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Going over the data provided by Coinmetrics, there is a weak correlation between the two (blue line is BTC vs Gold; red BTC vs S&P). Of course there will be point in time events that can make the two assets dance at a similar pace, but the general pattern overtime does not correlate their price:
https://coinmetrics.io/correlations/#assets=btc-s&p,btc-gldCharts display Spearmans correlation for BTC/S&P (red) and BTC/Gold (blue). Historical correlation data is within the range -0.2 .. +0.25, which points to a weak correlation.
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Correlation is an effect size and so we can verbally describe the strength of the correlation using the following guide for the absolute value of:
.00-.19 very weak
.20-.39 weak
.40-.59 moderate
.60-.79 strong
.80-1.0 very strong
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https://coinmetrics.io/correlations/#assets=btc-s&phttp://www.statstutor.ac.uk/resources/uploaded/spearmans.pdf