
Explanation:
Given:
The correlation between height and weight of certain plant = 0.75
To find:
Percentage of plant that cannot be calculated by height = ?
Solution:
The[tex]r^{2}[/tex] between the variables
The[tex]r^{2} = 0.75^{2}[/tex]
= 0.5625
which is 56.25% of variability in the plant weight calculated on the basis of height.
Hence, the variability which has not been explained by the model is,
= 1-0.5625
= 0.4375
= 43.75%
Percentage of plant that cannot be calculated by height is 43.75%
Given that the correlation between height and weight of a breed of plant is 0.75, the percentage of variability in the plant's height which is not explained by its height is: [tex]\mathbf{0.4375 $ or $ 43.75} \%}[/tex]
Recall:
Correlation coefficient between two variables does not represent percentage. i.e., 0.75 is not a percentage.
To find the percentage of variability between two variables, subtract the square of the correlation coefficient that accounts for variability between the two variables from 1.
Thus, variability not accounted for is given as: [tex]\mathbf{1 - r^2}[/tex]
Given:
Correlation (r) between height and weight of the plant = 0.75
Percentage of the variability in weight not explained by the height = [tex]1 - 0.75^2 = 1 - 0.5625 = 0.4375 $ or $ 43.75 \%[/tex]
In conclusion, given that the correlation between height and weight of a breed of plant is 0.75, the percentage of variability in the plant's height which is not explained by its height is: [tex]\mathbf{0.4375 $ or $ 43.75} \%}[/tex]
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https://brainly.com/question/19427912
