- legrange

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Plan1
	Lagrange
	P(x)	=	y0	(	x	-	x1	)	(	x	-	x2	)	(	x	-	x3	)	+	y1	(	x	-	x0	)	(	x	-	x2	)	(	x	-	x3	)	+	y2	(	x	-	x0	)	(	x	-	x1	)	(	x	-	x3	)	+	y3	(	x	-	x0	)	(	x	-	x1	)	(	x	-	x2	)
	i	xi	yi	(	x0	-	x1	)	(	x0	-	x2	)	(	x0	-	x3	)	(	x1	-	x0	)	(	x1	-	x2	)	(	x1	-	x3	)	(	x2	-	x0	)	(	x2	-	x1	)	(	x2	-	x3	)	(	x3	-	x0	)	(	x3	-	x1	)	(	x3	-	x2	)
	0	0.3	0.2500
	1	0.4	1.7250	P(x)	=	0.25	(	x	-	0.4000	)	(	x	-	0.6000	)	(	x	-	0.9000	)	+	1.7250	(	x	-	0.3000	)	(	x	-	0.6000	)	(	x	-	0.9000	)	+	3.7532	(	x	-	0.3000	)	(	x	-	0.4000	)	(	x	-	0.9000	)	+	6.8455	(	x	-	0.3000	)	(	x	-	0.4000	)	(	x	-	0.6000	)
	2	0.6	3.7532	(	0.3000	-	0.4000	)	(	0.3000	-	0.6000	)	(	0.3000	-	0.9000	)	(	0.4000	-	0.3000	)	(	0.4000	-	0.6000	)	(	0.4000	-	0.9000	)	(	0.6000	-	0.3000	)	(	0.6000	-	0.4000	)	(	0.6000	-	0.9000	)	(	0.9000	-	0.3000	)	(	0.9000	-	0.4000	)	(	0.9000	-	0.6000	)
	3	0.9	6.8455
	y0	y1	y2	y3
	p(x)	0.7
	x	-	0.4000	x	-	0.300	x	-	0.300	x	-	0.300
	x	-	0.6000	x	-	0.600	x	-	0.400	x	-	0.400
	x²	-	0,4x	x²	-	0,3x	x²	-	0,3x	x²	-	0,3x
	-	0,6x	+	0.240	-	0,6x	+	0.18	-	0,4x	+	0.12	-	0,4x	+	0.12
	x²	-	1x	+	0.240	x²	-	0,9x	+	0.18	x²	-	0,7x	+	0.12	x²	-	0,7x	+	0.12
	x	-	0.900	x	-	0.900	x	-	0.900	x	-	0.600
	x³	-	1x²	+	0,24x	x³	-	0,9x²	+	0,18x	x³	-	0,7x²	+	0,12x	x³	-	0,7x²	+	0,12x
	-	0,9x²	+	0,9x	-	0.2160	-	0,9x²	+	0,81x	-	0.162	-	0,9x²	+	0,63x	-	0.108	-	0,6x²	+	0,42x	-	0.072
	x³	-	1,9x²	+	1,14x	-	0.2160	x³	-	1,8x²	+	0,99x	-	0.162	x³	-	1,6x²	+	0,75x	-	0.108	x³	-	1,3x²	+	0,54x	-	0.072
	P(x)	=	0.25	x³	-	1,9x²	+	1,14x	-	0.2160	1.725	x³	-	1,8x²	+	0,99x	-	0.162	3.7532	x³	-	1,6x²	+	0,75x	-	0.108	6.8455	x³	-	1,3x²	+	0,54x	-	0.072
	-0.0180	0.01	-0.018	0.09
	+
	1.725	x³	-	1,8x²	+	0,99x	-	0.1620
	0.0100
	+
	3.7532	x³	-	1,6x²	+	0,75x	-	0.1080
	-0.0180
	+
	6.8455	x³	-	1,3x²	+	0,54x	-	0.0720
	0.0900
	P(x)	=	-13.8889	x³	-	1,9x²	+	1,14x	-	0.2160
	+
	172.5000	x³	-	1,8x²	+	0,99x	-	0.1620
	+
	-208.5111	x³	-	1,6x²	+	0,75x	-	0.1080
	+
	76.0611	x³	-	1,3x²	+	0,54x	-	0.0720
	P(x)	=	-13.8889	x³	+	26.3889	x²	-	15.8333	x	+	3.0000	26.3889	-15.8333	3
	172.5000	x³	-	310.5000	x²	+	170.7750	x	-	27.9450	-310.5	170.7750	-27.945
	-208.5111	x³	+	333.6178	x²	-	156.3833	x	+	22.5192	333.6177777778	-156.3833	22.5192
	76.0611	x³	-	98.8794	x²	+	41.0730	x	-	5.4764	-98.88	41.0730	-5.4764
	P(x)	=	26.1611	x³		-49.3728	x²	+	39.6313	x		-7.9022
	P(	0.7	)	=	26.1611	(0,7)³		-49.3728	(0,7)²	+	39.6313	(0,7)		-7.9022
	P(	0.7	)	=	26.1611	(0,343)		-49.3728	(0,49)	+	39.6313	(0,7)		-7.9022
	P(	0.7	)	=	8.9733		-24.1927	+	27.7419		-7.9022
	P(	0.7	)	=	4.6203
Plan2
	i	xi	yi	xi²	yi²	xi . Yi
	1	35	63	1225	3969	2205	1
	2	37	74	1369	5476	2738	2
	3	38	78	1444	6084	2964	3
	4	43	81	1849	6561	3483	4
	5	45	86	2025	7396	3870	5
	6	56	95	3136	9025	5320	6
	7	64	92	4096	8464	5888	7
	8	69	103	4761	10609	7107	8
	9	66	99	4356	9801	6534	9
	10	58	96	3364	9216	5568	10
	11	49	109	2401	11881	5341	11
	12	81	107	6561	11449	8667	12
	13	82	98	6724	9604	8036	13
	14	85	97	7225	9409	8245	14
	15	92	112	8464	12544	10304	15
	16	0	0	0	
	17	0	0	0	
	18	0	0	0		b1=	15	.	(	86270	)	-	(	900	.	1390	)
	19	0	0	0		15	.	(	59000	)	-	(	900	)	²
	20	0	0	0	
	b1=	1294050	-	1251000
	total	900	1390	59000	131488	86270	885000	-	810000
	Exi	900	b1=	43050
	Eyi	1390	75000
	Exiyi	59000
	Exi²	131488	b1=	0.574
	Eyi²	86270
	n	15	b0=	1390	-	(	900	)	(	0.574	)
	15
	b0=	58.2266666667
	yx=	58.2266666667	+	0.574	x
	R²	=	86270	-	(	900	)	(	1390	)
	15
	(	(	59000	)	-	(	900	)	²	)	((	131488	-	(	1390	)	²	)
	15	15
	R²	=	(	2870	)	²
	5000	.	2681.3333333333285
	R²	=	0.614388364
	i	xi	yi	residuo
	1	35	63	-15.3166666667
	2	37	74	-5.4646666667
	3	38	78	-2.0386666667
	4	43	81	-1.9086666667
	5	45	86	1.9433333333
	6	56	95	4.6293333333
	7	64	92	-2.9626666667
	8	69	103	5.1673333333
	9	66	99	2.8893333333
	10	58	96	4.4813333333
	11	49	109	22.6473333333
	12	81	107	2.2793333333
	13	82	98	-7.2946666667
	14	85	97	-10.0166666667
	15	92	112	0.9653333333
	16	0	0	
	17	0	0	
	18	0	0	
	19	0	0	
	20	0	0	
Plan3
	i	x1i	x2i	yi	x1i²	x2i²	yi²	x1ix2i	x1iyi	x2iyi	9
	1	-1	-3	5	1	9	25	3	-5	-15	1	|	9	46	32	|	|	bo	|	|	69	|	9.000	bo	+	46.000	b1	+	32.000	b2	=	69.000	|	-5.111	|
	2	0	-1	6	0	1	36	0	0	-6	2	|	46	400	296	|	|	b1	|	=	|	409	|	46.000	bo	+	400.000	b1	+	296.000	b2	=	409.000	|	-3.556	|
	3	2	0	4	4	0	16	0	8	0	3	|	32	296	236	|	|	b2	|	|	302	|	32.000	bo	+	296.000	b1	+	236.000	b2	=	302.000
	4	3	4	7	9	16	49	12	21	28	4
	5	5	5	8	25	25	64	25	40	40	5	9.000	bo	+	46.000	b1	+	32.000	b2	=	69.000	|	-0.803	|
	6	6	6	11	36	36	121	36	66	66	6	164.889	b1	+	132.444	b2	=	56.333
	7	9	6	13	81	36	169	54	117	78	7	132.444	b1	+	122.222	b2	=	56.667
	8	10	7	9	100	49	81	70	90	63	8
	9	12	8	6	144	64	36	96	72	48	9	9.000	bo	+	46.000	b1	+	32.000	b2	=	69.000
	10	0	0	0	0	0	0		164.889	b1	+	132.444	b2	=	56.333
	11	0	0	0	0	0	0		15.838	b2	=	11.418
	12	0	0	0	0	0	0	
	13	0	0	0	0	0	0		b2	=	11.418
	14	0	0	0	0	0	0		15.838
	15	0	0	0	0	0	0	
	16	0	0	0	0	0	0		b2	=	0.721
	17	0	0	0	0	0	0	
	18	0	0	0	0	0	0		164.889	b1	+ 132,444 .	0.721	=	56.333
	19	0	0	0	0	0	0	
	20	0	0	0	0	0	0		b1	=	56.333	+	-95.479
	soma	46	32	69	400	236	597	296	409	302	164.889
	b1	=	-0.237
	9.00	bo = 	69.000	+	-46 . 	-0.237	+	-32 . 	0.721
	9.00	bo = 	69.000	+	10.921	+	-23.069
	bo = 	56.852
	9.000
	bo = 	6.317
	Equação :	6,316 -0,237 x1 + 0,72 x2 
	R²=	1	-	|	6.316	|
	|	597	-	(	296	)	²	|
	|	9	|
	R²=	1	-	-0.001
	R²=	1.001