The correct answer is $\boxed{0.40}$.
The correlation coefficient is a measure of the strength and direction of the linear relationship between two variables. It is calculated by taking the covariance of the two variables and dividing it by the product of their standard deviations.
The covariance is a measure of how much two variables vary together. It is calculated by taking the sum of the products of the deviations of the values of each variable from their means.
The standard deviation is a measure of how spread out the values of a variable are. It is calculated by taking the square root of the variance.
The variance is a measure of how much the values of a variable vary from their mean. It is calculated by taking the sum of the squared deviations of the values of the variable from their mean.
In this case, $b_{xy} = 0.25$ and $b_{yx} = 0.64$. The correlation coefficient is therefore:
$$r = \frac{b_{xy}b_{yx}}{\sqrt{b_{xx}b_{yy}}} = \frac{0.25 \times 0.64}{\sqrt{0.25 \times 0.25} \times \sqrt{0.64 \times 0.64}} = 0.40$$
The correlation coefficient can range from -1 to 1. A correlation coefficient of 0 indicates that there is no linear relationship between the two variables. A correlation coefficient of 1 indicates that there is a perfect positive linear relationship between the two variables. A correlation coefficient of -1 indicates that there is a perfect negative linear relationship between the two variables.
In this case, the correlation coefficient is 0.40, which indicates that there is a moderate positive linear relationship between the two variables.