An example of the linear regression library, showing the regression of VX futures on the VIX. The beta might help you weight VX futures when hedging SPX vega exposure. A VX future has point multiplier of 1000, whereas SPX options have a point multiplier of 100. Suppose the front month VX future has a beta of 0.6 and the front month SPX straddle has a vega of 8.5. Using these approximations, the VX future will underhedge the SPX straddle, since (0.6 * 1000) < (8.5 * 100). The position will have about 2.5 ($250) vega. Use the R^2 (coefficient of determination) to check how well the model fits the relationship between VX and VIX. The further from one this value, the less useful the model.
(Note that the mini, VXM futures also have a 100 point multiplier).
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Using difference instead of log returns, which is more intuitive since VIX/VX are already expressed as percentages.