Reference sample size for multiple regression in corn

Cargnelutti Filho, Alberto; Toebe, Marcos

doi:10.1590/S1678-3921.pab2020.v55.01400

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Pesquisa Agropecuária Brasileira

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

Reference sample size for multiple regression in corn

Tamanho de amostra-referência para regressão múltipla em milho

Authorship SCIMAGO INSTITUTIONS RANKINGS

Abstract:

The objective of this work was to determine the number of plants required to model corn grain yield (Y) as a function of ear length (X₁) and ear diameter (X₂), using the multiple regression model Y = β₀ + β₁X₁ + β₂X₂. The Y, X₁, and X₂ traits were measured in 361, 373, and 416 plants, respectively, of single-, three-way, and double-cross hybrids in the 2008/2009 crop year; and in 1,777, 1,693, and 1,720 plants, respectively, of single-, three-way, and double-cross hybrids in the 2009/2010 crop year, totaling 6,340 plants. Descriptive statistics were calculated, and frequency histograms and scatterplots were created. The sample size (number of plants) for the estimate of the β₀, β₁, and β₂ parameters, of the residual standard error, the coefficient of determination, the variance inflation factor, and the condition number between the explanatory traits of the model (X₁ and X₂) were determined by resampling with replacement. Measuring 260 plants is sufficient to adjust precise multiple regression models of corn grain yield as a function of ear length and ear diameter. The Y = -229.76 + 0.54X₁ + 6.16X₂ model is a reference for estimating corn grain yield.

Index terms:
Zea mays; descriptive statistics; hybrids; modeling; resampling

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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