Regression between Gold Log Returns X Bitcoin Log Returns.

I'm gonna answer an user's earlier post regarding bitcoin and gold's relationship. https://preview.redd.it/2rb699bsph9h1.png?width=658&format=png&auto=webp&s=ee4178e7f3e992941455a8f0f0b8f3df6c69c0dc This was the post the user made and deleted (I think, he may have blocked me hahahaha). He made severe flaws in econometrical analysis which I think I can provide a solution. I even provided him with the classical [spurious correlation](https://www.tylervigen.com/spurious-correlations) link. To do the analysis we: * Collected futures prices from Yahoo Finance. * GC=F -> Gold Futures ; BTC=F -> Bitcoin Futures * Calculated the log returns for each asset. * In our regression, X = Gold Futures Log Returns. * While Y = Bitcoin Futures Log Returns. **Training Data results...** OLS Regression Results ============================================================================== Dep. Variable: y R-squared: 0.015 Model: OLS Adj. R-squared: 0.015 Method: Least Squares F-statistic: 13.30 Date: Thu, 25 Jun 2026 Prob (F-statistic): 0.000274 Time: 17:42:43 Log-Likelihood: 2530.2 No. Observations: 1497 AIC: -5056. Df Residuals: 1495 BIC: -5046. Df Model: 1 Covariance Type: HAC ============================================================================== coef std err z P>|z| [0.025 0.975] ------------------------------------------------------------------------------ const 0.0003 0.001 0.240 0.810 -0.002 0.003 x1 0.5919 0.162 3.647 0.000 0.274 0.910 ============================================================================== Omnibus: 163.642 Durbin-Watson: 2.058 Prob(Omnibus): 0.000 Jarque-Bera (JB): 1211.362 Skew: -0.187 Prob(JB): 9.04e-264 Kurtosis: 7.391 Cond. No. 106. ============================================================================== Notes: [1] Standard Errors are heteroscedasticity and autocorrelation robust (HAC) using 7 lags and without small sample correction Durbin-Watson Statistic: 2.0577 1.5 <= DW <= 2.5: No strong evidence of autocorrelation in the residuals. Breusch-Godfrey Test (lags=5): LM Statistic: 4.8194 P-value: 0.4383 P-value >= 0.05: No evidence of serial autocorrelation in the residuals. (HAC standard errors with 7 lags automatically selected) Overall Model Significance: The F-test p-value is 0.0003, which is less than 0.05. This indicates that the model as a whole is statistically significant. At least one explanatory variable has the power to predict the dependent variable. Significance of Explanatory Variables and Intercept: The Intercept (constant) has a p-value of 0.8101, which is greater than 0.05. Therefore, the intercept is NOT statistically significant in the model. The variable GC=F has a p-value of 0.0003, which is less than 0.05. Therefore, the variable GC=F is statistically significant in the model. Let's break this down, we found a low R-Squared (closer to zero basically, going against the belief of the prior post, gold in fact explains shit about bitcoin), although at the same time we found that the coef for gold log returns is significant. Coef GC=F: 0.59 For every 1% change in GC=F, BTC=F moves 0.59% on average. Let's see how the behavior persists on the test data. For the test data what we're basically doing is seeing if the coef found is predictive. This is the classic in-sample / out-of-sample method. **Test Data results...** R-Squared: -1.21% Mean Absolute Error: 0.02451 Root Mean Squared Error: 0.03216 Intercept: 0.02849% R_BTC=F = 0.0002849 + 0.59 * R_GC=F R-Squared went down, to negative values, which actually proves that gold futures doesn't explain shit about bitcoin futures. The coef found (0.59) wasn't useful / predictive at all. https://preview.redd.it/nrj4c5ylsh9h1.png?width=2994&format=png&auto=webp&s=f6d5fde81497736cb70072067f0946e1f482f974 https://preview.redd.it/il1edyfmsh9h1.png?width=2970&format=png&auto=webp&s=f7fdc21d7e9751244bdc84a73210c3de1619e0c5 Q-Q plot of residuals show the fat tail behavior seen in financial markets. https://preview.redd.it/xvjbc0vssh9h1.png?width=2970&format=png&auto=webp&s=ea91b217834933de187162fc4269810b46e67de5 https://preview.redd.it/d1vdqr7ush9h1.png?width=2928&format=png&auto=webp&s=893de3ea8b56953068e1fc694b82d6bc28e9147b I hope this helps! The conclusion is that the previous user tried to force a relationship where there isn't much to begin with. We found on gold log returns no explaining power to determine Bitcoin's log returns.