ds is equal to 4πr squared because the earth is approximately a sphere, and the surface area of ??the sphere is 4π r^2.

Let the circle y=√(R^2-x^2) rotate around the x-axis, and get the sphere x^2+y^2+z^2≤R^2.

Find the surface area of ??the ball.

Taking x as the integration variable, the integration limit is [-R, R].

Take any subinterval [x, x+△x] on [-R, R]. The area of ??the upper part of the sphere obtained by this arc around the x-axis is approximately 2π×y×ds, where ds is the arc length.

An R-squared of 1 indicates that the fund is fully correlated with the performance evaluation benchmark.

R-squared is 0, meaning the two are uncorrelated.

The lower the R-squared, the less reliable the beta coefficient is as an indicator of fund volatility.

The closer the R-squared is to 1, the better the β coefficient reflects the fund’s volatility.

In Morningstar's fund evaluation system, both beta coefficient and R-squared are listed.