Tamanho de amostra-referência para regressão múltipla em milho

Cargnelutti Filho, Alberto; Toebe, Marcos

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Sumário

STATISTICS • Pesq. agropec. bras. 55 • 2020 • https://doi.org/10.1590/S1678-3921.pab2020.v55.01400 copiar

Tamanho de amostra-referência para regressão múltipla em milho

Autoria SCIMAGO INSTITUTIONS RANKINGS

Resumo:

O objetivo deste trabalho foi determinar o número de plantas necessário para modelar a produtividade de grãos de milho (Y) em função do comprimento de espiga (X₁) e do diâmetro de espiga (X₂), por meio do modelo de regressão múltipla Y = β₀ + β₁X₁ + β₂X₂. Os caracteres Y, X₁ e X₂ foram mensurados em 361, 373 e 416 plantas, respectivamente, de híbridos simples, triplo e duplo no ano agrícola 2008/2009; e em 1.777, 1.693 e 1.720 plantas, respectivamente, de híbridos simples, triplo e duplo no ano agrícola 2009/2010, tendo-se totalizado 6.340 plantas. Foram calculadas estatísticas descritivas, e confeccionados histogramas de frequência e diagramas de dispersão. O tamanho de amostra (número de plantas) para a estimação dos parâmetros β₀, β₁ e β₂, do erro-padrão residual, do coeficiente de determinação, do fator de inflação da variância e do número de condição entre os caracteres explicativos do modelo (X₁ e X₂) foram determinados por reamostragem, com reposição. A mensuração de 260 plantas é suficiente para ajustar modelos de regressão múltipla precisos para produtividade de grãos de milho, em função do comprimento de espiga e do diâmetro de espiga. O modelo Y = -229,76 + 0,54X₁ + 6,16X₂ é referência para estimar a produtividade de grãos de milho.

Termos para indexação:
Zea mays; estatística descritiva; híbridos; modelagem; reamostragem

Embrapa Secretaria de Pesquisa e Desenvolvimento; Pesquisa Agropecuária Brasileira Caixa Postal 040315, 70770-901 Brasília DF Brazil, Tel. +55 61 3448-1813, Fax +55 61 3340-5483 - Brasília - DF - Brazil
E-mail: pab@embrapa.br

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[1] *Corresponding author: alberto.cargnelutti.filho@gmail.com

Traits⁽¹⁾	Mean	Median	Minimum	Maximum	SD	CV (%)	Skewness	Kurtosis	Correlation⁽¹⁾
Traits⁽¹⁾	Mean	Median	Minimum	Maximum	SD	CV (%)	Skewness	Kurtosis	X₁	X₂	Y
	P32R21 single-cross hybrid (n=361 plants) in the 2008/2009 crop year
X₁	146.66	148.00	56	211	29.79	20.31	-0.42	0.04	1.00	0.56	0.78
X₂	48.10	49.00	31	56	4.14	8.60	-1.18	1.71	0.56	1.00	0.83
Y	131.44	135.00	2	276	55.84	42.48	-0.08	-0.37	0.78	0.83	1.00
	DKB566 three-way cross hybrid (n=373 plants) in the 2008/2009 crop year
X₁	157.74	162.00	50	226	26.34	16.70	-0.84	1.55	1.00	0.66	0.83
X₂	46.44	47.00	30	55	4.02	8.67	-1.03	1.99	0.66	1.00	0.83
Y	153.25	155.00	2	273	54.45	35.53	-0.42	-0.13	0.83	0.83	1.00
	DKB747 double-cross hybrid (n=416 plants) in the 2008/2009 crop year
X₁	165.62	171.00	55	226	31.26	18.87	-0.68	0.42	1.00	0.61	0.84
X₂	45.56	46.00	31	54	3.52	7.73	-0.72	1.31	0.61	1.00	0.81
Y	144.85	149.00	10	259	46.15	31.86	-0.42	0.00	0.84	0.81	1.00
	30F53 single-cross hybrid (n=1,777 plants) in the 2009/2010 crop year
X₁	147.95	152.00	40	221	31.80	21.49	-0.48	-0.04	1.00	0.76	0.91
X₂	42.74	43.00	17	53	4.28	10.02	-1.13	2.39	0.76	1.00	0.86
Y	115.68	117.00	2	249	44.16	38.18	-0.15	-0.36	0.91	0.86	1.00
	DKB566 three-way cross hybrid (n=1,693 plants) in the 2009/2010 crop year
X₁	154.61	157.00	40	250	27.87	18.03	-0.71	1.05	1.00	0.62	0.77
X₂	41.24	42.00	18	52	4.90	11.89	-1.24	2.42	0.62	1.00	0.86
Y	116.62	121.00	2	245	48.49	41.58	-0.24	-0.51	0.77	0.86	1.00
	DKB747 double-cross hybrid (n=1,720 plants) in the 2009/2010 crop year
X₁	158.66	163.00	28	281	41.80	26.35	-0.34	-0.19	1.00	0.62	0.77
X₂	39.05	40.00	15	51	4.78	12.23	-0.98	1.85	0.62	1.00	0.82
Y	86.37	87.00	2	219	40.52	46.91	0.02	-0.49	0.77	0.82	1.00
	Overall (n=6,340 plants)
X₁	154.29	157.00	28	281	33.89	21.96	-0.40	0.35	1.00	0.53	0.71
X₂	42.05	43.00	15	56	5.22	12.41	-0.79	1.44	0.53	1.00	0.84
Y	113.00	114.00	2	276	49.89	44.15	0.02	-0.40	0.71	0.84	1.00

Plants	β₀		β₁		β₂		RSE		R²		VIF		CN
	ACI_i	AG_i⁽¹⁾	ACI_i	AG_i	ACI_i	AG_i	ACI_i	AG_i	ACI_i	AG_i	ACI_i	AG_i	ACI_i	AG_i
10	329.86	-	1.33	-	8.77	-	25.86	-	0.43	-	4.16	-	17.49	-
30	182.82	44.58	0.71	46.91	4.84	44.77	15.13	41.50	0.25	41.32	1.55	62.73	6.81	61.05
50	143.35	56.54	0.52	60.99	3.81	56.54	11.71	54.70	0.20	53.36	1.02	75.44	4.50	74.25
70	118.90	63.95	0.43	67.46	3.19	63.64	9.99	61.37	0.16	62.65	0.90	78.29	3.97	77.28
90	105.20	68.11	0.39	70.90	2.79	68.14	8.91	65.54	0.16	63.81	0.76	81.62	3.37	80.72
110	93.92	71.53	0.35	73.98	2.45	72.02	7.79	69.86	0.13	69.35	0.67	83.88	2.96	83.06
130	86.10	73.90	0.31	76.48	2.29	73.83	7.27	71.88	0.12	71.30	0.60	85.51	2.66	84.78
150	82.28	75.06	0.29	78.22	2.15	75.48	6.61	74.42	0.12	73.00	0.57	86.27	2.53	85.53
170	74.95	77.28	0.27	79.69	2.05	76.59	6.39	75.27	0.11	75.37	0.54	86.93	2.40	86.30
190	72.58	78.00	0.26	80.62	1.89	78.42	5.99	76.82	0.11	75.72	0.51	87.72	2.26	87.11
210	70.57	78.61	0.24	81.65	1.84	78.97	6.02	76.70	0.10	77.31	0.48	88.34	2.14	87.77
230	68.26	79.31	0.23	82.44	1.75	80.04	5.63	78.21	0.09	78.42	0.46	88.99	2.02	88.46
250	61.69	81.30	0.23	82.72	1.63	81.36	5.18	79.98	0.09	79.71	0.44	89.42	1.94	88.92
270	60.85	81.55	0.21	83.92	1.57	82.13	5.16	80.05	0.09	80.18	0.42	89.92	1.85	89.40
290	59.45	81.98	0.21	84.19	1.57	82.13	4.91	81.01	0.08	80.89	0.39	90.52	1.74	90.06
310	56.11	82.99	0.20	85.03	1.51	82.76	4.71	81.78	0.08	82.07	0.40	90.49	1.74	90.03
330	57.05	82.70	0.20	85.20	1.45	83.40	4.56	82.38	0.08	81.82	0.38	90.76	1.70	90.31
350	53.62	83.74	0.19	85.51	1.41	83.93	4.48	82.69	0.07	83.05	0.37	91.20	1.61	90.78
370	51.31	84.45	0.19	85.77	1.36	84.48	4.32	83.29	0.07	82.73	0.37	91.11	1.63	90.67
390	50.50	84.69	0.19	86.12	1.30	85.14	4.31	83.33	0.07	82.76	0.36	91.37	1.58	90.95
410	51.43	84.41	0.18	86.86	1.30	85.21	4.20	83.77	0.07	83.66	0.35	91.69	1.53	91.27
430	48.05	85.43	0.17	87.34	1.27	85.57	3.95	84.73	0.07	84.07	0.33	92.09	1.45	91.70
450	48.36	85.34	0.17	87.09	1.26	85.67	3.92	84.86	0.07	84.47	0.33	92.08	1.45	91.69
470	46.05	86.04	0.17	87.52	1.19	86.46	3.91	84.90	0.07	84.56	0.30	92.72	1.34	92.35
490	46.84	85.80	0.16	87.87	1.22	86.06	3.82	85.24	0.06	85.51	0.32	92.22	1.43	91.84
510	43.12	86.93	0.16	88.21	1.14	87.01	3.68	85.78	0.06	85.32	0.31	92.62	1.35	92.26
530	43.88	86.70	0.16	88.33	1.17	86.70	3.66	85.83	0.06	85.74	0.30	92.81	1.32	92.46
550	44.12	86.62	0.15	88.54	1.15	86.89	3.48	86.54	0.06	86.47	0.29	92.95	1.29	92.60
570	41.78	87.33	0.15	88.93	1.12	87.25	3.49	86.52	0.06	86.47	0.28	93.16	1.26	92.82
590	40.60	87.69	0.15	88.74	1.08	87.64	3.34	87.08	0.06	86.51	0.29	92.95	1.29	92.62
610	40.83	87.62	0.15	89.11	1.06	87.95	3.43	86.75	0.06	86.51	0.29	93.09	1.27	92.75
630	40.48	87.73	0.14	89.56	1.03	88.20	3.28	87.31	0.06	86.97	0.27	93.57	1.18	93.25
650	40.77	87.64	0.14	89.24	1.05	88.06	3.32	87.18	0.06	87.06	0.27	93.55	1.18	93.24
670	38.91	88.20	0.14	89.52	1.03	88.21	3.19	87.67	0.05	87.65	0.27	93.39	1.21	93.07
690	38.10	88.45	0.14	89.79	0.97	88.93	3.13	87.90	0.05	87.62	0.26	93.82	1.13	93.52
710	38.25	88.40	0.13	90.00	1.00	88.57	3.16	87.79	0.05	87.83	0.26	93.75	1.15	93.43
730	36.38	88.97	0.13	89.89	0.98	88.82	3.08	88.10	0.05	87.92	0.25	93.95	1.11	93.66
750	35.38	89.27	0.13	90.08	0.96	89.10	3.05	88.20	0.05	87.85	0.24	94.18	1.07	93.89
770	35.40	89.27	0.13	90.25	0.94	89.30	3.02	88.34	0.05	87.79	0.25	94.09	1.08	93.80
790	34.99	89.39	0.13	90.49	0.92	89.49	2.92	88.72	0.05	88.66	0.24	94.20	1.06	93.92
810	34.18	89.64	0.12	90.73	0.93	89.39	2.93	88.66	0.05	88.48	0.25	94.08	1.09	93.79
830	36.10	89.06	0.12	90.68	0.91	89.56	2.91	88.73	0.05	88.47	0.23	94.38	1.03	94.09
850	35.00	89.39	0.13	90.49	0.92	89.49	2.90	88.80	0.05	88.59	0.24	94.24	1.06	93.96
870	34.15	89.65	0.12	90.91	0.92	89.52	2.83	89.04	0.05	89.29	0.23	94.36	1.03	94.09
890	34.08	89.67	0.12	90.96	0.90	89.79	2.88	88.87	0.05	89.08	0.23	94.51	1.01	94.24
910	33.48	89.85	0.12	91.25	0.88	90.01	2.79	89.20	0.05	89.04	0.22	94.62	0.99	94.35
930	33.64	89.80	0.12	91.24	0.86	90.23	2.75	89.35	0.05	89.09	0.24	94.32	1.04	94.04
950	31.48	90.46	0.11	91.41	0.85	90.32	2.72	89.49	0.05	89.29	0.23	94.49	1.01	94.22
970	31.70	90.39	0.11	91.42	0.84	90.44	2.65	89.75	0.04	89.65	0.21	94.85	0.95	94.59
990	32.29	90.21	0.11	91.57	0.84	90.47	2.56	90.12	0.05	89.47	0.22	94.78	0.96	94.52
1,000	31.87	90.34	0.11	91.65	0.81	90.75	2.72	89.49	0.05	89.47	0.22	94.71	0.97	94.45