Caso 8

Objetivo

Aplicar e interpretar un modelo de regresión lineal múltiple.

Descripción

Aplicar un modelo de regresión lineal múltiple en el conjunto de datos FIFA, con variable dependiente ‘Value’ y varias variables independientes.

Proceso

1. Cargar librerías
1. Cargar los datos (conjunto FIFA)
1. Definir variables independientes.
1. Limpiar el conjunto de datos,
1. Partir en datos de entrenamiento y validación
1. Crear modelo de regresión líneal múltiple
  
  \(y = b0 + b_1x_1 + b_2x_2 + b_3x_3 + ... + b_kx_k\)
1. Predecir con el conjunto de datos de validación
1. Interpretar el caso, 180 a 200 palabras

Cargar librerías

library(readr)
library(dplyr)
library(caret)
library(knitr)

Cargar los datos (conjunto FIFA)

datos <- read.csv("C:/Users/cinth/Documents/ITD/Analisis inteligente de datos/Datos/data.csv", encoding = "UTF-8")

datos_slctd <- select(datos, Value, Age, Overall, Potential, 
        Wage, Special, International.Reputation,Weak.Foot,
        Skill.Moves, Jersey.Number, Height,
        Weight, Crossing, Finishing, HeadingAccuracy,
        ShortPassing, Volleys, Dribbling, Curve,
        FKAccuracy, LongPassing, BallControl, Acceleration,
        SprintSpeed, Agility, Reactions, Balance, ShotPower,
        Jumping, Stamina, Strength,LongShots, Aggression,
        Interceptions, Positioning, Vision,
        Penalties, Composure, Marking, StandingTackle,
        SlidingTackle)

kable(head(datos_slctd, 10), caption = "Variables numéricas seleccionadas (primeros díez registros)", row.names = 1:nrow(datos_slctd))

Variables numéricas seleccionadas (primeros díez registros)
	Value	Age	Overall	Potential	Wage	Special	International.Reputation	Weak.Foot	Skill.Moves	Jersey.Number	Height	Weight	Crossing	Finishing	HeadingAccuracy	ShortPassing	Volleys	Dribbling	Curve	FKAccuracy	LongPassing	BallControl	Acceleration	SprintSpeed	Agility	Reactions	Balance	ShotPower	Jumping	Stamina	Strength	LongShots	Aggression	Interceptions	Positioning	Vision	Penalties	Composure	Marking	StandingTackle	SlidingTackle
1	€110.5M	31	94	94	€565K	2202	5	4	4	10	5’7	159lbs	84	95	70	90	86	97	93	94	87	96	91	86	91	95	95	85	68	72	59	94	48	22	94	94	75	96	33	28	26
2	€77M	33	94	94	€405K	2228	5	4	5	7	6’2	183lbs	84	94	89	81	87	88	81	76	77	94	89	91	87	96	70	95	95	88	79	93	63	29	95	82	85	95	28	31	23
3	€118.5M	26	92	93	€290K	2143	5	5	5	10	5’9	150lbs	79	87	62	84	84	96	88	87	78	95	94	90	96	94	84	80	61	81	49	82	56	36	89	87	81	94	27	24	33
4	€72M	27	91	93	€260K	1471	4	3	1	1	6’4	168lbs	17	13	21	50	13	18	21	19	51	42	57	58	60	90	43	31	67	43	64	12	38	30	12	68	40	68	15	21	13
5	€102M	27	91	92	€355K	2281	4	5	4	7	5’11	154lbs	93	82	55	92	82	86	85	83	91	91	78	76	79	91	77	91	63	90	75	91	76	61	87	94	79	88	68	58	51
6	€93M	27	91	91	€340K	2142	4	4	4	10	5’8	163lbs	81	84	61	89	80	95	83	79	83	94	94	88	95	90	94	82	56	83	66	80	54	41	87	89	86	91	34	27	22
7	€67M	32	91	91	€420K	2280	4	4	4	10	5’8	146lbs	86	72	55	93	76	90	85	78	88	93	80	72	93	90	94	79	68	89	58	82	62	83	79	92	82	84	60	76	73
8	€80M	31	91	91	€455K	2346	5	4	3	9	6’0	190lbs	77	93	77	82	88	87	86	84	64	90	86	75	82	92	83	86	69	90	83	85	87	41	92	84	85	85	62	45	38
9	€51M	32	91	91	€380K	2201	4	3	3	15	6’0	181lbs	66	60	91	78	66	63	74	72	77	84	76	75	78	85	66	79	93	84	83	59	88	90	60	63	75	82	87	92	91
10	€68M	25	90	93	€94K	1331	3	3	1	1	6’2	192lbs	13	11	15	29	13	12	13	14	26	16	43	60	67	86	49	22	76	41	78	12	34	19	11	70	11	70	27	12	18

kable(tail(datos_slctd, 10), caption = "Variables numéricas seleccionadas (últimos díez registros)", row.names = 1:nrow(datos_slctd))

Variables numéricas seleccionadas (últimos díez registros)
	Value	Age	Overall	Potential	Wage	Special	International.Reputation	Weak.Foot	Skill.Moves	Jersey.Number	Height	Weight	Crossing	Finishing	HeadingAccuracy	ShortPassing	Volleys	Dribbling	Curve	FKAccuracy	LongPassing	BallControl	Acceleration	SprintSpeed	Agility	Reactions	Balance	ShotPower	Jumping	Stamina	Strength	LongShots	Aggression	Interceptions	Positioning	Vision	Penalties	Composure	Marking	StandingTackle	SlidingTackle
18198	€60K	18	47	61	€1K	1362	1	3	2	14	5’10	141lbs	44	44	36	53	43	50	48	46	52	51	68	62	58	41	62	50	55	50	38	37	37	28	39	48	49	52	41	47	38
18199	€60K	18	47	70	€1K	792	1	2	1	22	5’11	154lbs	14	8	14	19	8	10	13	10	21	11	18	24	22	36	47	26	56	20	38	5	25	6	5	37	14	34	15	11	13
18200	€70K	18	47	69	€1K	1303	1	3	2	65	5’6	150lbs	31	31	41	51	26	46	35	31	55	47	60	63	53	46	55	49	57	42	43	30	53	49	35	40	36	40	48	49	49
18201	€60K	18	47	62	€1K	1203	1	2	2	21	5’9	157lbs	28	47	47	42	37	39	32	25	30	41	65	48	64	54	80	44	77	31	31	51	26	16	46	37	58	50	15	17	14
18202	€60K	18	47	68	€1K	1098	1	3	2	29	6’1	168lbs	22	23	45	25	27	21	21	27	27	32	52	52	39	43	48	39	74	39	52	16	44	45	20	31	38	43	44	47	53
18203	€60K	19	47	65	€1K	1307	1	2	2	22	5’9	134lbs	34	38	40	49	25	42	30	34	45	43	54	57	60	49	76	43	55	40	47	38	46	46	39	52	43	45	40	48	47
18204	€60K	19	47	63	€1K	1098	1	2	2	21	6’3	170lbs	23	52	52	43	36	39	32	20	25	40	41	39	38	40	52	41	47	43	67	42	47	16	46	33	43	42	22	15	19
18205	€60K	16	47	67	€1K	1189	1	3	2	33	5’8	148lbs	25	40	46	38	38	45	38	27	28	44	70	69	50	47	58	45	60	55	32	45	32	15	48	43	55	41	32	13	11
18206	€60K	17	47	66	€1K	1228	1	3	2	34	5’10	154lbs	44	50	39	42	40	51	34	32	32	52	61	60	52	21	71	64	42	40	48	34	33	22	44	47	50	46	20	25	27
18207	€60K	16	46	66	€1K	1321	1	3	2	33	5’10	176lbs	41	34	46	48	30	43	40	34	44	51	57	55	55	51	63	43	62	47	60	32	56	42	34	49	33	43	40	43	50

Definir variables independientes.

paste("La variable dependiente 'y' es Value")

[1] "La variable dependiente 'y' es Value"

paste("Las variables independientes X1, X2, X3 ... Xn, son las elegidas anteriormente")

[1] "Las variables independientes X1, X2, X3 ... Xn, son las elegidas anteriormente"

Limpiar el conjunto de datos.

mk_to_pesos <- function(m_k) {
  options(scipen=999)
  pesos <- substr(m_k,2,nchar(m_k)-1)
  pesos <- as.numeric(pesos)
  pesos
}

feet_inch_to_m <- function(height){
  est_m <- as.numeric(substring(height, 1,1)) * 30.48 +
    as.numeric(substring(height, 3,4)) * 2.54
  est_m <- round(est_m/100,2)
  est_m
}

lb_to_kg <- function(pounds){
  kgs <- as.numeric(substring(pounds, 1,3))
  kgs <- round(kgs * 0.453592,2)
  kgs
}

a_minusculas <- function(words){
  names(words) <- tolower(names(words))
  words
}

datos_slctd <- datos_slctd %>% 
  mutate(Valor = ifelse(substr(Value, nchar(Value), nchar(Value)) == 'M', mk_to_pesos(Value) * 1000000, mk_to_pesos(Value) * 1000)) %>% 
  filter(Valor > 0)

datos_slctd <- datos_slctd %>% 
  mutate(Salario = ifelse(substr(Wage, nchar(Wage), nchar(Wage)) == 'M', mk_to_pesos(Wage) * 1000000, mk_to_pesos(Wage) * 1000)) %>% 
  filter(Valor > 0)

datos_slctd <- mutate(datos_slctd, Height_m = feet_inch_to_m(Height))

datos_slctd <- mutate(datos_slctd, Weight_kg = lb_to_kg(Weight))

datos_slctd <- a_minusculas(datos_slctd)

datos_slctd <- select(datos_slctd, -value, -wage, -height, -weight)

Observar datos limpios

kable(head(datos_slctd, 10), caption = "Variables numéricas seleccionadas (primeros díez registros)", row.names = 1:nrow(datos_slctd))

Variables numéricas seleccionadas (primeros díez registros)
	age	overall	potential	special	international.reputation	weak.foot	skill.moves	jersey.number	crossing	finishing	headingaccuracy	shortpassing	volleys	dribbling	curve	fkaccuracy	longpassing	ballcontrol	acceleration	sprintspeed	agility	reactions	balance	shotpower	jumping	stamina	strength	longshots	aggression	interceptions	positioning	vision	penalties	composure	marking	standingtackle	slidingtackle	valor	salario	height_m	weight_kg
1	31	94	94	2202	5	4	4	10	84	95	70	90	86	97	93	94	87	96	91	86	91	95	95	85	68	72	59	94	48	22	94	94	75	96	33	28	26	110500000	565000	1.70	72.12
2	33	94	94	2228	5	4	5	7	84	94	89	81	87	88	81	76	77	94	89	91	87	96	70	95	95	88	79	93	63	29	95	82	85	95	28	31	23	77000000	405000	1.88	83.01
3	26	92	93	2143	5	5	5	10	79	87	62	84	84	96	88	87	78	95	94	90	96	94	84	80	61	81	49	82	56	36	89	87	81	94	27	24	33	118500000	290000	1.75	68.04
4	27	91	93	1471	4	3	1	1	17	13	21	50	13	18	21	19	51	42	57	58	60	90	43	31	67	43	64	12	38	30	12	68	40	68	15	21	13	72000000	260000	1.93	76.20
5	27	91	92	2281	4	5	4	7	93	82	55	92	82	86	85	83	91	91	78	76	79	91	77	91	63	90	75	91	76	61	87	94	79	88	68	58	51	102000000	355000	1.80	69.85
6	27	91	91	2142	4	4	4	10	81	84	61	89	80	95	83	79	83	94	94	88	95	90	94	82	56	83	66	80	54	41	87	89	86	91	34	27	22	93000000	340000	1.73	73.94
7	32	91	91	2280	4	4	4	10	86	72	55	93	76	90	85	78	88	93	80	72	93	90	94	79	68	89	58	82	62	83	79	92	82	84	60	76	73	67000000	420000	1.73	66.22
8	31	91	91	2346	5	4	3	9	77	93	77	82	88	87	86	84	64	90	86	75	82	92	83	86	69	90	83	85	87	41	92	84	85	85	62	45	38	80000000	455000	1.83	86.18
9	32	91	91	2201	4	3	3	15	66	60	91	78	66	63	74	72	77	84	76	75	78	85	66	79	93	84	83	59	88	90	60	63	75	82	87	92	91	51000000	380000	1.83	82.10
10	25	90	93	1331	3	3	1	1	13	11	15	29	13	12	13	14	26	16	43	60	67	86	49	22	76	41	78	12	34	19	11	70	11	70	27	12	18	68000000	94000	1.88	87.09

kable(tail(datos_slctd, 10), caption = "Variables numéricas seleccionadas (últimos díez registros)", row.names = 1:nrow(datos_slctd))

Variables numéricas seleccionadas (últimos díez registros)
	age	overall	potential	special	international.reputation	weak.foot	skill.moves	jersey.number	crossing	finishing	headingaccuracy	shortpassing	volleys	dribbling	curve	fkaccuracy	longpassing	ballcontrol	acceleration	sprintspeed	agility	reactions	balance	shotpower	jumping	stamina	strength	longshots	aggression	interceptions	positioning	vision	penalties	composure	marking	standingtackle	slidingtackle	valor	salario	height_m	weight_kg
17946	18	47	61	1362	1	3	2	14	44	44	36	53	43	50	48	46	52	51	68	62	58	41	62	50	55	50	38	37	37	28	39	48	49	52	41	47	38	60000	1000	1.78	63.96
17947	18	47	70	792	1	2	1	22	14	8	14	19	8	10	13	10	21	11	18	24	22	36	47	26	56	20	38	5	25	6	5	37	14	34	15	11	13	60000	1000	1.80	69.85
17948	18	47	69	1303	1	3	2	65	31	31	41	51	26	46	35	31	55	47	60	63	53	46	55	49	57	42	43	30	53	49	35	40	36	40	48	49	49	70000	1000	1.68	68.04
17949	18	47	62	1203	1	2	2	21	28	47	47	42	37	39	32	25	30	41	65	48	64	54	80	44	77	31	31	51	26	16	46	37	58	50	15	17	14	60000	1000	1.75	71.21
17950	18	47	68	1098	1	3	2	29	22	23	45	25	27	21	21	27	27	32	52	52	39	43	48	39	74	39	52	16	44	45	20	31	38	43	44	47	53	60000	1000	1.85	76.20
17951	19	47	65	1307	1	2	2	22	34	38	40	49	25	42	30	34	45	43	54	57	60	49	76	43	55	40	47	38	46	46	39	52	43	45	40	48	47	60000	1000	1.75	60.78
17952	19	47	63	1098	1	2	2	21	23	52	52	43	36	39	32	20	25	40	41	39	38	40	52	41	47	43	67	42	47	16	46	33	43	42	22	15	19	60000	1000	1.91	77.11
17953	16	47	67	1189	1	3	2	33	25	40	46	38	38	45	38	27	28	44	70	69	50	47	58	45	60	55	32	45	32	15	48	43	55	41	32	13	11	60000	1000	1.73	67.13
17954	17	47	66	1228	1	3	2	34	44	50	39	42	40	51	34	32	32	52	61	60	52	21	71	64	42	40	48	34	33	22	44	47	50	46	20	25	27	60000	1000	1.78	69.85
17955	16	46	66	1321	1	3	2	33	41	34	46	48	30	43	40	34	44	51	57	55	55	51	63	43	62	47	60	32	56	42	34	49	33	43	40	43	50	60000	1000	1.78	79.83

Partir en datos de entrenamiento y validación (70 - 30)

set.seed(2020)
conjunto_entrenamiento <- createDataPartition(y = datos_slctd$overall, p = 0.7, list = FALSE, times = 1)

datos_entrenamiento <- datos_slctd[conjunto_entrenamiento, ]

datos_validacion <- datos_slctd[-conjunto_entrenamiento, ]

kable(head(datos_entrenamiento, 10), caption = "Datos de entrenamiento (primeros díez registros)", row.names = 1:nrow(datos_entrenamiento))

Datos de entrenamiento (primeros díez registros)
	age	overall	potential	special	international.reputation	weak.foot	skill.moves	jersey.number	crossing	finishing	headingaccuracy	shortpassing	volleys	dribbling	curve	fkaccuracy	longpassing	ballcontrol	acceleration	sprintspeed	agility	reactions	balance	shotpower	jumping	stamina	strength	longshots	aggression	interceptions	positioning	vision	penalties	composure	marking	standingtackle	slidingtackle	valor	salario	height_m	weight_kg
1	31	94	94	2202	5	4	4	10	84	95	70	90	86	97	93	94	87	96	91	86	91	95	95	85	68	72	59	94	48	22	94	94	75	96	33	28	26	110500000	565000	1.70	72.12
2	33	94	94	2228	5	4	5	7	84	94	89	81	87	88	81	76	77	94	89	91	87	96	70	95	95	88	79	93	63	29	95	82	85	95	28	31	23	77000000	405000	1.88	83.01
3	26	92	93	2143	5	5	5	10	79	87	62	84	84	96	88	87	78	95	94	90	96	94	84	80	61	81	49	82	56	36	89	87	81	94	27	24	33	118500000	290000	1.75	68.04
5	27	91	92	2281	4	5	4	7	93	82	55	92	82	86	85	83	91	91	78	76	79	91	77	91	63	90	75	91	76	61	87	94	79	88	68	58	51	102000000	355000	1.80	69.85
6	27	91	91	2142	4	4	4	10	81	84	61	89	80	95	83	79	83	94	94	88	95	90	94	82	56	83	66	80	54	41	87	89	86	91	34	27	22	93000000	340000	1.73	73.94
7	32	91	91	2280	4	4	4	10	86	72	55	93	76	90	85	78	88	93	80	72	93	90	94	79	68	89	58	82	62	83	79	92	82	84	60	76	73	67000000	420000	1.73	66.22
8	31	91	91	2346	5	4	3	9	77	93	77	82	88	87	86	84	64	90	86	75	82	92	83	86	69	90	83	85	87	41	92	84	85	85	62	45	38	80000000	455000	1.83	86.18
11	29	90	90	2152	4	4	4	9	62	91	85	83	89	85	77	86	65	89	77	78	78	90	78	88	84	78	84	84	80	39	91	77	88	86	34	42	19	77000000	205000	1.83	79.83
12	28	90	90	2190	4	5	3	8	88	76	54	92	82	81	86	84	93	90	64	62	70	89	71	87	30	75	73	92	60	82	79	86	73	85	72	79	69	76500000	355000	1.83	76.20
14	32	90	90	2115	4	2	4	21	84	76	54	93	82	89	82	77	87	94	70	64	92	90	90	72	64	78	52	75	57	50	89	92	75	93	59	53	29	60000000	285000	1.73	67.13

kable(head(datos_validacion, 10), caption = "Datos de validación (últimos díez registros)", row.names = 1:nrow(datos_validacion))

Datos de validación (últimos díez registros)
	age	overall	potential	special	international.reputation	weak.foot	skill.moves	jersey.number	crossing	finishing	headingaccuracy	shortpassing	volleys	dribbling	curve	fkaccuracy	longpassing	ballcontrol	acceleration	sprintspeed	agility	reactions	balance	shotpower	jumping	stamina	strength	longshots	aggression	interceptions	positioning	vision	penalties	composure	marking	standingtackle	slidingtackle	valor	salario	height_m	weight_kg
4	27	91	93	1471	4	3	1	1	17	13	21	50	13	18	21	19	51	42	57	58	60	90	43	31	67	43	64	12	38	30	12	68	40	68	15	21	13	72000000	260000	1.93	76.20
9	32	91	91	2201	4	3	3	15	66	60	91	78	66	63	74	72	77	84	76	75	78	85	66	79	93	84	83	59	88	90	60	63	75	82	87	92	91	51000000	380000	1.83	82.10
10	25	90	93	1331	3	3	1	1	13	11	15	29	13	12	13	14	26	16	43	60	67	86	49	22	76	41	78	12	34	19	11	70	11	70	27	12	18	68000000	94000	1.88	87.09
13	32	90	90	1946	3	3	2	10	55	42	92	79	47	53	49	51	70	76	68	68	58	85	54	67	91	66	88	43	89	88	48	52	50	82	90	89	89	44000000	125000	1.88	78.02
16	24	89	94	2092	3	3	4	21	82	84	68	87	88	92	88	88	75	92	87	83	91	86	85	82	75	80	65	88	48	32	84	87	86	84	23	20	20	89000000	205000	1.78	74.84
22	31	89	89	2161	4	4	3	21	70	89	89	78	90	80	77	76	52	82	75	76	77	91	59	87	88	92	78	79	84	48	93	77	85	82	52	45	39	60000000	200000	1.85	77.11
23	32	89	89	1473	5	4	1	1	15	13	25	55	11	30	14	11	59	48	54	60	51	84	35	25	77	43	80	16	29	30	12	70	47	70	17	10	11	38000000	130000	1.93	92.08
25	33	89	89	1841	4	3	2	3	58	33	83	59	45	58	60	31	59	57	63	75	54	82	55	78	89	65	89	49	92	88	28	50	50	84	93	93	90	27000000	215000	1.88	84.82
30	27	88	88	2017	3	3	4	10	86	77	56	85	74	90	87	77	78	93	94	86	94	83	93	75	53	75	44	84	34	26	83	87	61	83	51	24	22	62000000	165000	1.63	58.97
31	26	88	91	2137	3	3	4	22	75	79	55	89	65	94	88	76	83	95	75	69	87	77	90	69	64	70	59	87	58	64	78	89	76	86	60	64	51	73500000	315000	1.75	78.93

Crear modelo de regresión líneal múltiple \(y = b0 + b_1x_1 + b_2x_2 + b_3x_3 + ... + b_kx_k\)

modelo_regresion_multiple <- lm(formula = valor ~ ., datos_entrenamiento)

summary(modelo_regresion_multiple)


Call:
lm(formula = valor ~ ., data = datos_entrenamiento)

Residuals:
      Min        1Q    Median        3Q       Max 
-19161476   -832836    -60785    700651  56366387 

Coefficients:
                             Estimate   Std. Error t value             Pr(>|t|)
(Intercept)              -6237527.444  1293049.221  -4.824  0.00000142445759378
age                       -260441.896    10830.032 -24.048 < 0.0000000000000002
overall                    263151.521    12324.511  21.352 < 0.0000000000000002
potential                  -45061.430     9216.102  -4.889  0.00000102388538355
special                     -4971.156     1050.494  -4.732  0.00000224521357859
international.reputation  2096975.406    80512.189  26.045 < 0.0000000000000002
weak.foot                   64861.448    37182.465   1.744             0.081112
skill.moves                227777.379    60540.118   3.762             0.000169
jersey.number               -5180.184     1478.922  -3.503             0.000462
crossing                    -4564.702     3279.621  -1.392             0.163996
finishing                   19777.935     3898.800   5.073  0.00000039756985080
headingaccuracy             -3149.386     2946.924  -1.069             0.285224
shortpassing                 -403.627     5483.003  -0.074             0.941319
volleys                     10266.460     3483.094   2.948             0.003209
dribbling                   -4145.766     4894.856  -0.847             0.397031
curve                        -914.425     3441.961  -0.266             0.790498
fkaccuracy                  19978.179     3058.942   6.531  0.00000000006782730
longpassing                 17968.651     4230.417   4.247  0.00002177436178140
ballcontrol                -23414.482     5821.108  -4.022  0.00005796128114699
acceleration                 7772.372     4605.084   1.688             0.091478
sprintspeed                 -1521.284     4289.824  -0.355             0.722876
agility                     -1031.663     3552.756  -0.290             0.771528
reactions                   34476.184     5330.003   6.468  0.00000000010278779
balance                      5856.472     3586.184   1.633             0.102480
shotpower                   -9906.667     3540.906  -2.798             0.005153
jumping                       549.760     2690.688   0.204             0.838107
stamina                     22668.921     2876.934   7.880  0.00000000000000356
strength                     3944.760     3414.156   1.155             0.247943
longshots                     771.132     3840.908   0.201             0.840883
aggression                   3220.423     2690.702   1.197             0.231379
interceptions               -4011.602     3769.712  -1.064             0.287274
positioning                  9072.650     3724.818   2.436             0.014876
vision                      10036.751     3659.156   2.743             0.006098
penalties                   -7407.033     3273.003  -2.263             0.023648
composure                     896.362     3767.794   0.238             0.811962
marking                      9743.854     2960.754   3.291             0.001001
standingtackle              21022.779     5464.713   3.847             0.000120
slidingtackle              -19840.500     5183.721  -3.827             0.000130
salario                       160.301        1.456 110.081 < 0.0000000000000002
height_m                 -1159502.240   664549.743  -1.745             0.081045
weight_kg                    1722.922     5678.866   0.303             0.761596
                            
(Intercept)              ***
age                      ***
overall                  ***
potential                ***
special                  ***
international.reputation ***
weak.foot                .  
skill.moves              ***
jersey.number            ***
crossing                    
finishing                ***
headingaccuracy             
shortpassing                
volleys                  ** 
dribbling                   
curve                       
fkaccuracy               ***
longpassing              ***
ballcontrol              ***
acceleration             .  
sprintspeed                 
agility                     
reactions                ***
balance                     
shotpower                ** 
jumping                     
stamina                  ***
strength                    
longshots                   
aggression                  
interceptions               
positioning              *  
vision                   ** 
penalties                *  
composure                   
marking                  ** 
standingtackle           ***
slidingtackle            ***
salario                  ***
height_m                 .  
weight_kg                   
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 2527000 on 12504 degrees of freedom
  (25 observations deleted due to missingness)
Multiple R-squared:  0.8088,    Adjusted R-squared:  0.8082 
F-statistic:  1323 on 40 and 12504 DF,  p-value: < 0.00000000000000022

Optimización del modelo

Selección de variables que el primer modelo no identifica como estadísticamente signitificativas.

modelo_regresion_multiple_2 <- lm(formula = valor ~ age + overall + potential + special + international.reputation + jersey.number + finishing +  fkaccuracy + longpassing + ballcontrol + reactions +  stamina + salario , datos_entrenamiento)

summary(modelo_regresion_multiple_2)


Call:
lm(formula = valor ~ age + overall + potential + special + international.reputation + 
    jersey.number + finishing + fkaccuracy + longpassing + ballcontrol + 
    reactions + stamina + salario, data = datos_entrenamiento)

Residuals:
      Min        1Q    Median        3Q       Max 
-18997420   -824040    -75785    697276  56424654 

Coefficients:
                            Estimate  Std. Error t value             Pr(>|t|)
(Intercept)              -7857348.39   452119.77 -17.379 < 0.0000000000000002
age                       -266566.73    10213.53 -26.099 < 0.0000000000000002
overall                    254603.39    10507.57  24.230 < 0.0000000000000002
potential                  -44787.95     9087.82  -4.928   0.0000008398819053
special                     -3549.32      372.39  -9.531 < 0.0000000000000002
international.reputation  2102462.29    80084.70  26.253 < 0.0000000000000002
jersey.number               -5350.31     1478.81  -3.618             0.000298
finishing                   22222.02     2169.52  10.243 < 0.0000000000000002
fkaccuracy                  18559.56     2463.89   7.533   0.0000000000000531
longpassing                 16414.29     3085.71   5.319   0.0000001058745305
ballcontrol                -19753.30     4063.23  -4.861   0.0000011792807544
reactions                   36293.34     5005.88   7.250   0.0000000000004408
stamina                     22403.91     2712.00   8.261 < 0.0000000000000002
salario                       160.60        1.46 110.037 < 0.0000000000000002
                            
(Intercept)              ***
age                      ***
overall                  ***
potential                ***
special                  ***
international.reputation ***
jersey.number            ***
finishing                ***
fkaccuracy               ***
longpassing              ***
ballcontrol              ***
reactions                ***
stamina                  ***
salario                  ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 2538000 on 12531 degrees of freedom
  (25 observations deleted due to missingness)
Multiple R-squared:  0.8068,    Adjusted R-squared:  0.8066 
F-statistic:  4026 on 13 and 12531 DF,  p-value: < 0.00000000000000022

Predecir con el conjunto de datos de validación

Tomaremos el modelo optimizado y haremos la predicción con la función \(\textit{predict()}\)

prediccion <- predict(object = modelo_regresion_multiple_2, newdata = datos_validacion)

Agregar al conjunto de datos las predicciones, para comparar con los datos de validación.

datos_validacion_df <- mutate(datos_validacion, predicho = prediccion)

kable(head(datos_validacion_df, 10), caption = "Primeros díez registros con sus respectivas predicciones")

Primeros díez registros con sus respectivas predicciones
age	overall	potential	special	international.reputation	weak.foot	skill.moves	jersey.number	crossing	finishing	headingaccuracy	shortpassing	volleys	dribbling	curve	fkaccuracy	longpassing	ballcontrol	acceleration	sprintspeed	agility	reactions	balance	shotpower	jumping	stamina	strength	longshots	aggression	interceptions	positioning	vision	penalties	composure	marking	standingtackle	slidingtackle	valor	salario	height_m	weight_kg	predicho
27	91	93	1471	4	3	1	1	17	13	21	50	13	18	21	19	51	42	57	58	60	90	43	31	67	43	64	12	38	30	12	68	40	68	15	21	13	72000000	260000	1.93	76.20	53767689
32	91	91	2201	4	3	3	15	66	60	91	78	66	63	74	72	77	84	76	75	78	85	66	79	93	84	83	59	88	90	60	63	75	82	87	92	91	51000000	380000	1.83	82.10	71493065
25	90	93	1331	3	3	1	1	13	11	15	29	13	12	13	14	26	16	43	60	67	86	49	22	76	41	78	12	34	19	11	70	11	70	27	12	18	68000000	94000	1.88	87.09	25556761
32	90	90	1946	3	3	2	10	55	42	92	79	47	53	49	51	70	76	68	68	58	85	54	67	91	66	88	43	89	88	48	52	50	82	90	89	89	44000000	125000	1.88	78.02	28009254
24	89	94	2092	3	3	4	21	82	84	68	87	88	92	88	88	75	92	87	83	91	86	85	82	75	80	65	88	48	32	84	87	86	84	23	20	20	89000000	205000	1.78	74.84	43715121
31	89	89	2161	4	4	3	21	70	89	89	78	90	80	77	76	52	82	75	76	77	91	59	87	88	92	78	79	84	48	93	77	85	82	52	45	39	60000000	200000	1.85	77.11	43286358
32	89	89	1473	5	4	1	1	15	13	25	55	11	30	14	11	59	48	54	60	51	84	35	25	77	43	80	16	29	30	12	70	47	70	17	10	11	38000000	130000	1.93	92.08	32968482
33	89	89	1841	4	3	2	3	58	33	83	59	45	58	60	31	59	57	63	75	54	82	55	78	89	65	89	49	92	88	28	50	50	84	93	93	90	27000000	215000	1.88	84.82	43991912
27	88	88	2017	3	3	4	10	86	77	56	85	74	90	87	77	78	93	94	86	94	83	93	75	53	75	44	84	34	26	83	87	61	83	51	24	22	62000000	165000	1.63	58.97	36279405
26	88	91	2137	3	3	4	22	75	79	55	89	65	94	88	76	83	95	75	69	87	77	90	69	64	70	59	87	58	64	78	89	76	86	60	64	51	73500000	315000	1.75	78.93	59750432

kable(tail(datos_validacion_df, 10), caption = "Últimos díez registros con sus respectivas predicciones")

Últimos díez registros con sus respectivas predicciones
	age	overall	potential	special	international.reputation	weak.foot	skill.moves	jersey.number	crossing	finishing	headingaccuracy	shortpassing	volleys	dribbling	curve	fkaccuracy	longpassing	ballcontrol	acceleration	sprintspeed	agility	reactions	balance	shotpower	jumping	stamina	strength	longshots	aggression	interceptions	positioning	vision	penalties	composure	marking	standingtackle	slidingtackle	valor	salario	height_m	weight_kg	predicho
5376	19	48	59	1152	1	3	2	28	28	23	45	27	24	25	21	26	29	28	63	50	47	42	76	35	65	49	49	21	45	46	25	29	37	43	42	54	54	40000	1000	1.73	72.12	-1780511
5377	18	48	63	1370	1	3	3	24	38	34	49	54	34	49	33	37	50	41	67	61	61	46	59	50	56	64	55	35	52	39	46	45	36	44	44	40	41	60000	1000	1.85	73.03	-1427709
5378	17	48	66	1296	1	2	2	32	45	46	46	38	27	46	28	24	34	38	61	57	56	47	66	39	59	60	48	33	53	46	43	37	33	38	43	49	45	50000	1000	1.80	60.78	-1306960
5379	18	48	55	1368	1	3	2	33	33	24	42	54	33	44	34	36	50	47	61	57	57	44	58	47	64	59	66	31	53	49	35	46	37	42	47	49	53	40000	1000	1.85	81.19	-1654365
5380	18	47	67	1285	1	3	2	32	32	32	45	48	31	41	32	43	47	37	53	55	31	47	61	41	54	61	55	34	44	44	51	54	34	46	35	44	47	60000	1000	1.75	79.83	-1536809
5381	18	47	64	1191	1	2	2	4	36	25	40	27	27	46	31	25	23	29	64	58	55	54	81	22	56	54	40	22	48	49	35	30	32	32	41	48	48	50000	1000	1.73	66.22	-1547318
5382	19	47	61	1333	1	3	2	26	31	28	40	53	31	46	39	37	48	48	58	58	60	48	79	42	63	35	51	30	55	44	28	51	44	35	41	44	54	60000	1000	1.70	66.22	-2620240
5383	18	47	69	1303	1	3	2	65	31	31	41	51	26	46	35	31	55	47	60	63	53	46	55	49	57	42	43	30	53	49	35	40	36	40	48	49	49	70000	1000	1.68	68.04	-2639956
5384	19	47	65	1307	1	2	2	22	34	38	40	49	25	42	30	34	45	43	54	57	60	49	76	43	55	40	47	38	46	46	39	52	43	45	40	48	47	60000	1000	1.75	60.78	-2321330
5385	16	46	66	1321	1	3	2	33	41	34	46	48	30	43	40	34	44	51	57	55	55	51	63	43	62	47	60	32	56	42	34	49	33	43	40	43	50	60000	1000	1.78	79.83	-1963480

8. Interpretar el caso, 180 a 200 palabras

Al aplicar un modelo de regresión líneal múltiple tomamos como variable dependiente “Value” y como independientes las que arrojaron mayor valor estadísticamente signficativo, con estas variables se busca encontrar qué factores determinan el precio económico de un jugador. Se realizaron dos versiones de este modelo, uno con todas las variables y uno más optimizado, en el primer modelo encontramos que su R-squared es de 0.8088 y su Adjusted R-squared de 0.8082, mientas que en el segundo modelo sus valores son de 0.8068 y 0.8066 respectivamente, presentando una pequeña disminución en ambos valores a comparación del primer modelo. No sabemos con certeza si el modelo este haciendo bien sus predicciones, dado que en comparaciones con valores reales en el dataset algunos de los jugadores en vez de ganas por jugar, terminan pagando por lo mismo, algunos de los valores son muy cercanos a los establecidos en el conjunto de datos, pero otros como se menciono anteriormente están muy lejos de serlo, dándonos así una mejor visión del funcionamiento y comportamiento de las variables de este conjunto.