Question

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%

Answer 1

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

`p = 43.75`%

Explanation:

From the question we are told that

The correlation between height and weight is
`r = 0.75`

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

`R - square = r^2`

substituting values

`R - square = 0.75^2`

`R - square = 0.563`

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

`p = 100 - 56.3`

`p = 43.75`%