Modelos sobre Casen-Censo

0 Lectura de la tabla madre

tabla_001 <- readRDS("tabla_001.rds")
r3_100 <- tabla_001[c(1:100),]
kbl(r3_100) %>%
  kable_styling(bootstrap_options = c("striped", "hover")) %>%
  kable_paper() %>%
  scroll_box(width = "100%", height = "300px")

zona	código.x	Freq.x	anio	p	comuna.x	promedio_i	año	comuna.y	personas	Ingresos_expandidos	Freq.y	p_poblacional	código.y	multi_pob	p_variable
10101011001	10101	60	2017	0.0055366	Puerto Montt	268732.4	2017	10101	245902	66081845388	584	0.0023749	10101	156939747	0.0002440
10101011002	10101	177	2017	0.0163329	Puerto Montt	268732.4	2017	10101	245902	66081845388	2941	0.0119600	10101	790342117	0.0007198
10101021001	10101	82	2017	0.0075667	Puerto Montt	268732.4	2017	10101	245902	66081845388	3953	0.0160755	10101	1062299350	0.0003335
10101021002	10101	77	2017	0.0071053	Puerto Montt	268732.4	2017	10101	245902	66081845388	1107	0.0045018	10101	297486815	0.0003131
10101021003	10101	70	2017	0.0064594	Puerto Montt	268732.4	2017	10101	245902	66081845388	2294	0.0093289	10101	616472226	0.0002847
10101021004	10101	99	2017	0.0091354	Puerto Montt	268732.4	2017	10101	245902	66081845388	3391	0.0137900	10101	911271717	0.0004026
10101021005	10101	171	2017	0.0157793	Puerto Montt	268732.4	2017	10101	245902	66081845388	2564	0.0104269	10101	689029986	0.0006954
10101031001	10101	133	2017	0.0122728	Puerto Montt	268732.4	2017	10101	245902	66081845388	4530	0.0184220	10101	1217357970	0.0005409
10101031002	10101	115	2017	0.0106118	Puerto Montt	268732.4	2017	10101	245902	66081845388	4740	0.0192760	10101	1273791783	0.0004677
10101031003	10101	94	2017	0.0086740	Puerto Montt	268732.4	2017	10101	245902	66081845388	4107	0.0167018	10101	1103684147	0.0003823
10101031004	10101	88	2017	0.0081203	Puerto Montt	268732.4	2017	10101	245902	66081845388	2856	0.0116144	10101	767499859	0.0003579
10101031005	10101	146	2017	0.0134724	Puerto Montt	268732.4	2017	10101	245902	66081845388	5690	0.0231393	10101	1529087605	0.0005937
10101031006	10101	94	2017	0.0086740	Puerto Montt	268732.4	2017	10101	245902	66081845388	2460	0.0100040	10101	661081812	0.0003823
10101031007	10101	39	2017	0.0035988	Puerto Montt	268732.4	2017	10101	245902	66081845388	2292	0.0093208	10101	615934761	0.0001586
10101031008	10101	54	2017	0.0049829	Puerto Montt	268732.4	2017	10101	245902	66081845388	3585	0.0145790	10101	963405811	0.0002196
10101031009	10101	166	2017	0.0153179	Puerto Montt	268732.4	2017	10101	245902	66081845388	4436	0.0180397	10101	1192097121	0.0006751
10101031010	10101	92	2017	0.0084894	Puerto Montt	268732.4	2017	10101	245902	66081845388	3566	0.0145017	10101	958299894	0.0003741
10101031011	10101	49	2017	0.0045215	Puerto Montt	268732.4	2017	10101	245902	66081845388	2757	0.0112118	10101	740895347	0.0001993
10101031012	10101	94	2017	0.0086740	Puerto Montt	268732.4	2017	10101	245902	66081845388	1849	0.0075193	10101	496886289	0.0003823
10101031013	10101	73	2017	0.0067362	Puerto Montt	268732.4	2017	10101	245902	66081845388	3945	0.0160430	10101	1060149491	0.0002969
10101031014	10101	109	2017	0.0100581	Puerto Montt	268732.4	2017	10101	245902	66081845388	2265	0.0092110	10101	608678985	0.0004433
10101031015	10101	31	2017	0.0028606	Puerto Montt	268732.4	2017	10101	245902	66081845388	1930	0.0078487	10101	518653616	0.0001261
10101031016	10101	248	2017	0.0228846	Puerto Montt	268732.4	2017	10101	245902	66081845388	3071	0.0124887	10101	825277335	0.0010085
10101031017	10101	60	2017	0.0055366	Puerto Montt	268732.4	2017	10101	245902	66081845388	3885	0.0157990	10101	1044025544	0.0002440
10101032002	10101	2	2017	0.0001846	Puerto Montt	268732.4	2017	10101	245902	66081845388	129	0.0005246	10101	34666485	0.0000081
10101032011	10101	20	2017	0.0018455	Puerto Montt	268732.4	2017	10101	245902	66081845388	426	0.0017324	10101	114480021	0.0000813
10101032019	10101	32	2017	0.0029528	Puerto Montt	268732.4	2017	10101	245902	66081845388	829	0.0033713	10101	222779196	0.0001301
10101041001	10101	70	2017	0.0064594	Puerto Montt	268732.4	2017	10101	245902	66081845388	4342	0.0176574	10101	1166836271	0.0002847
10101041002	10101	55	2017	0.0050752	Puerto Montt	268732.4	2017	10101	245902	66081845388	2169	0.0088206	10101	582880671	0.0002237
10101041003	10101	774	2017	0.0714220	Puerto Montt	268732.4	2017	10101	245902	66081845388	5202	0.0211548	10101	1397946172	0.0031476
10101051001	10101	246	2017	0.0227000	Puerto Montt	268732.4	2017	10101	245902	66081845388	2463	0.0100162	10101	661888009	0.0010004
10101051002	10101	33	2017	0.0030451	Puerto Montt	268732.4	2017	10101	245902	66081845388	1913	0.0077795	10101	514085165	0.0001342
10101051003	10101	65	2017	0.0059980	Puerto Montt	268732.4	2017	10101	245902	66081845388	3272	0.0133061	10101	879292556	0.0002643
10101051004	10101	307	2017	0.0283289	Puerto Montt	268732.4	2017	10101	245902	66081845388	3633	0.0147742	10101	976304968	0.0012485
10101061001	10101	1239	2017	0.1143305	Puerto Montt	268732.4	2017	10101	245902	66081845388	6787	0.0276004	10101	1823887096	0.0050386
10101061002	10101	329	2017	0.0303590	Puerto Montt	268732.4	2017	10101	245902	66081845388	2729	0.0110979	10101	733370839	0.0013379
10101061003	10101	160	2017	0.0147642	Puerto Montt	268732.4	2017	10101	245902	66081845388	3668	0.0149165	10101	985710604	0.0006507
10101061004	10101	110	2017	0.0101504	Puerto Montt	268732.4	2017	10101	245902	66081845388	2995	0.0121796	10101	804853669	0.0004473
10101061005	10101	312	2017	0.0287903	Puerto Montt	268732.4	2017	10101	245902	66081845388	2571	0.0104554	10101	690911113	0.0012688
10101061006	10101	401	2017	0.0370029	Puerto Montt	268732.4	2017	10101	245902	66081845388	4130	0.0167953	10101	1109864993	0.0016307
10101061007	10101	12	2017	0.0011073	Puerto Montt	268732.4	2017	10101	245902	66081845388	817	0.0033225	10101	219554407	0.0000488
10101061008	10101	388	2017	0.0358033	Puerto Montt	268732.4	2017	10101	245902	66081845388	2109	0.0085766	10101	566756724	0.0015779
10101061009	10101	1	2017	0.0000923	Puerto Montt	268732.4	2017	10101	245902	66081845388	168	0.0006832	10101	45147051	0.0000041
10101061010	10101	6	2017	0.0005537	Puerto Montt	268732.4	2017	10101	245902	66081845388	1543	0.0062749	10101	414654161	0.0000244
10101062003	10101	10	2017	0.0009228	Puerto Montt	268732.4	2017	10101	245902	66081845388	158	0.0006425	10101	42459726	0.0000407
10101062008	10101	72	2017	0.0066439	Puerto Montt	268732.4	2017	10101	245902	66081845388	581	0.0023627	10101	156133550	0.0002928
10101062013	10101	61	2017	0.0056289	Puerto Montt	268732.4	2017	10101	245902	66081845388	571	0.0023221	10101	153446225	0.0002481
10101062029	10101	1	2017	0.0000923	Puerto Montt	268732.4	2017	10101	245902	66081845388	47	0.0001911	10101	12630425	0.0000041
10101062039	10101	4	2017	0.0003691	Puerto Montt	268732.4	2017	10101	245902	66081845388	67	0.0002725	10101	18005074	0.0000163
10101071001	10101	20	2017	0.0018455	Puerto Montt	268732.4	2017	10101	245902	66081845388	2352	0.0095648	10101	632058708	0.0000813
10101071002	10101	54	2017	0.0049829	Puerto Montt	268732.4	2017	10101	245902	66081845388	3919	0.0159372	10101	1053162447	0.0002196
10101071003	10101	112	2017	0.0103350	Puerto Montt	268732.4	2017	10101	245902	66081845388	4978	0.0202438	10101	1337750105	0.0004555
10101071004	10101	75	2017	0.0069207	Puerto Montt	268732.4	2017	10101	245902	66081845388	3443	0.0140015	10101	925245804	0.0003050
10101071005	10101	61	2017	0.0056289	Puerto Montt	268732.4	2017	10101	245902	66081845388	2751	0.0111874	10101	739282953	0.0002481
10101071006	10101	60	2017	0.0055366	Puerto Montt	268732.4	2017	10101	245902	66081845388	4214	0.0171369	10101	1132438518	0.0002440
10101071007	10101	29	2017	0.0026760	Puerto Montt	268732.4	2017	10101	245902	66081845388	2345	0.0095363	10101	630177581	0.0001179
10101071008	10101	77	2017	0.0071053	Puerto Montt	268732.4	2017	10101	245902	66081845388	5480	0.0222853	10101	1472653792	0.0003131
10101071009	10101	49	2017	0.0045215	Puerto Montt	268732.4	2017	10101	245902	66081845388	3549	0.0144326	10101	953731443	0.0001993
10101071010	10101	48	2017	0.0044293	Puerto Montt	268732.4	2017	10101	245902	66081845388	3521	0.0143187	10101	946206935	0.0001952
10101071011	10101	43	2017	0.0039679	Puerto Montt	268732.4	2017	10101	245902	66081845388	3094	0.0125822	10101	831458181	0.0001749
10101071012	10101	47	2017	0.0043370	Puerto Montt	268732.4	2017	10101	245902	66081845388	2621	0.0106587	10101	704347735	0.0001911
10101071014	10101	26	2017	0.0023992	Puerto Montt	268732.4	2017	10101	245902	66081845388	875	0.0035583	10101	235140888	0.0001057
10101072014	10101	36	2017	0.0033220	Puerto Montt	268732.4	2017	10101	245902	66081845388	997	0.0040545	10101	267926246	0.0001464
10101072021	10101	4	2017	0.0003691	Puerto Montt	268732.4	2017	10101	245902	66081845388	44	0.0001789	10101	11824228	0.0000163
10101072028	10101	4	2017	0.0003691	Puerto Montt	268732.4	2017	10101	245902	66081845388	145	0.0005897	10101	38966204	0.0000163
10101072029	10101	36	2017	0.0033220	Puerto Montt	268732.4	2017	10101	245902	66081845388	1051	0.0042741	10101	282437798	0.0001464
10101072036	10101	1	2017	0.0000923	Puerto Montt	268732.4	2017	10101	245902	66081845388	118	0.0004799	10101	31710428	0.0000041
10101072045	10101	7	2017	0.0006459	Puerto Montt	268732.4	2017	10101	245902	66081845388	113	0.0004595	10101	30366766	0.0000285
10101082016	10101	13	2017	0.0011996	Puerto Montt	268732.4	2017	10101	245902	66081845388	121	0.0004921	10101	32516626	0.0000529
10101082017	10101	5	2017	0.0004614	Puerto Montt	268732.4	2017	10101	245902	66081845388	38	0.0001545	10101	10211833	0.0000203
10101082018	10101	13	2017	0.0011996	Puerto Montt	268732.4	2017	10101	245902	66081845388	623	0.0025335	10101	167420312	0.0000529
10101082030	10101	3	2017	0.0002768	Puerto Montt	268732.4	2017	10101	245902	66081845388	176	0.0007157	10101	47296910	0.0000122
10101082034	10101	5	2017	0.0004614	Puerto Montt	268732.4	2017	10101	245902	66081845388	66	0.0002684	10101	17736341	0.0000203
10101082042	10101	12	2017	0.0011073	Puerto Montt	268732.4	2017	10101	245902	66081845388	253	0.0010289	10101	67989308	0.0000488
10101082045	10101	6	2017	0.0005537	Puerto Montt	268732.4	2017	10101	245902	66081845388	123	0.0005002	10101	33054091	0.0000244
10101092004	10101	6	2017	0.0005537	Puerto Montt	268732.4	2017	10101	245902	66081845388	97	0.0003945	10101	26067047	0.0000244
10101092008	10101	83	2017	0.0076589	Puerto Montt	268732.4	2017	10101	245902	66081845388	752	0.0030581	10101	202086798	0.0003375
10101092037	10101	11	2017	0.0010150	Puerto Montt	268732.4	2017	10101	245902	66081845388	276	0.0011224	10101	74170154	0.0000447
10101092040	10101	33	2017	0.0030451	Puerto Montt	268732.4	2017	10101	245902	66081845388	509	0.0020699	10101	136784814	0.0001342
10101092041	10101	44	2017	0.0040602	Puerto Montt	268732.4	2017	10101	245902	66081845388	1683	0.0068442	10101	452276703	0.0001789
10101092044	10101	21	2017	0.0019378	Puerto Montt	268732.4	2017	10101	245902	66081845388	530	0.0021553	10101	142428195	0.0000854
10101102005	10101	1	2017	0.0000923	Puerto Montt	268732.4	2017	10101	245902	66081845388	147	0.0005978	10101	39503669	0.0000041
10101102007	10101	12	2017	0.0011073	Puerto Montt	268732.4	2017	10101	245902	66081845388	824	0.0033509	10101	221435534	0.0000488
10101102035	10101	22	2017	0.0020301	Puerto Montt	268732.4	2017	10101	245902	66081845388	940	0.0038227	10101	252608497	0.0000895
10101102037	10101	3	2017	0.0002768	Puerto Montt	268732.4	2017	10101	245902	66081845388	164	0.0006669	10101	44072121	0.0000122
10101102051	10101	1	2017	0.0000923	Puerto Montt	268732.4	2017	10101	245902	66081845388	57	0.0002318	10101	15317749	0.0000041
10101112025	10101	13	2017	0.0011996	Puerto Montt	268732.4	2017	10101	245902	66081845388	1078	0.0043839	10101	289693574	0.0000529
10101122024	10101	6	2017	0.0005537	Puerto Montt	268732.4	2017	10101	245902	66081845388	952	0.0038715	10101	255833286	0.0000244
10101131001	10101	88	2017	0.0081203	Puerto Montt	268732.4	2017	10101	245902	66081845388	604	0.0024563	10101	162314396	0.0003579
10101132022	10101	15	2017	0.0013841	Puerto Montt	268732.4	2017	10101	245902	66081845388	703	0.0028589	10101	188918908	0.0000610
10101132023	10101	12	2017	0.0011073	Puerto Montt	268732.4	2017	10101	245902	66081845388	603	0.0024522	10101	162045664	0.0000488
10101132027	10101	1	2017	0.0000923	Puerto Montt	268732.4	2017	10101	245902	66081845388	105	0.0004270	10101	28216907	0.0000041
10101132049	10101	77	2017	0.0071053	Puerto Montt	268732.4	2017	10101	245902	66081845388	1883	0.0076575	10101	506023192	0.0003131
10101142009	10101	2	2017	0.0001846	Puerto Montt	268732.4	2017	10101	245902	66081845388	59	0.0002399	10101	15855214	0.0000081
10101142015	10101	4	2017	0.0003691	Puerto Montt	268732.4	2017	10101	245902	66081845388	124	0.0005043	10101	33322823	0.0000163
10101142027	10101	4	2017	0.0003691	Puerto Montt	268732.4	2017	10101	245902	66081845388	192	0.0007808	10101	51596629	0.0000163
10101142038	10101	3	2017	0.0002768	Puerto Montt	268732.4	2017	10101	245902	66081845388	53	0.0002155	10101	14242820	0.0000122
10101142046	10101	9	2017	0.0008305	Puerto Montt	268732.4	2017	10101	245902	66081845388	317	0.0012891	10101	85188185	0.0000366
10101142047	10101	11	2017	0.0010150	Puerto Montt	268732.4	2017	10101	245902	66081845388	263	0.0010695	10101	70676633	0.0000447
10101142049	10101	61	2017	0.0056289	Puerto Montt	268732.4	2017	10101	245902	66081845388	973	0.0039569	10101	261476668	0.0002481

nrow(tabla_001)

## [1] 12671

summary(tabla_001)

##           zona         código.x             Freq.x            anio          
##  10101011001:    1   Length:12671       Min.   :   1.00   Length:12671      
##  10101011002:    1   Class :character   1st Qu.:   3.00   Class :character  
##  10101021001:    1   Mode  :character   Median :  13.00   Mode  :character  
##  10101021002:    1                      Mean   :  88.55                     
##  10101021003:    1                      3rd Qu.:  99.00                     
##  10101021004:    1                      Max.   :2209.00                     
##  (Other)    :12665                                                          
##        p               comuna.x           promedio_i         año           
##  Min.   :0.0000161   Length:12671       Min.   :156649   Length:12671      
##  1st Qu.:0.0038380   Class :character   1st Qu.:221772   Class :character  
##  Median :0.0099865   Mode  :character   Median :258970   Mode  :character  
##  Mean   :0.0272275                      Mean   :263123                     
##  3rd Qu.:0.0259991                      3rd Qu.:297912                     
##  Max.   :1.0000000                      Max.   :469344                     
##                                         NA's   :134                        
##     comuna.y        personas      Ingresos_expandidos     Freq.y     
##  Min.   : 1101   Min.   :  1250   Min.   :2.925e+08   Min.   :    1  
##  1st Qu.: 6303   1st Qu.: 16394   1st Qu.:3.817e+09   1st Qu.:  100  
##  Median : 9104   Median : 38013   Median :8.862e+09   Median :  374  
##  Mean   : 9346   Mean   : 95867   Mean   :2.922e+10   Mean   : 1372  
##  3rd Qu.:13117   3rd Qu.:147041   3rd Qu.:4.259e+10   3rd Qu.: 2556  
##  Max.   :16305   Max.   :568106   Max.   :1.808e+11   Max.   :11700  
##  NA's   :134     NA's   :134      NA's   :134                        
##  p_poblacional         código.y           multi_pob           p_variable     
##  Min.   :0.0000166   Length:12671       Min.   :2.291e+05   Min.   :0.00000  
##  1st Qu.:0.0038052   Class :character   1st Qu.:2.338e+07   1st Qu.:0.00013  
##  Median :0.0103905   Mode  :character   Median :9.259e+07   Median :0.00038  
##  Mean   :0.0259502                      Mean   :4.130e+08   Mean   :0.00114  
##  3rd Qu.:0.0252357                      3rd Qu.:7.532e+08   3rd Qu.:0.00115  
##  Max.   :0.9060475                      Max.   :4.695e+09   Max.   :0.04290  
##                                         NA's   :134         NA's   :134

1 NAs y outliers

1.1 Existencia y tratamiento de NAs

Descubramos si los campos multi_pob y p_variable poseen valores NA

any(is.na(tabla_001$multi_pob))

## [1] TRUE

any(is.na(tabla_001$p_variable))

## [1] TRUE

Reemplazaremos los valores NAs con los promedios de cada campo, generando dos nuevas columnas:

tabla_001$multi_pob_mean <- ifelse(is.na(tabla_001$multi_pob),
                                   mean(tabla_001$multi_pob, na.rm = TRUE),
                                   tabla_001$multi_pob                             
                                   )

tabla_001$p_variable_mean <- ifelse(is.na(tabla_001$p_variable),
                                   mean(tabla_001$p_variable, na.rm = TRUE),
                                   tabla_001$p_variable                             
                                   )

Verificamos:

any(is.na(tabla_001$multi_pob_mean))

## [1] FALSE

any(is.na(tabla_001$p_variable_mean))

## [1] FALSE

1.2 Outliers

A veces los outliers pueden distorsionar mucho un modelo. La manera más fácil de identificarlos es por medio del análisis de diagramas de caja y bigotes.

Observemos cómo quedaron nuestros nuevos campos:

r3_100 <- tabla_001[c(1:100),]
kbl(r3_100) %>%
  kable_styling(bootstrap_options = c("striped", "hover")) %>%
  kable_paper() %>%
  scroll_box(width = "100%", height = "300px")

zona	código.x	Freq.x	anio	p	comuna.x	promedio_i	año	comuna.y	personas	Ingresos_expandidos	Freq.y	p_poblacional	código.y	multi_pob	p_variable	multi_pob_mean	p_variable_mean
10101011001	10101	60	2017	0.0055366	Puerto Montt	268732.4	2017	10101	245902	66081845388	584	0.0023749	10101	156939747	0.0002440	156939747	0.0002440
10101011002	10101	177	2017	0.0163329	Puerto Montt	268732.4	2017	10101	245902	66081845388	2941	0.0119600	10101	790342117	0.0007198	790342117	0.0007198
10101021001	10101	82	2017	0.0075667	Puerto Montt	268732.4	2017	10101	245902	66081845388	3953	0.0160755	10101	1062299350	0.0003335	1062299350	0.0003335
10101021002	10101	77	2017	0.0071053	Puerto Montt	268732.4	2017	10101	245902	66081845388	1107	0.0045018	10101	297486815	0.0003131	297486815	0.0003131
10101021003	10101	70	2017	0.0064594	Puerto Montt	268732.4	2017	10101	245902	66081845388	2294	0.0093289	10101	616472226	0.0002847	616472226	0.0002847
10101021004	10101	99	2017	0.0091354	Puerto Montt	268732.4	2017	10101	245902	66081845388	3391	0.0137900	10101	911271717	0.0004026	911271717	0.0004026
10101021005	10101	171	2017	0.0157793	Puerto Montt	268732.4	2017	10101	245902	66081845388	2564	0.0104269	10101	689029986	0.0006954	689029986	0.0006954
10101031001	10101	133	2017	0.0122728	Puerto Montt	268732.4	2017	10101	245902	66081845388	4530	0.0184220	10101	1217357970	0.0005409	1217357970	0.0005409
10101031002	10101	115	2017	0.0106118	Puerto Montt	268732.4	2017	10101	245902	66081845388	4740	0.0192760	10101	1273791783	0.0004677	1273791783	0.0004677
10101031003	10101	94	2017	0.0086740	Puerto Montt	268732.4	2017	10101	245902	66081845388	4107	0.0167018	10101	1103684147	0.0003823	1103684147	0.0003823
10101031004	10101	88	2017	0.0081203	Puerto Montt	268732.4	2017	10101	245902	66081845388	2856	0.0116144	10101	767499859	0.0003579	767499859	0.0003579
10101031005	10101	146	2017	0.0134724	Puerto Montt	268732.4	2017	10101	245902	66081845388	5690	0.0231393	10101	1529087605	0.0005937	1529087605	0.0005937
10101031006	10101	94	2017	0.0086740	Puerto Montt	268732.4	2017	10101	245902	66081845388	2460	0.0100040	10101	661081812	0.0003823	661081812	0.0003823
10101031007	10101	39	2017	0.0035988	Puerto Montt	268732.4	2017	10101	245902	66081845388	2292	0.0093208	10101	615934761	0.0001586	615934761	0.0001586
10101031008	10101	54	2017	0.0049829	Puerto Montt	268732.4	2017	10101	245902	66081845388	3585	0.0145790	10101	963405811	0.0002196	963405811	0.0002196
10101031009	10101	166	2017	0.0153179	Puerto Montt	268732.4	2017	10101	245902	66081845388	4436	0.0180397	10101	1192097121	0.0006751	1192097121	0.0006751
10101031010	10101	92	2017	0.0084894	Puerto Montt	268732.4	2017	10101	245902	66081845388	3566	0.0145017	10101	958299894	0.0003741	958299894	0.0003741
10101031011	10101	49	2017	0.0045215	Puerto Montt	268732.4	2017	10101	245902	66081845388	2757	0.0112118	10101	740895347	0.0001993	740895347	0.0001993
10101031012	10101	94	2017	0.0086740	Puerto Montt	268732.4	2017	10101	245902	66081845388	1849	0.0075193	10101	496886289	0.0003823	496886289	0.0003823
10101031013	10101	73	2017	0.0067362	Puerto Montt	268732.4	2017	10101	245902	66081845388	3945	0.0160430	10101	1060149491	0.0002969	1060149491	0.0002969
10101031014	10101	109	2017	0.0100581	Puerto Montt	268732.4	2017	10101	245902	66081845388	2265	0.0092110	10101	608678985	0.0004433	608678985	0.0004433
10101031015	10101	31	2017	0.0028606	Puerto Montt	268732.4	2017	10101	245902	66081845388	1930	0.0078487	10101	518653616	0.0001261	518653616	0.0001261
10101031016	10101	248	2017	0.0228846	Puerto Montt	268732.4	2017	10101	245902	66081845388	3071	0.0124887	10101	825277335	0.0010085	825277335	0.0010085
10101031017	10101	60	2017	0.0055366	Puerto Montt	268732.4	2017	10101	245902	66081845388	3885	0.0157990	10101	1044025544	0.0002440	1044025544	0.0002440
10101032002	10101	2	2017	0.0001846	Puerto Montt	268732.4	2017	10101	245902	66081845388	129	0.0005246	10101	34666485	0.0000081	34666485	0.0000081
10101032011	10101	20	2017	0.0018455	Puerto Montt	268732.4	2017	10101	245902	66081845388	426	0.0017324	10101	114480021	0.0000813	114480021	0.0000813
10101032019	10101	32	2017	0.0029528	Puerto Montt	268732.4	2017	10101	245902	66081845388	829	0.0033713	10101	222779196	0.0001301	222779196	0.0001301
10101041001	10101	70	2017	0.0064594	Puerto Montt	268732.4	2017	10101	245902	66081845388	4342	0.0176574	10101	1166836271	0.0002847	1166836271	0.0002847
10101041002	10101	55	2017	0.0050752	Puerto Montt	268732.4	2017	10101	245902	66081845388	2169	0.0088206	10101	582880671	0.0002237	582880671	0.0002237
10101041003	10101	774	2017	0.0714220	Puerto Montt	268732.4	2017	10101	245902	66081845388	5202	0.0211548	10101	1397946172	0.0031476	1397946172	0.0031476
10101051001	10101	246	2017	0.0227000	Puerto Montt	268732.4	2017	10101	245902	66081845388	2463	0.0100162	10101	661888009	0.0010004	661888009	0.0010004
10101051002	10101	33	2017	0.0030451	Puerto Montt	268732.4	2017	10101	245902	66081845388	1913	0.0077795	10101	514085165	0.0001342	514085165	0.0001342
10101051003	10101	65	2017	0.0059980	Puerto Montt	268732.4	2017	10101	245902	66081845388	3272	0.0133061	10101	879292556	0.0002643	879292556	0.0002643
10101051004	10101	307	2017	0.0283289	Puerto Montt	268732.4	2017	10101	245902	66081845388	3633	0.0147742	10101	976304968	0.0012485	976304968	0.0012485
10101061001	10101	1239	2017	0.1143305	Puerto Montt	268732.4	2017	10101	245902	66081845388	6787	0.0276004	10101	1823887096	0.0050386	1823887096	0.0050386
10101061002	10101	329	2017	0.0303590	Puerto Montt	268732.4	2017	10101	245902	66081845388	2729	0.0110979	10101	733370839	0.0013379	733370839	0.0013379
10101061003	10101	160	2017	0.0147642	Puerto Montt	268732.4	2017	10101	245902	66081845388	3668	0.0149165	10101	985710604	0.0006507	985710604	0.0006507
10101061004	10101	110	2017	0.0101504	Puerto Montt	268732.4	2017	10101	245902	66081845388	2995	0.0121796	10101	804853669	0.0004473	804853669	0.0004473
10101061005	10101	312	2017	0.0287903	Puerto Montt	268732.4	2017	10101	245902	66081845388	2571	0.0104554	10101	690911113	0.0012688	690911113	0.0012688
10101061006	10101	401	2017	0.0370029	Puerto Montt	268732.4	2017	10101	245902	66081845388	4130	0.0167953	10101	1109864993	0.0016307	1109864993	0.0016307
10101061007	10101	12	2017	0.0011073	Puerto Montt	268732.4	2017	10101	245902	66081845388	817	0.0033225	10101	219554407	0.0000488	219554407	0.0000488
10101061008	10101	388	2017	0.0358033	Puerto Montt	268732.4	2017	10101	245902	66081845388	2109	0.0085766	10101	566756724	0.0015779	566756724	0.0015779
10101061009	10101	1	2017	0.0000923	Puerto Montt	268732.4	2017	10101	245902	66081845388	168	0.0006832	10101	45147051	0.0000041	45147051	0.0000041
10101061010	10101	6	2017	0.0005537	Puerto Montt	268732.4	2017	10101	245902	66081845388	1543	0.0062749	10101	414654161	0.0000244	414654161	0.0000244
10101062003	10101	10	2017	0.0009228	Puerto Montt	268732.4	2017	10101	245902	66081845388	158	0.0006425	10101	42459726	0.0000407	42459726	0.0000407
10101062008	10101	72	2017	0.0066439	Puerto Montt	268732.4	2017	10101	245902	66081845388	581	0.0023627	10101	156133550	0.0002928	156133550	0.0002928
10101062013	10101	61	2017	0.0056289	Puerto Montt	268732.4	2017	10101	245902	66081845388	571	0.0023221	10101	153446225	0.0002481	153446225	0.0002481
10101062029	10101	1	2017	0.0000923	Puerto Montt	268732.4	2017	10101	245902	66081845388	47	0.0001911	10101	12630425	0.0000041	12630425	0.0000041
10101062039	10101	4	2017	0.0003691	Puerto Montt	268732.4	2017	10101	245902	66081845388	67	0.0002725	10101	18005074	0.0000163	18005074	0.0000163
10101071001	10101	20	2017	0.0018455	Puerto Montt	268732.4	2017	10101	245902	66081845388	2352	0.0095648	10101	632058708	0.0000813	632058708	0.0000813
10101071002	10101	54	2017	0.0049829	Puerto Montt	268732.4	2017	10101	245902	66081845388	3919	0.0159372	10101	1053162447	0.0002196	1053162447	0.0002196
10101071003	10101	112	2017	0.0103350	Puerto Montt	268732.4	2017	10101	245902	66081845388	4978	0.0202438	10101	1337750105	0.0004555	1337750105	0.0004555
10101071004	10101	75	2017	0.0069207	Puerto Montt	268732.4	2017	10101	245902	66081845388	3443	0.0140015	10101	925245804	0.0003050	925245804	0.0003050
10101071005	10101	61	2017	0.0056289	Puerto Montt	268732.4	2017	10101	245902	66081845388	2751	0.0111874	10101	739282953	0.0002481	739282953	0.0002481
10101071006	10101	60	2017	0.0055366	Puerto Montt	268732.4	2017	10101	245902	66081845388	4214	0.0171369	10101	1132438518	0.0002440	1132438518	0.0002440
10101071007	10101	29	2017	0.0026760	Puerto Montt	268732.4	2017	10101	245902	66081845388	2345	0.0095363	10101	630177581	0.0001179	630177581	0.0001179
10101071008	10101	77	2017	0.0071053	Puerto Montt	268732.4	2017	10101	245902	66081845388	5480	0.0222853	10101	1472653792	0.0003131	1472653792	0.0003131
10101071009	10101	49	2017	0.0045215	Puerto Montt	268732.4	2017	10101	245902	66081845388	3549	0.0144326	10101	953731443	0.0001993	953731443	0.0001993
10101071010	10101	48	2017	0.0044293	Puerto Montt	268732.4	2017	10101	245902	66081845388	3521	0.0143187	10101	946206935	0.0001952	946206935	0.0001952
10101071011	10101	43	2017	0.0039679	Puerto Montt	268732.4	2017	10101	245902	66081845388	3094	0.0125822	10101	831458181	0.0001749	831458181	0.0001749
10101071012	10101	47	2017	0.0043370	Puerto Montt	268732.4	2017	10101	245902	66081845388	2621	0.0106587	10101	704347735	0.0001911	704347735	0.0001911
10101071014	10101	26	2017	0.0023992	Puerto Montt	268732.4	2017	10101	245902	66081845388	875	0.0035583	10101	235140888	0.0001057	235140888	0.0001057
10101072014	10101	36	2017	0.0033220	Puerto Montt	268732.4	2017	10101	245902	66081845388	997	0.0040545	10101	267926246	0.0001464	267926246	0.0001464
10101072021	10101	4	2017	0.0003691	Puerto Montt	268732.4	2017	10101	245902	66081845388	44	0.0001789	10101	11824228	0.0000163	11824228	0.0000163
10101072028	10101	4	2017	0.0003691	Puerto Montt	268732.4	2017	10101	245902	66081845388	145	0.0005897	10101	38966204	0.0000163	38966204	0.0000163
10101072029	10101	36	2017	0.0033220	Puerto Montt	268732.4	2017	10101	245902	66081845388	1051	0.0042741	10101	282437798	0.0001464	282437798	0.0001464
10101072036	10101	1	2017	0.0000923	Puerto Montt	268732.4	2017	10101	245902	66081845388	118	0.0004799	10101	31710428	0.0000041	31710428	0.0000041
10101072045	10101	7	2017	0.0006459	Puerto Montt	268732.4	2017	10101	245902	66081845388	113	0.0004595	10101	30366766	0.0000285	30366766	0.0000285
10101082016	10101	13	2017	0.0011996	Puerto Montt	268732.4	2017	10101	245902	66081845388	121	0.0004921	10101	32516626	0.0000529	32516626	0.0000529
10101082017	10101	5	2017	0.0004614	Puerto Montt	268732.4	2017	10101	245902	66081845388	38	0.0001545	10101	10211833	0.0000203	10211833	0.0000203
10101082018	10101	13	2017	0.0011996	Puerto Montt	268732.4	2017	10101	245902	66081845388	623	0.0025335	10101	167420312	0.0000529	167420312	0.0000529
10101082030	10101	3	2017	0.0002768	Puerto Montt	268732.4	2017	10101	245902	66081845388	176	0.0007157	10101	47296910	0.0000122	47296910	0.0000122
10101082034	10101	5	2017	0.0004614	Puerto Montt	268732.4	2017	10101	245902	66081845388	66	0.0002684	10101	17736341	0.0000203	17736341	0.0000203
10101082042	10101	12	2017	0.0011073	Puerto Montt	268732.4	2017	10101	245902	66081845388	253	0.0010289	10101	67989308	0.0000488	67989308	0.0000488
10101082045	10101	6	2017	0.0005537	Puerto Montt	268732.4	2017	10101	245902	66081845388	123	0.0005002	10101	33054091	0.0000244	33054091	0.0000244
10101092004	10101	6	2017	0.0005537	Puerto Montt	268732.4	2017	10101	245902	66081845388	97	0.0003945	10101	26067047	0.0000244	26067047	0.0000244
10101092008	10101	83	2017	0.0076589	Puerto Montt	268732.4	2017	10101	245902	66081845388	752	0.0030581	10101	202086798	0.0003375	202086798	0.0003375
10101092037	10101	11	2017	0.0010150	Puerto Montt	268732.4	2017	10101	245902	66081845388	276	0.0011224	10101	74170154	0.0000447	74170154	0.0000447
10101092040	10101	33	2017	0.0030451	Puerto Montt	268732.4	2017	10101	245902	66081845388	509	0.0020699	10101	136784814	0.0001342	136784814	0.0001342
10101092041	10101	44	2017	0.0040602	Puerto Montt	268732.4	2017	10101	245902	66081845388	1683	0.0068442	10101	452276703	0.0001789	452276703	0.0001789
10101092044	10101	21	2017	0.0019378	Puerto Montt	268732.4	2017	10101	245902	66081845388	530	0.0021553	10101	142428195	0.0000854	142428195	0.0000854
10101102005	10101	1	2017	0.0000923	Puerto Montt	268732.4	2017	10101	245902	66081845388	147	0.0005978	10101	39503669	0.0000041	39503669	0.0000041
10101102007	10101	12	2017	0.0011073	Puerto Montt	268732.4	2017	10101	245902	66081845388	824	0.0033509	10101	221435534	0.0000488	221435534	0.0000488
10101102035	10101	22	2017	0.0020301	Puerto Montt	268732.4	2017	10101	245902	66081845388	940	0.0038227	10101	252608497	0.0000895	252608497	0.0000895
10101102037	10101	3	2017	0.0002768	Puerto Montt	268732.4	2017	10101	245902	66081845388	164	0.0006669	10101	44072121	0.0000122	44072121	0.0000122
10101102051	10101	1	2017	0.0000923	Puerto Montt	268732.4	2017	10101	245902	66081845388	57	0.0002318	10101	15317749	0.0000041	15317749	0.0000041
10101112025	10101	13	2017	0.0011996	Puerto Montt	268732.4	2017	10101	245902	66081845388	1078	0.0043839	10101	289693574	0.0000529	289693574	0.0000529
10101122024	10101	6	2017	0.0005537	Puerto Montt	268732.4	2017	10101	245902	66081845388	952	0.0038715	10101	255833286	0.0000244	255833286	0.0000244
10101131001	10101	88	2017	0.0081203	Puerto Montt	268732.4	2017	10101	245902	66081845388	604	0.0024563	10101	162314396	0.0003579	162314396	0.0003579
10101132022	10101	15	2017	0.0013841	Puerto Montt	268732.4	2017	10101	245902	66081845388	703	0.0028589	10101	188918908	0.0000610	188918908	0.0000610
10101132023	10101	12	2017	0.0011073	Puerto Montt	268732.4	2017	10101	245902	66081845388	603	0.0024522	10101	162045664	0.0000488	162045664	0.0000488
10101132027	10101	1	2017	0.0000923	Puerto Montt	268732.4	2017	10101	245902	66081845388	105	0.0004270	10101	28216907	0.0000041	28216907	0.0000041
10101132049	10101	77	2017	0.0071053	Puerto Montt	268732.4	2017	10101	245902	66081845388	1883	0.0076575	10101	506023192	0.0003131	506023192	0.0003131
10101142009	10101	2	2017	0.0001846	Puerto Montt	268732.4	2017	10101	245902	66081845388	59	0.0002399	10101	15855214	0.0000081	15855214	0.0000081
10101142015	10101	4	2017	0.0003691	Puerto Montt	268732.4	2017	10101	245902	66081845388	124	0.0005043	10101	33322823	0.0000163	33322823	0.0000163
10101142027	10101	4	2017	0.0003691	Puerto Montt	268732.4	2017	10101	245902	66081845388	192	0.0007808	10101	51596629	0.0000163	51596629	0.0000163
10101142038	10101	3	2017	0.0002768	Puerto Montt	268732.4	2017	10101	245902	66081845388	53	0.0002155	10101	14242820	0.0000122	14242820	0.0000122
10101142046	10101	9	2017	0.0008305	Puerto Montt	268732.4	2017	10101	245902	66081845388	317	0.0012891	10101	85188185	0.0000366	85188185	0.0000366
10101142047	10101	11	2017	0.0010150	Puerto Montt	268732.4	2017	10101	245902	66081845388	263	0.0010695	10101	70676633	0.0000447	70676633	0.0000447
10101142049	10101	61	2017	0.0056289	Puerto Montt	268732.4	2017	10101	245902	66081845388	973	0.0039569	10101	261476668	0.0002481	261476668	0.0002481

par(mfrow = c(1,2))
boxplot(tabla_001$multi_pob_mean,  col="#FF6B00" , xlab="bottom & left box",
        main = "multi_pob_mean",
        boxwex = 0.9)
boxplot(tabla_001$p_variable_mean , col="#2398AB" , xlab="bottom & left box",
        main = "p_variable_mean",
        boxwex = 0.9)

La línea central es la mediana y los extremos de la caja el primer y el tercer cuartil (rango intercuartílico), en el que cae el 50% de las observaciones.

1.3 Transformaciones sobre outliers

Podemos enmascarar outliers con transformaciones. Por ejemplo, podemos reemplazar los valores que estén debajo del quinto percentil y los que estén por sobre el 95 avo percentil con los valores medios, tal como lo hicimos previamente sobre los NAs o con las medianas.

1.3.1 Reemplazo de outliers con promedios:

sobre multi_pob_mean:

outliers <- function(x, removeNA = TRUE){
      quantiles <- quantile(x, c(0.05, 0.95), na.rm = removeNA)
      x[x < quantiles[1]] <- mean(x, na.rm = removeNA)
      x[x > quantiles[2]] <- mean(x, na.rm = removeNA)
      x
}

outliers_data <- outliers(tabla_001$multi_pob_mean)

par(mfrow = c(1,2))
boxplot(tabla_001$multi_pob,   col="#FF6B00" , xlab="multi_pob_mean", main = "con outliers")
boxplot(outliers_data,  col="#FF6B00" , xlab="multi_pob_mean", main = "sin outliers")

1.3.2 Reemplazo de outliers con medianas:

sobre multi_pob_mean:

outliers <- function(x, removeNA = TRUE){
      quantiles <- quantile(x, c(0.05, 0.95), na.rm = removeNA)
      x[x < quantiles[1]] <- median(x, na.rm = removeNA)
      x[x > quantiles[2]] <- median(x, na.rm = removeNA)
      x
}

outliers_data <- outliers(tabla_001$multi_pob_mean)

par(mfrow = c(1,2))
boxplot(tabla_001$multi_pob_mean,   col="#FF6B00" , xlab="multi_pob_mean medianas", main = "con outliers")
boxplot(outliers_data,  col="#FF6B00" , xlab="multi_pob_mean medianas", main = "sin outliers")

1.3.3 Sustitución de outliers

Sustituímos los valores que están fuera de los bigotes con los valores del percentil 5 y el 95 respectivamente.

sobre multi_pob_mean:

replace_outliers <- function(x, removeNA = TRUE){
     qrts <- quantile(x, probs = c(0.25, 0.75), na.rm =removeNA) 
      caps <- quantile(x, probs = c(0.05, 0.95), na.rm =removeNA)  
      iqr <- qrts[2] - qrts[1]
      h <- 1.5*iqr
      x[x < qrts[1] - h] <- caps[1]
      x[x > qrts[2] + h] <- caps[2]
      x
}

multi_pob_capped <- replace_outliers(tabla_001$multi_pob_mean)
par(mfrow = c(1,2))
boxplot(tabla_001$multi_pob_mean,    col="#FF6B00" , xlab="multi_pob_mean", main = "con outliers")
boxplot(multi_pob_capped, col="#FF6B00" , xlab="multi_pob_mean", main = "sin outliers")

length(multi_pob_capped)

## [1] 12671

Vemos que resulta mucho mejor ésta última técnica, por lo que lo aplicamos para los campos multi_pob_mean y p_variable_mean.

p_variable_capped_multi_pob_mean <- replace_outliers(tabla_001$multi_pob_mean)
p_variable_capped_p_variable_mean <- replace_outliers(tabla_001$p_variable_mean)

par(mfrow = c(1,2))

boxplot(p_variable_capped_multi_pob_mean, col="#FF6B00" , xlab="multi_pob_mean", main = "multi_pob_mean sin outliers")

boxplot(p_variable_capped_p_variable_mean, col="#2398AB" , xlab="p_variable_mean", main = "p_variable_mean sin outliers")

2 Histogramas y densidades

Histograma y densidad para multi_pob_mean sin outliers

par(mfrow = c(1,2))
hist(p_variable_capped_multi_pob_mean, col="#FF6B00", main="Histograma")
plot(density(p_variable_capped_multi_pob_mean), main="Densidad", col="red")

Histograma y densidad para p_variable_mean sin outliers

par(mfrow = c(1,2))
hist(p_variable_capped_p_variable_mean, col="#2398AB" ,main="Histograma")
plot(density(p_variable_capped_p_variable_mean), main="Densidad", col="red")

3 Aplicación al dataframe

x <- quantile(tabla_001$multi_pob_mean,c(0.05,0.95))
data_clean <- tabla_001[tabla_001$multi_pob_mean >= x[1] & tabla_001$multi_pob_mean <= x[2],]

y <- quantile(data_clean$p_variable_mean,c(0.05,0.95))
data_clean <- data_clean[data_clean$p_variable_mean >= y[1] & data_clean$p_variable_mean <= y[2],]

head(data_clean,10)

##           zona código.x Freq.x anio           p     comuna.x promedio_i  año
## 1  10101011001    10101     60 2017 0.005536588 Puerto Montt   268732.4 2017
## 2  10101011002    10101    177 2017 0.016332933 Puerto Montt   268732.4 2017
## 3  10101021001    10101     82 2017 0.007566670 Puerto Montt   268732.4 2017
## 4  10101021002    10101     77 2017 0.007105287 Puerto Montt   268732.4 2017
## 5  10101021003    10101     70 2017 0.006459352 Puerto Montt   268732.4 2017
## 6  10101021004    10101     99 2017 0.009135370 Puerto Montt   268732.4 2017
## 7  10101021005    10101    171 2017 0.015779275 Puerto Montt   268732.4 2017
## 8  10101031001    10101    133 2017 0.012272769 Puerto Montt   268732.4 2017
## 9  10101031002    10101    115 2017 0.010611793 Puerto Montt   268732.4 2017
## 10 10101031003    10101     94 2017 0.008673987 Puerto Montt   268732.4 2017
##    comuna.y personas Ingresos_expandidos Freq.y p_poblacional código.y
## 1     10101   245902         66081845388    584   0.002374930    10101
## 2     10101   245902         66081845388   2941   0.011960049    10101
## 3     10101   245902         66081845388   3953   0.016075510    10101
## 4     10101   245902         66081845388   1107   0.004501793    10101
## 5     10101   245902         66081845388   2294   0.009328920    10101
## 6     10101   245902         66081845388   3391   0.013790046    10101
## 7     10101   245902         66081845388   2564   0.010426918    10101
## 8     10101   245902         66081845388   4530   0.018421973    10101
## 9     10101   245902         66081845388   4740   0.019275972    10101
## 10    10101   245902         66081845388   4107   0.016701776    10101
##     multi_pob   p_variable multi_pob_mean p_variable_mean
## 1   156939747 0.0002439996      156939747    0.0002439996
## 2   790342117 0.0007197989      790342117    0.0007197989
## 3  1062299350 0.0003334662     1062299350    0.0003334662
## 4   297486815 0.0003131329      297486815    0.0003131329
## 5   616472226 0.0002846662      616472226    0.0002846662
## 6   911271717 0.0004025994      911271717    0.0004025994
## 7   689029986 0.0006953990      689029986    0.0006953990
## 8  1217357970 0.0005408659     1217357970    0.0005408659
## 9  1273791783 0.0004676660     1273791783    0.0004676660
## 10 1103684147 0.0003822661     1103684147    0.0003822661

4 Modelo lineal

scatter.smooth(x=data_clean$p_variable_mean, y=data_clean$multi_pob_mean, main="p_variable ~ multi_pob")

ggplot(data_clean, aes(x = p_variable_mean, y = multi_pob_mean)) + 
  geom_point() +
  stat_smooth(method = "lm", col = "red")

## `geom_smooth()` using formula 'y ~ x'

linearMod <- lm( multi_pob_mean~p_variable_mean , data=data_clean)  
summary(linearMod)

## 
## Call:
## lm(formula = multi_pob_mean ~ p_variable_mean, data = data_clean)
## 
## Residuals:
##        Min         1Q     Median         3Q        Max 
## -1.161e+09 -2.168e+08 -1.712e+08  1.945e+08  1.279e+09 
## 
## Coefficients:
##                  Estimate Std. Error t value Pr(>|t|)    
## (Intercept)     1.862e+08  5.119e+06   36.38   <2e-16 ***
## p_variable_mean 2.271e+11  4.537e+09   50.05   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 394700000 on 10271 degrees of freedom
## Multiple R-squared:  0.1961, Adjusted R-squared:  0.196 
## F-statistic:  2505 on 1 and 10271 DF,  p-value: < 2.2e-16

4.1 Análisis del \(R^2\) (coeficiente de determinación)

El \(R^2\) es una medida estadística de qué tan cerca están los datos de la línea de regresión ajustada.

Es el porcentaje de la variación en la variable de respuesta que es explicado por un modelo lineal. Es decir:

\[ R^2 = \frac{Variación\ explicada}{variación\ total} \]

Cuanto mayor sea la varianza explicada por el modelo de regresión, más cerca estarán los puntos de los datos de la línea de regresión ajustada.

Un valor bajo de \(R^2\) no es inherentemente malo. Si el valor del \(R^2\) es bajo pero se tienen predictores estadísticamente significativos, aún se puede obtener conclusiones importantes acerca de la asociación entre los cambios en los valores de los predictores y los cambios en el valor de respuesta. Independientemente del \(R^2\), los coeficientes significativos aún representan el cambio medio en la respuesta para una unidad de cambio en el predictor mientras se mantienen constantes los otros predictores del modelo.

4.2 Análisis de los residuos

Los residuos son los errores que se cometen en la estimación.

boxplot(linearMod$residuals)

par(mfrow = c (2,2))
plot(linearMod)

4.2.1 Residuos versus valores ajustados

Corroboramos que los residuos sigan un patrón lineal. La línea es recta y horizontal, por lo que deducimos que la relación es efectivamente lineal. Se busca verificar la linealidad entre las variables de entrada y salida. Un modelo lineal nunca podrá capturar una relación no lineal.

4.2.2 Q-Q

Aquí verificamos que los errores del modelo estén normalmente distribuídos. Parece cumplirse pues los valores están muy próximos a la línea recta punteada.

4.2.3 Raíz cuadrada de los residuos ajustados versus valores ajustados

Verificamos las condiciones de homocedasticidad, es decir que todos los residuos posean la misma varianza, que es uno de los supuestos al realizar un análisis de regresión. El supuesto parace cumplirse pues la línea roja no parece seguir ningún patrón.

4.2.4 Residuos versus apalancamiento

Acá podemos identificar los outliers influyentes en el análisis de regresión, que pueden sesgar el modelo. Parece haber dos valores influyentes (caen fuera de la distancia de Cook).

5 Fórmulas alternativas del modelo lineal

5.1 Función cuadrática

\[ \hat Y = \beta_0 + \beta_1 X^2 \]

linearMod <- lm( multi_pob_mean~p_variable_mean^2 , data=data_clean)  
summary(linearMod)

## 
## Call:
## lm(formula = multi_pob_mean ~ p_variable_mean^2, data = data_clean)
## 
## Residuals:
##        Min         1Q     Median         3Q        Max 
## -1.161e+09 -2.168e+08 -1.712e+08  1.945e+08  1.279e+09 
## 
## Coefficients:
##                  Estimate Std. Error t value Pr(>|t|)    
## (Intercept)     1.862e+08  5.119e+06   36.38   <2e-16 ***
## p_variable_mean 2.271e+11  4.537e+09   50.05   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 394700000 on 10271 degrees of freedom
## Multiple R-squared:  0.1961, Adjusted R-squared:  0.196 
## F-statistic:  2505 on 1 and 10271 DF,  p-value: < 2.2e-16

5.2 Función logarítmica

\[ \hat Y = \beta_0 + \beta_1 logX \]

linearMod <- lm( multi_pob_mean~log(p_variable_mean) , data=data_clean)
summary(linearMod)

## 
## Call:
## lm(formula = multi_pob_mean ~ log(p_variable_mean), data = data_clean)
## 
## Residuals:
##        Min         1Q     Median         3Q        Max 
## -787823248 -263759357  -83185338  176681879 1249525349 
## 
## Coefficients:
##                       Estimate Std. Error t value Pr(>|t|)    
## (Intercept)          1.828e+09  2.452e+07   74.54   <2e-16 ***
## log(p_variable_mean) 1.873e+08  3.076e+06   60.87   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 377400000 on 10271 degrees of freedom
## Multiple R-squared:  0.2651, Adjusted R-squared:  0.265 
## F-statistic:  3705 on 1 and 10271 DF,  p-value: < 2.2e-16

5.3 Función cúbica

\[ \hat Y = \beta_0 + \beta_1 X^3 \]

linearMod <- lm( multi_pob_mean~p_variable_mean^3 , data=data_clean)  
summary(linearMod)

## 
## Call:
## lm(formula = multi_pob_mean ~ p_variable_mean^3, data = data_clean)
## 
## Residuals:
##        Min         1Q     Median         3Q        Max 
## -1.161e+09 -2.168e+08 -1.712e+08  1.945e+08  1.279e+09 
## 
## Coefficients:
##                  Estimate Std. Error t value Pr(>|t|)    
## (Intercept)     1.862e+08  5.119e+06   36.38   <2e-16 ***
## p_variable_mean 2.271e+11  4.537e+09   50.05   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 394700000 on 10271 degrees of freedom
## Multiple R-squared:  0.1961, Adjusted R-squared:  0.196 
## F-statistic:  2505 on 1 and 10271 DF,  p-value: < 2.2e-16

Vemos que el ajuste logarítmico nos ofrece el mayor \(R^2\).