I tried to predict gold prices with a trend line. It lost to doing nothing.

Same gold-in-rand dataset from the piece on ten years of gold prices, ninety-five months, split the last twenty months off as a holdout, and asked two models to predict them having only seen the earlier months. Model one: fit a least-squares line to the training data and extend it. Model two: for each month, just predict whatever last month's actual value was. No trend, no model, no fitting. The second one is usually called the naive baseline, and it exists specifically so you have something to beat.

The naive baseline scored 5.1% mean absolute percentage error. The fitted linear trend scored 28.2%. The thing built with math lost to the thing built with none, by a factor of five and a half.

Why the "better" model did worse

A least-squares line fit on ten years of a strongly-trending series learns the average slope of the whole training period and then extrapolates that exact slope forever. Gold's actual path was not a straight line, it accelerated hard in the final two years of the training window, so the line drawn through ten years of history undershoots badly right when the holdout period needed it to keep up. The naive baseline has no such commitment. Every month it just restates the most recent price, which means it automatically incorporates the acceleration the line-fit averaged away.

train, test = values[:split], values[split:]

# naive: this month's guess is just last month's actual
rolling_naive = [train[-1]] + test[:-1]

# linear trend: fit once on train, extrapolate forward
coeffs = np.polyfit(range(len(train)), train, 1)
trend_preds = [coeffs[0]*(len(train)+i) + coeffs[1] for i in range(len(test))]

The lesson is not "don't use linear regression"

It's narrower and more useful than that: on a series with a strong, non-constant trend, a naive baseline is a legitimate model, not a placeholder to beat before the real work starts. Reporting a forecasting result without the naive baseline next to it hides exactly the comparison that would tell you whether the fancier approach earned its complexity. Five and a half times worse than doing nothing is the kind of number that only shows up if you actually run the naive case instead of assuming it's beneath checking.