상관관계분석의 개념과 원리

상관관계분석의 개념과 원리

개념

• 두 연속형 변수 간의 상관 정도를 파악

• 상관계수를 통해 표준화된 상관관계를 도출

• 주로 회귀분석을 하기 전에 독립변수 , 종속변수 간의 상관이 있는지 탐색

a <- read.csv('cosmetics.csv',header = T)

a

gender	marriage	edu	job	mincome	aware	count	amount	decision	propensity	skin	promo	location	satisf_b	satisf_i	satisf_al	repurchase
1	1	4	1	2	2	1	11000	2	1	1	1	2	5	2	2	2
2	1	4	9	2	1	4	30000	1	1	3	2	3	2	3	3	4
2	2	4	4	3	1	6	100000	3	2	3	2	2	4	5	4	4
2	2	4	7	5	2	6	65000	3	2	5	2	3	3	4	4	4
1	2	6	6	5	2	2	50000	2	2	3	2	3	3	3	3	3
2	2	2	7	3	1	2	100000	2	1	4	2	3	3	4	4	3
2	1	6	4	5	1	5	100000	3	2	5	2	3	2	2	3	4
1	1	6	4	5	4	10	39000	3	2	2	1	2	4	4	4	4
2	2	4	5	2	2	2	40000	3	2	3	2	3	3	4	4	4
2	2	4	5	2	1	2	100000	3	3	3	1	3	2	3	4	4
2	1	7	4	3	10	3	50000	1	3	1	2	3	3	3	4	4
1	1	2	5	3	2	1	30000	3	2	3	2	2	3	3	3	3
2	2	4	4	3	4	4	320000	2	3	3	3	2	4	4	4	4
2	2	4	4	2	3	2	200000	1	2	3	1	3	3	3	3	3
1	2	4	4	6	2	2	60000	3	2	1	2	5	3	3	3	4
2	1	4	5	2	2	3	50000	1	2	4	1	3	3	4	3	3
1	2	8	3	2	5	3	1000000	1	3	1	2	2	3	3	3	3
2	1	3	8	5	1	6	1500000	3	3	2	4	1	4	4	4	4
1	2	2	6	2	4	1	80000	2	3	1	2	3	3	3	4	4
1	1	4	4	3	8	3	30000	2	2	3	2	3	3	3	3	3
2	2	2	4	2	8	4	350000	3	2	3	2	2	3	4	4	4
2	2	4	7	6	1	4	250000	3	3	2	2	3	2	3	4	4
2	2	4	7	3	1	25	50000	2	2	1	2	3	3	4	4	4
2	2	2	9	1	1	1	20000	1	1	5	1	3	3	3	3	3
1	1	3	8	4	2	3	42000	1	2	3	1	3	3	3	4	4
1	1	4	8	4	2	3	42000	3	3	2	1	3	3	4	4	4
2	1	4	4	3	2	20	40000	3	1	5	2	3	2	4	4	4
2	2	4	4	6	1	6	70000	3	3	5	2	1	3	4	4	4
2	2	8	4	5	5	6	200000	2	1	4	1	1	4	4	4	3
1	2	4	2	6	2	1	200000	3	2	1	2	2	3	4	4	4
...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...
2	2	4	5	2	1	10	30000	2	2	2	4	3	3	4	4	4
1	2	4	6	6	7	5	50000	3	2	4	2	2	3	4	4	4
1	2	4	1	4	1	1	10000	1	3	1	1	1	5	1	3	1
1	1	4	4	3	2	1	10000	1	1	4	3	2	2	3	3	3
1	1	4	4	3	2	3	50000	3	2	5	2	3	2	4	4	4
1	2	2	5	4	2	1	60000	1	1	1	4	5	3	3	3	3
1	1	6	1	3	2	2	50000	3	2	5	1	2	4	4	3	4
2	2	6	4	6	1	3	500000	3	3	5	2	1	3	4	4	4
1	2	4	1	3	2	1	50000	3	2	1	2	3	2	3	3	3
2	2	6	3	4	1	1	100000	3	2	1	2	1	3	3	3	3
2	2	4	7	4	1	2	50000	3	1	5	2	2	3	2	3	4
2	2	4	4	2	2	12	20000	2	2	3	2	3	3	3	3	3
1	1	4	4	4	2	4	35000	2	2	1	3	2	3	3	4	4
1	1	4	4	4	2	4	30000	2	2	1	2	3	3	4	4	3
2	2	4	7	1	2	2	50000	1	1	3	2	5	3	4	4	4
2	2	4	7	1	2	3	50000	1	2	3	2	5	3	3	3	3
2	1	4	4	2	2	7	80000	3	2	3	2	2	3	3	3	3
1	1	4	1	3	2	6	20000	3	1	3	1	3	2	3	4	4
1	1	4	10	2	2	2	25000	3	1	3	2	3	3	4	4	4
2	1	3	8	1	1	7	100000	2	1	5	2	3	3	3	1	2
1	2	4	4	3	2	2	50000	1	2	5	2	2	3	4	3	3
1	2	4	4	5	2	1	80000	2	2	1	2	3	3	3	3	3
2	2	6	7	5	1	2	300000	3	3	2	3	2	3	4	3	3
2	2	7	7	4	1	2	200000	2	2	4	3	2	3	3	3	3
1	1	2	1	2	2	5	3000	1	1	2	1	1	1	1	1	1
1	1	4	2	3	2	6	4000	1	1	1	1	4	2	1	1	1
2	2	4	4	2	1	10	150000	3	2	2	1	2	3	4	4	4
2	2	7	8	1	2	3	100000	1	2	1	1	5	2	5	4	4
1	1	4	6	1	3	2	20000	3	1	1	1	3	4	3	3	2
2	2	6	10	1	1	10	1000000	3	2	3	1	3	2	3	3	3

install.packages('corrplot')
library(corrplot)

  There is a binary version available but the source version is later:
         binary source needs_compilation
corrplot   0.88   0.92             FALSE



installing the source package 'corrplot'

corrplot 0.92 loaded

Correlation, Variance and Covariance (Matrices)

Description

var, cov and cor compute the variance of x and the covariance or correlation of x and y if these are vectors. If x and y are matrices then the covariances (or correlations) between the columns of x and the columns of y are computed. cov2cor scales a covariance matrix into the corresponding correlation matrix efficiently.

• Usage

var(x, y = NULL, na.rm = FALSE, use)

cov(x, y = NULL, use = “everything”, method = c(“pearson”, “kendall”, “spearman”))

cor(x, y = NULL, use = “everything”, method = c(“pearson”, “kendall”, “spearman”))

cov2cor(V)

• Arguments

x : a numeric vector, matrix or data frame.

y : NULL (default) or a vector, matrix or data frame with compatible dimensions to x. The default is equivalent to y = x (but more efficient).

na.rm : logical. Should missing values be removed?

use : an optional character string giving a method for computing covariances in the presence of missing values. This must be (an abbreviation of) one of the strings “everything”, “all.obs”, “complete.obs”, “na.or.complete”, or “pairwise.complete.obs”.

method : a character string indicating which correlation coefficient (or covariance) is to be computed. One of “pearson” (default), “kendall”, or “spearman”: can be abbreviated.

V : symmetric numeric matrix, usually positive definite such as a covariance matrix.

cor(a, method='pearson')

	gender	marriage	edu	job	mincome	aware	count	amount	decision	propensity	skin	promo	location	satisf_b	satisf_i	satisf_al	repurchase
gender	1.00000000	0.018950432	-0.015141892	0.234495300	-0.24322115	-0.173258517	0.26720736	0.07060766	0.024599925	0.105123747	0.100927559	0.031070486	-0.07987533	0.068425536	0.03371565	0.031582421	0.13717521
marriage	0.01895043	1.000000000	0.090430642	-0.097376313	0.34672053	0.002746706	-0.03388587	0.11179503	0.065853663	0.161741172	0.000243840	0.056206150	-0.06633169	0.037174065	0.08363306	0.104428021	0.16562358
edu	-0.01514189	0.090430642	1.000000000	-0.152514543	0.29125234	-0.053224463	0.02317484	0.10287980	0.008078891	0.144735867	-0.048833264	0.016601180	-0.16879183	-0.017346951	0.09259939	0.020172944	0.03726943
job	0.23449530	-0.097376313	-0.152514543	1.000000000	-0.29724975	-0.037035494	0.06774745	-0.04452342	0.015581175	-0.148122023	0.036206215	0.033042235	0.21765244	-0.007970738	0.07370249	-0.054013630	0.04257733
mincome	-0.24322115	0.346720533	0.291252342	-0.297249748	1.00000000	0.033181017	-0.03751775	0.12555069	0.093481119	0.291048862	0.002721420	0.041308095	-0.27159896	0.041790891	0.11493493	0.121591093	0.11494068
aware	-0.17325852	0.002746706	-0.053224463	-0.037035494	0.03318102	1.000000000	-0.14045380	0.02599560	0.083566385	0.002056555	-0.057377153	0.004190501	-0.01139770	0.097678118	-0.02809058	0.016987040	-0.09646385
count	0.26720736	-0.033885869	0.023174842	0.067747449	-0.03751775	-0.140453801	1.00000000	-0.06605694	-0.034378011	0.010766170	0.039127374	0.010843867	0.01737366	-0.023712383	0.17298313	0.121654091	0.19176923
amount	0.07060766	0.111795032	0.102879797	-0.044523425	0.12555069	0.025995598	-0.06605694	1.00000000	-0.092237915	0.248702226	0.039647452	0.167832282	-0.21865952	0.151351288	0.05486640	0.063516185	0.05797403
decision	0.02459993	0.065853663	0.008078891	0.015581175	0.09348112	0.083566385	-0.03437801	-0.09223791	1.000000000	0.104598639	0.103755420	0.022390779	-0.10788193	0.003375614	0.13588654	0.189271220	0.21929154
propensity	0.10512375	0.161741172	0.144735867	-0.148122023	0.29104886	0.002056555	0.01076617	0.24870223	0.104598639	1.000000000	-0.098094475	0.197142362	-0.27947384	0.323968388	0.21183616	0.180745009	0.22548460
skin	0.10092756	0.000243840	-0.048833264	0.036206215	0.00272142	-0.057377153	0.03912737	0.03964745	0.103755420	-0.098094475	1.000000000	0.003177493	0.02155061	-0.127471531	0.06872337	0.011722962	0.02536274
promo	0.03107049	0.056206150	0.016601180	0.033042235	0.04130810	0.004190501	0.01084387	0.16783228	0.022390779	0.197142362	0.003177493	1.000000000	-0.03164168	0.072483016	0.13940641	-0.005563814	0.10102533
location	-0.07987533	-0.066331688	-0.168791830	0.217652440	-0.27159896	-0.011397701	0.01737366	-0.21865952	-0.107881932	-0.279473839	0.021550612	-0.031641677	1.00000000	-0.254221863	-0.08922635	-0.095974739	0.05341473
satisf_b	0.06842554	0.037174065	-0.017346951	-0.007970738	0.04179089	0.097678118	-0.02371238	0.15135129	0.003375614	0.323968388	-0.127471531	0.072483016	-0.25422186	1.000000000	0.01837903	-0.031382338	-0.02892399
satisf_i	0.03371565	0.083633059	0.092599391	0.073702488	0.11493493	-0.028090585	0.17298313	0.05486640	0.135886536	0.211836156	0.068723366	0.139406409	-0.08922635	0.018379033	1.00000000	0.584506125	0.51077138
satisf_al	0.03158242	0.104428021	0.020172944	-0.054013630	0.12159109	0.016987040	0.12165409	0.06351618	0.189271220	0.180745009	0.011722962	-0.005563814	-0.09597474	-0.031382338	0.58450612	1.000000000	0.56502825
repurchase	0.13717521	0.165623585	0.037269434	0.042577334	0.11494068	-0.096463853	0.19176923	0.05797403	0.219291539	0.225484605	0.025362744	0.101025333	0.05341473	-0.028923989	0.51077138	0.565028245	1.00000000

attach(a)

The following objects are masked from a (pos = 3):

    amount, aware, count, decision, edu, gender, job, location,
    marriage, mincome, promo, propensity, repurchase, satisf_al,
    satisf_b, satisf_i, skin

library(base)

cor <- cbind(decision,satisf_b, satisf_i, satisf_al, repurchase)

cor

decision	satisf_b	satisf_i	satisf_al	repurchase
2	5	2	2	2
1	2	3	3	4
3	4	5	4	4
3	3	4	4	4
2	3	3	3	3
2	3	4	4	3
3	2	2	3	4
3	4	4	4	4
3	3	4	4	4
3	2	3	4	4
1	3	3	4	4
3	3	3	3	3
2	4	4	4	4
1	3	3	3	3
3	3	3	3	4
1	3	4	3	3
1	3	3	3	3
3	4	4	4	4
2	3	3	4	4
2	3	3	3	3
3	3	4	4	4
3	2	3	4	4
2	3	4	4	4
1	3	3	3	3
1	3	3	4	4
3	3	4	4	4
3	2	4	4	4
3	3	4	4	4
2	4	4	4	3
3	3	4	4	4
...	...	...	...	...
2	3	4	4	4
3	3	4	4	4
1	5	1	3	1
1	2	3	3	3
3	2	4	4	4
1	3	3	3	3
3	4	4	3	4
3	3	4	4	4
3	2	3	3	3
3	3	3	3	3
3	3	2	3	4
2	3	3	3	3
2	3	3	4	4
2	3	4	4	3
1	3	4	4	4
1	3	3	3	3
3	3	3	3	3
3	2	3	4	4
3	3	4	4	4
2	3	3	1	2
1	3	4	3	3
2	3	3	3	3
3	3	4	3	3
2	3	3	3	3
1	1	1	1	1
1	2	1	1	1
3	3	4	4	4
1	2	5	4	4
3	4	3	3	2
3	2	3	3	3

cor(cor, method='pearson')

	decision	satisf_b	satisf_i	satisf_al	repurchase
decision	1.000000000	0.003375614	0.13588654	0.18927122	0.21929154
satisf_b	0.003375614	1.000000000	0.01837903	-0.03138234	-0.02892399
satisf_i	0.135886536	0.018379033	1.00000000	0.58450612	0.51077138
satisf_al	0.189271220	-0.031382338	0.58450612	1.00000000	0.56502825
repurchase	0.219291539	-0.028923989	0.51077138	0.56502825	1.00000000

pairs(cor)

library(ggplot2)

ggplot(as.data.frame(cor),aes(x=satisf_al, y= repurchase)) + geom_point()

ggplot(as.data.frame(cor),aes(x=satisf_al, y= repurchase, shape=factor(decision))) + geom_point(color= 'red',fill='blue', alpha=0.5, size=6,stroke=2)

ggplot(as.data.frame(cor),aes(x=satisf_al, y= repurchase)) + geom_smooth(method=lm)

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

• 회색부분이 신뢰구간을 나타내 준다,