Question

Suppose the correlation between height and weight for adults is 0.80. What proportion (or percent) of the variability in weight can be explained by the relationship with height

Answer 1

Answer: 64% of the variability in weight can be explained by the relationship with height.

Step-by-step explanation:

• In statistics, Correlation coefficient is denoted by 'r' is a measure of the strength of the relationship between two variables.
• Coefficient of determination, $r^2$, is a measure of variability in one variable can be explained variation in the other.

Here, r= 0.80

$\Rightarrow\ r^2= (0.80)^2=0.64$

That means 64% of the variability in weight can be explained by the relationship with height.

Answer 2

The variability in weight is 64 % , explained by the relationship with height.

Correlation coefficients are always values between -1 and 1, where -1 shows a perfect, linear negative correlation, and 1 shows a perfect, linear positive correlation.

The correlation coefficient is measure the strength of the linear relationship between two variables in a correlation analysis.

Correlation coefficient is represented by r.

Given that, the correlation between height and weight for adults is 0.80.

                   $r=0.8$

The variability in weight is, = $r^{2}=(0.8)^{2} =0.64$

Thus, the variability in weight is 64 % , explained by the relationship with height.

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