Table 1 Features selected using the mixed-integer programming procedure described in Insolia et al. (2021)⁵⁰ for the years 2015-2019, with corresponding coefficient estimates, standard errors, t-statistics and p-values computed on a subset encompassing 90% of the observations (these are 607 selected as “non-outlying”, concurrently with the feature selection). Group-constraints are used to ensure that the terms introduced to represent each categorical control, e.g., the three terms representing quarters (the first one being January-March), are either all selected or all excluded (the categorical controls used are year, quarter and climatic region). The model has an \(R^2=0.601\).

Coefficient	Estimate	Std. Error	\({\varvec{t}}\) value	Pr\({\varvec{(> \|t \|)}}\)
(Intercept)	−2.9903	0.2501	−11.96	\(< 2^{-16}\)
Year 2015	0.1353	0.0558	2.42	0.0156
Year 2016	0.0231	0.0553	0.42	0.6762
Year 2017	0.0014	0.0541	0.03	0.9788
Year 2018	−0.0202	0.0540	−0.37	0.7080
Region West	−0.3010	0.1050	−2.87	0.0043
Region Northwest	−0.6381	0.0844	−7.56	\(<1.6^{-13}\)
Region Southwest	−0.0582	0.0939	−0.62	0.5357
Region West North Central	−0.6265	0.0841	−7.45	\(<3.5^{-13}\)
Region South	−0.1443	0.0634	−2.28	0.0231
Region Southeast	0.0401	0.0562	0.71	0.4755
Region East North Central	−0.1672	0.0618	−2.71	0.0070
Region Northeast	−0.1657	0.0597	−2.77	0.0057
Quarter 1	0.4264	0.0480	8.88	\(< 2^{-16}\)
Quarter 2	−0.3433	0.0523	−6.57	\(< 1.1^{-10}\)
Quarter 3	0.0302	0.0744	0.41	0.6845
Varroa Destructor	0.1988	0.0209	9.51	\(<2^{-16}\)
Other pests and parasites	−0.0791	0.0162	−4.88	\(<1.4^{-6}\)
Pesticides	0.0345	0.0123	2.81	0.0051
Other	0.1524	0.0177	8.60	\(< 2^{-16}\)
Min. temp. std. dev.	0.0527	0.0205	2.58	0.0102
Min. temp. skewness	0.1777	0.0499	3.56	0.0004
Min. temp. kurtosis	0.5408	0.1187	4.55	\(<6.4^{-6}\)
Min. temp. alpha index	−0.2357	0.0735	−3.21	0.0014
Max. temp. kurtosis	0.3212	0.1071	3.00	0.0028
Precipitation entropy	0.0875	0.0302	2.90	0.0039
Green-area index	0.1304	0.0352	3.71	0.0002

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