Replication data for: Improving forecasts using equally weighted predictors

The usual procedure for developing linear models to predict any kind of target variable is to identify a subset of most important predictors and to estimate weights that provide the best possible solution for a given sample. The resulting \"optimally\" weighted linear composite is then used when predicting new data. This approach is useful in situations with large and reliable datasets and few predictor variables. However, a large body of analytical and empirical evidence since the 1970s shows that the weighting of variables is of little, if any, value in situations with small and noisy datasets and a large number of predictor variables. In such situations, including all relevant variables is more important than their weighting. These findings have yet to impact many fields. This study uses data from nine established U.S. election-forecasting models whose forecasts are regularly published in academic journals to demonstrate (a) the value of weighting all predictors equally and (b) including all relevant variables in the model. Across the ten elections from 1976 to 2012, equally weighted predictors yielded a lower forecast error than regression weights for six of the nine models. On average, the error of the equal weights models was 5% lower than the error of the original regression models. An equal-weights model that uses all 27 variables that are included in the nine models missed the final results of the ten elections on average by only 1.3 percentage points. This error is 48% lower than the error of the typical, and 29% lower than the error of the most accurate, individual model.

构建用于预测任意目标变量的线性模型的常规流程，通常是筛选出最重要的预测变量子集，并估计权重以针对给定样本生成最优解。由此得到的经‘最优’加权的线性组合，随后便用于新数据的预测。该方法在数据集规模庞大且可靠、预测变量数量较少的场景中颇具效用。然而，自20世纪70年代以来，大量分析与实证研究表明，在数据集规模较小且存在噪声、预测变量数量较多的场景中，变量加权的价值微乎其微，即便存在价值也可忽略不计。在此类场景中，纳入所有相关变量远比为变量加权更为关键。上述发现尚未对众多研究领域产生显著影响。本研究采用九种已成熟的美国选举预测模型的数据（这些模型的预测结果会定期发表于学术期刊），以验证两个结论：(a) 对所有预测变量进行均等加权的应用价值，以及(b) 在模型中纳入所有相关变量的必要性。在1976年至2012年的十次选举案例中，相较于回归权重，使用均等加权预测变量的方式在九个模型中的六个上取得了更低的预测误差。平均而言，均等加权模型的预测误差较原始回归模型低5%。一个纳入了九个模型全部27个变量的均等加权模型，其对十次选举最终结果的平均预测偏差仅为1.3个百分点。该预测偏差较典型个体模型低48%，较精度最高的单个模型也低29%。