Matis10
Richard Gale
2024-04-24
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library(qcc)## Warning: package 'qcc' was built under R version 4.3.3## Package 'qcc' version 2.7## Type 'citation("qcc")' for citing this R package in publications.library(stats)
library(MASS)
library(Hmisc)## Warning: package 'Hmisc' was built under R version 4.3.3##
## Attaching package: 'Hmisc'## The following objects are masked from 'package:base':
##
## format.pval, unitslibrary(corrplot)## Warning: package 'corrplot' was built under R version 4.3.3## corrplot 0.92 loadedlibrary(greybox)## Warning: package 'greybox' was built under R version 4.3.3## Package "greybox", v2.0.0 loaded.Test test test…why is power point not copying…gotta go visual…
No model - how are the sets of variables related? We’ll restrict to bivariate. We want a single number that measures the strength of the relationship, -1 to 1 or 0 to 1. What do the variables look like?
Seems pretty reasonable. Now, correlation…
If both variables are numeric, we can calculate a correlation. We speak about this generally, bu it strictly refers to a linear relationship. What is the Pearson coefficient of correlation?
Easy to do in R:
data()
mtcars## mpg cyl disp hp drat wt qsec vs am gear carb
## Mazda RX4 21.0 6 160.0 110 3.90 2.620 16.46 0 1 4 4
## Mazda RX4 Wag 21.0 6 160.0 110 3.90 2.875 17.02 0 1 4 4
## Datsun 710 22.8 4 108.0 93 3.85 2.320 18.61 1 1 4 1
## Hornet 4 Drive 21.4 6 258.0 110 3.08 3.215 19.44 1 0 3 1
## Hornet Sportabout 18.7 8 360.0 175 3.15 3.440 17.02 0 0 3 2
## Valiant 18.1 6 225.0 105 2.76 3.460 20.22 1 0 3 1
## Duster 360 14.3 8 360.0 245 3.21 3.570 15.84 0 0 3 4
## Merc 240D 24.4 4 146.7 62 3.69 3.190 20.00 1 0 4 2
## Merc 230 22.8 4 140.8 95 3.92 3.150 22.90 1 0 4 2
## Merc 280 19.2 6 167.6 123 3.92 3.440 18.30 1 0 4 4
## Merc 280C 17.8 6 167.6 123 3.92 3.440 18.90 1 0 4 4
## Merc 450SE 16.4 8 275.8 180 3.07 4.070 17.40 0 0 3 3
## Merc 450SL 17.3 8 275.8 180 3.07 3.730 17.60 0 0 3 3
## Merc 450SLC 15.2 8 275.8 180 3.07 3.780 18.00 0 0 3 3
## Cadillac Fleetwood 10.4 8 472.0 205 2.93 5.250 17.98 0 0 3 4
## Lincoln Continental 10.4 8 460.0 215 3.00 5.424 17.82 0 0 3 4
## Chrysler Imperial 14.7 8 440.0 230 3.23 5.345 17.42 0 0 3 4
## Fiat 128 32.4 4 78.7 66 4.08 2.200 19.47 1 1 4 1
## Honda Civic 30.4 4 75.7 52 4.93 1.615 18.52 1 1 4 2
## Toyota Corolla 33.9 4 71.1 65 4.22 1.835 19.90 1 1 4 1
## Toyota Corona 21.5 4 120.1 97 3.70 2.465 20.01 1 0 3 1
## Dodge Challenger 15.5 8 318.0 150 2.76 3.520 16.87 0 0 3 2
## AMC Javelin 15.2 8 304.0 150 3.15 3.435 17.30 0 0 3 2
## Camaro Z28 13.3 8 350.0 245 3.73 3.840 15.41 0 0 3 4
## Pontiac Firebird 19.2 8 400.0 175 3.08 3.845 17.05 0 0 3 2
## Fiat X1-9 27.3 4 79.0 66 4.08 1.935 18.90 1 1 4 1
## Porsche 914-2 26.0 4 120.3 91 4.43 2.140 16.70 0 1 5 2
## Lotus Europa 30.4 4 95.1 113 3.77 1.513 16.90 1 1 5 2
## Ford Pantera L 15.8 8 351.0 264 4.22 3.170 14.50 0 1 5 4
## Ferrari Dino 19.7 6 145.0 175 3.62 2.770 15.50 0 1 5 6
## Maserati Bora 15.0 8 301.0 335 3.54 3.570 14.60 0 1 5 8
## Volvo 142E 21.4 4 121.0 109 4.11 2.780 18.60 1 1 4 2plot(mtcars$mpg,mtcars$wt,xlab="mpg",ylab="weight", main="mpg by weight")
quantify relationship
cor.test(mtcars$mpg,mtcars$wt)##
## Pearson's product-moment correlation
##
## data: mtcars$mpg and mtcars$wt
## t = -9.559, df = 30, p-value = 1.294e-10
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## -0.9338264 -0.7440872
## sample estimates:
## cor
## -0.8676594We can also do a hypothesis test: H0: rho = 0, H1: rho != 0
qt(0.025, 30)## [1] -2.042272Thing is we can hack the p value by adding more and more data. Usually we know the correlation is not zero. Won’t tell you whether it’s strong relationship or not. That needs a significant amount of experience. You can always get a better p value by adding more data.
Now let’s look at all correlations:
mtcars2<-mtcars[,c(1,3,4,5,6,7)]
mtcars2## mpg disp hp drat wt qsec
## Mazda RX4 21.0 160.0 110 3.90 2.620 16.46
## Mazda RX4 Wag 21.0 160.0 110 3.90 2.875 17.02
## Datsun 710 22.8 108.0 93 3.85 2.320 18.61
## Hornet 4 Drive 21.4 258.0 110 3.08 3.215 19.44
## Hornet Sportabout 18.7 360.0 175 3.15 3.440 17.02
## Valiant 18.1 225.0 105 2.76 3.460 20.22
## Duster 360 14.3 360.0 245 3.21 3.570 15.84
## Merc 240D 24.4 146.7 62 3.69 3.190 20.00
## Merc 230 22.8 140.8 95 3.92 3.150 22.90
## Merc 280 19.2 167.6 123 3.92 3.440 18.30
## Merc 280C 17.8 167.6 123 3.92 3.440 18.90
## Merc 450SE 16.4 275.8 180 3.07 4.070 17.40
## Merc 450SL 17.3 275.8 180 3.07 3.730 17.60
## Merc 450SLC 15.2 275.8 180 3.07 3.780 18.00
## Cadillac Fleetwood 10.4 472.0 205 2.93 5.250 17.98
## Lincoln Continental 10.4 460.0 215 3.00 5.424 17.82
## Chrysler Imperial 14.7 440.0 230 3.23 5.345 17.42
## Fiat 128 32.4 78.7 66 4.08 2.200 19.47
## Honda Civic 30.4 75.7 52 4.93 1.615 18.52
## Toyota Corolla 33.9 71.1 65 4.22 1.835 19.90
## Toyota Corona 21.5 120.1 97 3.70 2.465 20.01
## Dodge Challenger 15.5 318.0 150 2.76 3.520 16.87
## AMC Javelin 15.2 304.0 150 3.15 3.435 17.30
## Camaro Z28 13.3 350.0 245 3.73 3.840 15.41
## Pontiac Firebird 19.2 400.0 175 3.08 3.845 17.05
## Fiat X1-9 27.3 79.0 66 4.08 1.935 18.90
## Porsche 914-2 26.0 120.3 91 4.43 2.140 16.70
## Lotus Europa 30.4 95.1 113 3.77 1.513 16.90
## Ford Pantera L 15.8 351.0 264 4.22 3.170 14.50
## Ferrari Dino 19.7 145.0 175 3.62 2.770 15.50
## Maserati Bora 15.0 301.0 335 3.54 3.570 14.60
## Volvo 142E 21.4 121.0 109 4.11 2.780 18.60and what are the correlations?
cor(mtcars2)## mpg disp hp drat wt qsec
## mpg 1.0000000 -0.8475514 -0.7761684 0.68117191 -0.8676594 0.41868403
## disp -0.8475514 1.0000000 0.7909486 -0.71021393 0.8879799 -0.43369788
## hp -0.7761684 0.7909486 1.0000000 -0.44875912 0.6587479 -0.70822339
## drat 0.6811719 -0.7102139 -0.4487591 1.00000000 -0.7124406 0.09120476
## wt -0.8676594 0.8879799 0.6587479 -0.71244065 1.0000000 -0.17471588
## qsec 0.4186840 -0.4336979 -0.7082234 0.09120476 -0.1747159 1.00000000Let’s get a plot:
library(corrplot)
corrplot::corrplot(cor(mtcars2))
#here, the corrplot::corrplot tells R where to find the libraryA little more clear but a little busy. We can get rid of the bubbles, and clean up the plot as below.
library(corrplot)
corrplot::corrplot(cor(mtcars2), type="upper",method="number")
Yeah, that’s a little better.
What about a weak correlation?
plot (mtcars$mpg,mtcars$qsec)
If we wanted additional information about the strength of correlations, we can get the p values. Need new package Hmisc.
#install.packages("Hmisc")
library(Hmisc)Hmisc::rcorr(as.matrix(mtcars2))## mpg disp hp drat wt qsec
## mpg 1.00 -0.85 -0.78 0.68 -0.87 0.42
## disp -0.85 1.00 0.79 -0.71 0.89 -0.43
## hp -0.78 0.79 1.00 -0.45 0.66 -0.71
## drat 0.68 -0.71 -0.45 1.00 -0.71 0.09
## wt -0.87 0.89 0.66 -0.71 1.00 -0.17
## qsec 0.42 -0.43 -0.71 0.09 -0.17 1.00
##
## n= 32
##
##
## P
## mpg disp hp drat wt qsec
## mpg 0.0000 0.0000 0.0000 0.0000 0.0171
## disp 0.0000 0.0000 0.0000 0.0000 0.0131
## hp 0.0000 0.0000 0.0100 0.0000 0.0000
## drat 0.0000 0.0000 0.0100 0.0000 0.6196
## wt 0.0000 0.0000 0.0000 0.0000 0.3389
## qsec 0.0171 0.0131 0.0000 0.6196 0.3389Moving right along now…
Spearmans looks for a monotonic relationship. Rank the data, get rid of the data, analyze the ranks.
Order x’s and y’s. Then throw out the data.
cor(mtcars$mpg,mtcars$wt,method="spearman")## [1] -0.886422cor.test(mtcars$mpg,mtcars$wt,method="spearman")## Warning in cor.test.default(mtcars$mpg, mtcars$wt, method = "spearman"): Cannot
## compute exact p-value with ties##
## Spearman's rank correlation rho
##
## data: mtcars$mpg and mtcars$wt
## S = 10292, p-value = 1.488e-11
## alternative hypothesis: true rho is not equal to 0
## sample estimates:
## rho
## -0.886422cor(mtcars2,method="spearman")## mpg disp hp drat wt qsec
## mpg 1.0000000 -0.9088824 -0.8946646 0.65145546 -0.8864220 0.46693575
## disp -0.9088824 1.0000000 0.8510426 -0.68359210 0.8977064 -0.45978176
## hp -0.8946646 0.8510426 1.0000000 -0.52012499 0.7746767 -0.66660602
## drat 0.6514555 -0.6835921 -0.5201250 1.00000000 -0.7503904 0.09186863
## wt -0.8864220 0.8977064 0.7746767 -0.75039041 1.0000000 -0.22540120
## qsec 0.4669358 -0.4597818 -0.6666060 0.09186863 -0.2254012 1.00000000Hmisc::rcorr(as.matrix(mtcars2), type="spearman")## mpg disp hp drat wt qsec
## mpg 1.00 -0.91 -0.89 0.65 -0.89 0.47
## disp -0.91 1.00 0.85 -0.68 0.90 -0.46
## hp -0.89 0.85 1.00 -0.52 0.77 -0.67
## drat 0.65 -0.68 -0.52 1.00 -0.75 0.09
## wt -0.89 0.90 0.77 -0.75 1.00 -0.23
## qsec 0.47 -0.46 -0.67 0.09 -0.23 1.00
##
## n= 32
##
##
## P
## mpg disp hp drat wt qsec
## mpg 0.0000 0.0000 0.0000 0.0000 0.0071
## disp 0.0000 0.0000 0.0000 0.0000 0.0081
## hp 0.0000 0.0000 0.0023 0.0000 0.0000
## drat 0.0000 0.0000 0.0023 0.0000 0.6170
## wt 0.0000 0.0000 0.0000 0.0000 0.2148
## qsec 0.0071 0.0081 0.0000 0.6170 0.2148Do the graphs:
cor(mtcars$mpg,mtcars$wt,method="spearman")## [1] -0.886422corrplot::corrplot(cor(mtcars2,method="spearman"), type="upper",method="number")
In this example, there isn’t a lot of difference between Pearsons and Spearmans.
Another example:
#install.packages(MASS)
library(MASS)
data("Boston")
head(Boston)## crim zn indus chas nox rm age dis rad tax ptratio black lstat
## 1 0.00632 18 2.31 0 0.538 6.575 65.2 4.0900 1 296 15.3 396.90 4.98
## 2 0.02731 0 7.07 0 0.469 6.421 78.9 4.9671 2 242 17.8 396.90 9.14
## 3 0.02729 0 7.07 0 0.469 7.185 61.1 4.9671 2 242 17.8 392.83 4.03
## 4 0.03237 0 2.18 0 0.458 6.998 45.8 6.0622 3 222 18.7 394.63 2.94
## 5 0.06905 0 2.18 0 0.458 7.147 54.2 6.0622 3 222 18.7 396.90 5.33
## 6 0.02985 0 2.18 0 0.458 6.430 58.7 6.0622 3 222 18.7 394.12 5.21
## medv
## 1 24.0
## 2 21.6
## 3 34.7
## 4 33.4
## 5 36.2
## 6 28.7plot(Boston$medv,Boston$lstat,xlab="median home value", ylab="% below poverty")
Curvy…maybe we should try Spearman’s…also lots of spread, non constant variance
cor(Boston$medv,Boston$lstat)## [1] -0.7376627cor(Boston$medv,Boston$lstat, method="spearman")## [1] -0.8529141Stronger correlation: nonlinear relationship, non-constant variance
Ok, what if we have classification, non-numerical. Let’s look at Cramer’s V:
Cramers V, useful for categorical vs. categorical. Like to have at least 5 observations per cell. An example:
#install.packages("greybox")
library(greybox)
greybox::tableplot(mtcars$am,mtcars$gear) #ignore ordinality of variables
greybox::tableplot(mtcars$am,mtcars$gear)
greybox::cramer(mtcars$am,mtcars$gear)## Cramer's V: 0.7808
## Chi^2 statistics = 20.9447, df: 2, p-value: 0greybox::tableplot(mtcars$am,mtcars$vs)
greybox::cramer(mtcars$am,mtcars$vs)## Cramer's V: 0
## Chi^2 statistics = 0.3475, df: 1, p-value: 0.5555How about binary by numerical?
plot(mtcars$mpg,mtcars$am)
cor.test(mtcars$mpg,mtcars$am)##
## Pearson's product-moment correlation
##
## data: mtcars$mpg and mtcars$am
## t = 4.1061, df = 30, p-value = 0.000285
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## 0.3175583 0.7844520
## sample estimates:
## cor
## 0.5998324So, some relationship between these variables. Next association, numerical vs. categorical
Now x is a category and y is a numerical variable. We need a beta for each category, with coefficients 0 (it is not a cat) and 1 (it us a cat). R tells us the strength of the relationship. Back to mtcars:
mtcars## mpg cyl disp hp drat wt qsec vs am gear carb
## Mazda RX4 21.0 6 160.0 110 3.90 2.620 16.46 0 1 4 4
## Mazda RX4 Wag 21.0 6 160.0 110 3.90 2.875 17.02 0 1 4 4
## Datsun 710 22.8 4 108.0 93 3.85 2.320 18.61 1 1 4 1
## Hornet 4 Drive 21.4 6 258.0 110 3.08 3.215 19.44 1 0 3 1
## Hornet Sportabout 18.7 8 360.0 175 3.15 3.440 17.02 0 0 3 2
## Valiant 18.1 6 225.0 105 2.76 3.460 20.22 1 0 3 1
## Duster 360 14.3 8 360.0 245 3.21 3.570 15.84 0 0 3 4
## Merc 240D 24.4 4 146.7 62 3.69 3.190 20.00 1 0 4 2
## Merc 230 22.8 4 140.8 95 3.92 3.150 22.90 1 0 4 2
## Merc 280 19.2 6 167.6 123 3.92 3.440 18.30 1 0 4 4
## Merc 280C 17.8 6 167.6 123 3.92 3.440 18.90 1 0 4 4
## Merc 450SE 16.4 8 275.8 180 3.07 4.070 17.40 0 0 3 3
## Merc 450SL 17.3 8 275.8 180 3.07 3.730 17.60 0 0 3 3
## Merc 450SLC 15.2 8 275.8 180 3.07 3.780 18.00 0 0 3 3
## Cadillac Fleetwood 10.4 8 472.0 205 2.93 5.250 17.98 0 0 3 4
## Lincoln Continental 10.4 8 460.0 215 3.00 5.424 17.82 0 0 3 4
## Chrysler Imperial 14.7 8 440.0 230 3.23 5.345 17.42 0 0 3 4
## Fiat 128 32.4 4 78.7 66 4.08 2.200 19.47 1 1 4 1
## Honda Civic 30.4 4 75.7 52 4.93 1.615 18.52 1 1 4 2
## Toyota Corolla 33.9 4 71.1 65 4.22 1.835 19.90 1 1 4 1
## Toyota Corona 21.5 4 120.1 97 3.70 2.465 20.01 1 0 3 1
## Dodge Challenger 15.5 8 318.0 150 2.76 3.520 16.87 0 0 3 2
## AMC Javelin 15.2 8 304.0 150 3.15 3.435 17.30 0 0 3 2
## Camaro Z28 13.3 8 350.0 245 3.73 3.840 15.41 0 0 3 4
## Pontiac Firebird 19.2 8 400.0 175 3.08 3.845 17.05 0 0 3 2
## Fiat X1-9 27.3 4 79.0 66 4.08 1.935 18.90 1 1 4 1
## Porsche 914-2 26.0 4 120.3 91 4.43 2.140 16.70 0 1 5 2
## Lotus Europa 30.4 4 95.1 113 3.77 1.513 16.90 1 1 5 2
## Ford Pantera L 15.8 8 351.0 264 4.22 3.170 14.50 0 1 5 4
## Ferrari Dino 19.7 6 145.0 175 3.62 2.770 15.50 0 1 5 6
## Maserati Bora 15.0 8 301.0 335 3.54 3.570 14.60 0 1 5 8
## Volvo 142E 21.4 4 121.0 109 4.11 2.780 18.60 1 1 4 2greybox::mcor(mtcars$gear,mtcars$mpg)## Multiple correlations value: 0.6551
## F-statistics = 10.9007, df: 2, df resid: 29, p-value: 3e-04plot (mtcars$gear,mtcars$mpg)
summary(lm(mpg~factor(gear),data=mtcars))##
## Call:
## lm(formula = mpg ~ factor(gear), data = mtcars)
##
## Residuals:
## Min 1Q Median 3Q Max
## -6.7333 -3.2333 -0.9067 2.8483 9.3667
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 16.107 1.216 13.250 7.87e-14 ***
## factor(gear)4 8.427 1.823 4.621 7.26e-05 ***
## factor(gear)5 5.273 2.431 2.169 0.0384 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 4.708 on 29 degrees of freedom
## Multiple R-squared: 0.4292, Adjusted R-squared: 0.3898
## F-statistic: 10.9 on 2 and 29 DF, p-value: 0.0002948#all associations
str(mtcars)## 'data.frame': 32 obs. of 11 variables:
## $ mpg : num 21 21 22.8 21.4 18.7 18.1 14.3 24.4 22.8 19.2 ...
## $ cyl : num 6 6 4 6 8 6 8 4 4 6 ...
## $ disp: num 160 160 108 258 360 ...
## $ hp : num 110 110 93 110 175 105 245 62 95 123 ...
## $ drat: num 3.9 3.9 3.85 3.08 3.15 2.76 3.21 3.69 3.92 3.92 ...
## $ wt : num 2.62 2.88 2.32 3.21 3.44 ...
## $ qsec: num 16.5 17 18.6 19.4 17 ...
## $ vs : num 0 0 1 1 0 1 0 1 1 1 ...
## $ am : num 1 1 1 0 0 0 0 0 0 0 ...
## $ gear: num 4 4 4 3 3 3 3 4 4 4 ...
## $ carb: num 4 4 1 1 2 1 4 2 2 4 ...greybox::assoc(mtcars)## Associations:
## values:
## mpg cyl disp hp drat wt qsec vs am
## mpg 1.0000 0.8558 -0.8476 -0.7762 0.6812 -0.8677 0.4187 0.6640 0.5998
## cyl 0.8558 1.0000 0.9152 0.8449 0.7018 0.7826 0.5913 0.7889 0.4643
## disp -0.8476 0.9152 1.0000 0.7909 -0.7102 0.8880 -0.4337 0.7104 0.5912
## hp -0.7762 0.8449 0.7909 1.0000 -0.4488 0.6587 -0.7082 0.7231 0.2432
## drat 0.6812 0.7018 -0.7102 -0.4488 1.0000 -0.7124 0.0912 0.4403 0.7127
## wt -0.8677 0.7826 0.8880 0.6587 -0.7124 1.0000 -0.1747 0.5549 0.6925
## qsec 0.4187 0.5913 -0.4337 -0.7082 0.0912 -0.1747 1.0000 0.7445 0.2299
## vs 0.6640 0.7889 0.7104 0.7231 0.4403 0.5549 0.7445 1.0000 0.0000
## am 0.5998 0.4643 0.5912 0.2432 0.7127 0.6925 0.2299 0.0000 1.0000
## gear 0.6551 0.4820 0.7671 0.6638 0.8319 0.6587 0.6334 0.5728 0.7808
## carb 0.6667 0.4847 0.5605 0.7873 0.3344 0.6129 0.6695 0.5733 0.1864
## gear carb
## mpg 0.6551 0.6667
## cyl 0.4820 0.4847
## disp 0.7671 0.5605
## hp 0.6638 0.7873
## drat 0.8319 0.3344
## wt 0.6587 0.6129
## qsec 0.6334 0.6695
## vs 0.5728 0.5733
## am 0.7808 0.1864
## gear 1.0000 0.3217
## carb 0.3217 1.0000
##
## p-values:
## mpg cyl disp hp drat wt qsec vs am gear
## mpg 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0171 0.0000 0.0003 0.0003
## cyl 0.0000 0.0000 0.0000 0.0000 0.0001 0.0000 0.0020 0.0000 0.0126 0.0012
## disp 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0131 0.0000 0.0004 0.0000
## hp 0.0000 0.0000 0.0000 0.0000 0.0100 0.0000 0.0000 0.0000 0.1798 0.0002
## drat 0.0000 0.0001 0.0000 0.0100 0.0000 0.0000 0.6196 0.0117 0.0000 0.0000
## wt 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.3389 0.0010 0.0000 0.0003
## qsec 0.0171 0.0020 0.0131 0.0000 0.6196 0.3389 0.0000 0.0000 0.2057 0.0006
## vs 0.0000 0.0000 0.0000 0.0000 0.0117 0.0010 0.0000 0.0000 0.5555 0.0022
## am 0.0003 0.0126 0.0004 0.1798 0.0000 0.0000 0.2057 0.5555 0.0000 0.0000
## gear 0.0003 0.0012 0.0000 0.0002 0.0000 0.0003 0.0006 0.0022 0.0000 0.0000
## carb 0.0065 0.0066 0.0662 0.0001 0.6607 0.0242 0.0061 0.0090 0.2838 0.0857
## carb
## mpg 0.0065
## cyl 0.0066
## disp 0.0662
## hp 0.0001
## drat 0.6607
## wt 0.0242
## qsec 0.0061
## vs 0.0090
## am 0.2838
## gear 0.0857
## carb 0.0000
##
## types:
## mpg cyl disp hp drat wt qsec
## mpg "none" "mcor" "pearson" "pearson" "pearson" "pearson" "pearson"
## cyl "mcor" "none" "mcor" "mcor" "mcor" "mcor" "mcor"
## disp "pearson" "mcor" "none" "pearson" "pearson" "pearson" "pearson"
## hp "pearson" "mcor" "pearson" "none" "pearson" "pearson" "pearson"
## drat "pearson" "mcor" "pearson" "pearson" "none" "pearson" "pearson"
## wt "pearson" "mcor" "pearson" "pearson" "pearson" "none" "pearson"
## qsec "pearson" "mcor" "pearson" "pearson" "pearson" "pearson" "none"
## vs "mcor" "cramer" "mcor" "mcor" "mcor" "mcor" "mcor"
## am "mcor" "cramer" "mcor" "mcor" "mcor" "mcor" "mcor"
## gear "mcor" "cramer" "mcor" "mcor" "mcor" "mcor" "mcor"
## carb "mcor" "cramer" "mcor" "mcor" "mcor" "mcor" "mcor"
## vs am gear carb
## mpg "mcor" "mcor" "mcor" "mcor"
## cyl "cramer" "cramer" "cramer" "cramer"
## disp "mcor" "mcor" "mcor" "mcor"
## hp "mcor" "mcor" "mcor" "mcor"
## drat "mcor" "mcor" "mcor" "mcor"
## wt "mcor" "mcor" "mcor" "mcor"
## qsec "mcor" "mcor" "mcor" "mcor"
## vs "none" "cramer" "cramer" "cramer"
## am "cramer" "none" "cramer" "cramer"
## gear "cramer" "cramer" "none" "cramer"
## carb "cramer" "cramer" "cramer" "none"greybox::spread(mtcars)
Finally….