Exploratory Data Analysis: USNews-State-Rankings
Mir Quddus
5/1/2022
Objective: Conduct exploratory data analysis to determine the major factors associated with “living potential” in a state.
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## compactEDA Step 0: import the excel data - states and overall summary
## states
##
## 10 Variables 50 Observations
## --------------------------------------------------------------------------------
## Rank
## n missing distinct Info Mean Gmd .05 .10
## 50 0 50 1 25.5 17 3.45 5.90
## .25 .50 .75 .90 .95
## 13.25 25.50 37.75 45.10 47.55
##
## lowest : 1 2 3 4 5, highest: 46 47 48 49 50
## --------------------------------------------------------------------------------
## State
## n missing distinct
## 50 0 50
##
## lowest : Alabama Alaska Arizona Arkansas California
## highest: Virginia Washington WestVirginia Wisconsin Wyoming
## --------------------------------------------------------------------------------
## Health Care
## n missing distinct Info Mean Gmd .05 .10
## 50 0 50 1 25.5 17 3.45 5.90
## .25 .50 .75 .90 .95
## 13.25 25.50 37.75 45.10 47.55
##
## lowest : 1 2 3 4 5, highest: 46 47 48 49 50
## --------------------------------------------------------------------------------
## Education
## n missing distinct Info Mean Gmd .05 .10
## 50 0 50 1 25.5 17 3.45 5.90
## .25 .50 .75 .90 .95
## 13.25 25.50 37.75 45.10 47.55
##
## lowest : 1 2 3 4 5, highest: 46 47 48 49 50
## --------------------------------------------------------------------------------
## Economy
## n missing distinct Info Mean Gmd .05 .10
## 50 0 50 1 25.5 17 3.45 5.90
## .25 .50 .75 .90 .95
## 13.25 25.50 37.75 45.10 47.55
##
## lowest : 1 2 3 4 5, highest: 46 47 48 49 50
## --------------------------------------------------------------------------------
## Infrastructure
## n missing distinct Info Mean Gmd .05 .10
## 50 0 50 1 25.5 17 3.45 5.90
## .25 .50 .75 .90 .95
## 13.25 25.50 37.75 45.10 47.55
##
## lowest : 1 2 3 4 5, highest: 46 47 48 49 50
## --------------------------------------------------------------------------------
## Opportunity
## n missing distinct Info Mean Gmd .05 .10
## 50 0 50 1 25.5 17 3.45 5.90
## .25 .50 .75 .90 .95
## 13.25 25.50 37.75 45.10 47.55
##
## lowest : 1 2 3 4 5, highest: 46 47 48 49 50
## --------------------------------------------------------------------------------
## Fiscal Stability
## n missing distinct Info Mean Gmd .05 .10
## 50 0 50 1 25.5 17 3.45 5.90
## .25 .50 .75 .90 .95
## 13.25 25.50 37.75 45.10 47.55
##
## lowest : 1 2 3 4 5, highest: 46 47 48 49 50
## --------------------------------------------------------------------------------
## Crime & Corrections
## n missing distinct Info Mean Gmd .05 .10
## 50 0 50 1 25.5 17 3.45 5.90
## .25 .50 .75 .90 .95
## 13.25 25.50 37.75 45.10 47.55
##
## lowest : 1 2 3 4 5, highest: 46 47 48 49 50
## --------------------------------------------------------------------------------
## Natural Environment
## n missing distinct Info Mean Gmd .05 .10
## 50 0 50 1 25.5 17 3.45 5.90
## .25 .50 .75 .90 .95
## 13.25 25.50 37.75 45.10 47.55
##
## lowest : 1 2 3 4 5, highest: 46 47 48 49 50
## --------------------------------------------------------------------------------## [1] "Rank" "State" "Health Care"
## [4] "Education" "Economy" "Infrastructure"
## [7] "Opportunity" "Fiscal Stability" "Crime & Corrections"
## [10] "Natural Environment"## [1] 50 10## Rows: 50
## Columns: 10
## $ Rank <dbl> 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 1…
## $ State <chr> "Washington", "Minnesota", "Utah", "NewHampshire…
## $ `Health Care` <dbl> 8, 16, 11, 13, 24, 28, 12, 15, 2, 25, 18, 20, 30…
## $ Education <dbl> 4, 17, 10, 13, 29, 9, 12, 8, 2, 3, 15, 18, 7, 25…
## $ Economy <dbl> 4, 15, 1, 11, 3, 20, 13, 26, 5, 8, 25, 27, 17, 3…
## $ Infrastructure <dbl> 3, 9, 5, 34, 10, 6, 39, 24, 42, 20, 12, 19, 22, …
## $ Opportunity <dbl> 25, 2, 30, 3, 24, 10, 8, 9, 36, 33, 17, 1, 28, 2…
## $ `Fiscal Stability` <dbl> 6, 21, 5, 33, 4, 17, 18, 9, 43, 8, 37, 23, 7, 16…
## $ `Crime & Corrections` <dbl> 19, 15, 8, 1, 10, 31, 9, 25, 4, 26, 3, 14, 20, 1…
## $ `Natural Environment` <dbl> 15, 10, 47, 2, 12, 6, 19, 17, 4, 18, 9, 20, 27, …## # A tibble: 5 × 10
## Rank State `Health Care` Education Economy Infrastructure Opportunity
## <dbl> <chr> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 1 Washington 8 4 4 3 25
## 2 2 Minnesota 16 17 15 9 2
## 3 3 Utah 11 10 1 5 30
## 4 4 NewHampshire 13 13 11 34 3
## 5 5 Idaho 24 29 3 10 24
## # … with 3 more variables: `Fiscal Stability` <dbl>,
## # `Crime & Corrections` <dbl>, `Natural Environment` <dbl>## Rank State Health Care Education
## Min. : 1.00 Length:50 Min. : 1.00 Min. : 1.00
## 1st Qu.:13.25 Class :character 1st Qu.:13.25 1st Qu.:13.25
## Median :25.50 Mode :character Median :25.50 Median :25.50
## Mean :25.50 Mean :25.50 Mean :25.50
## 3rd Qu.:37.75 3rd Qu.:37.75 3rd Qu.:37.75
## Max. :50.00 Max. :50.00 Max. :50.00
## Economy Infrastructure Opportunity Fiscal Stability
## Min. : 1.00 Min. : 1.00 Min. : 1.00 Min. : 1.00
## 1st Qu.:13.25 1st Qu.:13.25 1st Qu.:13.25 1st Qu.:13.25
## Median :25.50 Median :25.50 Median :25.50 Median :25.50
## Mean :25.50 Mean :25.50 Mean :25.50 Mean :25.50
## 3rd Qu.:37.75 3rd Qu.:37.75 3rd Qu.:37.75 3rd Qu.:37.75
## Max. :50.00 Max. :50.00 Max. :50.00 Max. :50.00
## Crime & Corrections Natural Environment
## Min. : 1.00 Min. : 1.00
## 1st Qu.:13.25 1st Qu.:13.25
## Median :25.50 Median :25.50
## Mean :25.50 Mean :25.50
## 3rd Qu.:37.75 3rd Qu.:37.75
## Max. :50.00 Max. :50.00Based on the above analysis, we can conclude the following: - This table contains 50 rows and 10 columns - names of the columns(Factors):
[1] “Rank” “State”
[3] “Health Care” “Education”
[5] “Economy” “Infrastructure”
[7] “Opportunity” “Fiscal Stability”
[9] “Crime & Corrections” “Natural Environment” - No missing data -
The data is ordered by the “Rank column” - The table contains data of 50
states. Order of the rank: best: 1, worst:50 - According to the above
criteria, Washington State has the highest living potential followed by
Louisiana as worst.
In order to understand the factors responsible for determining the living potential of a state, we will conduct the rest of the Exploratory Data Analysis (EDA).
EDA Step 1: Gain visual insights
Box-whisker chart top 10 states
Objective:
In order to understand the factors associated with the best states to live, we conduct the Box-Whiskers plot of the top 10 US states. This plot uses X-axis (Factors) and Y-axis (Rank and States). # Results: - Five factors are important: Healthcare, Education, Economy, Crime and Natural Environment. These factors are positively influencing the living potential in these states. - There are two outliers: Education and Natural Environment, which might be driving the spread of the data
## Warning in melt(data = top10States, id.vars = c("Rank", "State"), variable.name
## = "Factors", : The melt generic in data.table has been passed a tbl_df and will
## attempt to redirect to the relevant reshape2 method; please note that reshape2
## is deprecated, and this redirection is now deprecated as well. To continue using
## melt methods from reshape2 while both libraries are attached, e.g. melt.list,
## you can prepend the namespace like reshape2::melt(top10States). In the next
## version, this warning will become an error.box and whisker chart for bottom 10 states
Objective:
In order to understand the factors associated with the worst states to live, we conduct the Box-Whiskers plot of the bottom 10 US states. This plot uses X-axis (Factors) and Y-axis (Rank and States). # Results: - As identified above, these five factors (Healthcare, Education, Economy, Crime and Natural Environment) are driving the living potential negatively. - It is noticeable that crime is higher for the bottom 10 states compared to top 10. - The outlier in Economy is influencing the spread of the data.
## Warning in melt(data = bottom10States, id.vars = c("Rank", "State"),
## variable.name = "Categories", : The melt generic in data.table has been
## passed a tbl_df and will attempt to redirect to the relevant reshape2
## method; please note that reshape2 is deprecated, and this redirection is now
## deprecated as well. To continue using melt methods from reshape2 while both
## libraries are attached, e.g. melt.list, you can prepend the namespace like
## reshape2::melt(bottom10States). In the next version, this warning will become an
## error.EDA Step 2A: Correlation Analysis
Column correlation Analysis: Factors and Sub-Factors
Objective:
In order to further understand the importance of the identified
factors and the sub-factors driving the decision to categorize as the
best and worst states to live.
# Results: - The dark blue circles indicate significant correlation
between factor-to-factor and factor-to-sub-factor. - From the plot, it
can be observed that five factors (Healthcare, Education, Economy, Crime
and Natural Environment) and their interaction with the sub-factors are
driving the living potential both positively and negatively.
## Health Care Access Health Care Quality Public Health
## Health Care Access 1.00 0.25 0.54
## Health Care Quality 0.25 1.00 0.65
## Public Health 0.54 0.65 1.00
## Business Environment 0.11 0.40 0.53
## Employment 0.12 0.28 0.50
## Growth -0.20 0.21 0.16
## Higher Education -0.11 0.30 0.41
## Pre-K-12 0.67 0.33 0.58
## Energy -0.34 -0.03 0.02
## Internet Access -0.03 0.22 0.36
## Transportation -0.38 -0.06 -0.08
## Affordability -0.27 -0.71 -0.72
## Economic Opportunity 0.49 0.60 0.73
## Equality 0.43 -0.02 -0.03
## Long-Term -0.16 0.10 0.00
## Short-Term -0.59 -0.12 -0.27
## Corrections 0.28 0.40 0.49
## Public Safety 0.56 0.10 0.38
## Air & Water Quality 0.38 -0.05 0.24
## Pollution 0.17 0.16 0.37
## Business Environment Employment Growth Higher Education
## Health Care Access 0.11 0.12 -0.20 -0.11
## Health Care Quality 0.40 0.28 0.21 0.30
## Public Health 0.53 0.50 0.16 0.41
## Business Environment 1.00 0.46 0.50 0.27
## Employment 0.46 1.00 0.63 0.41
## Growth 0.50 0.63 1.00 0.28
## Higher Education 0.27 0.41 0.28 1.00
## Pre-K-12 0.36 0.47 0.13 0.12
## Energy -0.03 0.36 0.49 0.46
## Internet Access 0.43 0.42 0.34 0.53
## Transportation 0.04 0.27 0.37 0.43
## Affordability -0.37 -0.26 -0.14 -0.22
## Economic Opportunity 0.30 0.55 0.11 0.33
## Equality 0.00 -0.16 -0.06 -0.28
## Long-Term 0.26 0.35 0.49 0.42
## Short-Term -0.06 0.14 0.24 0.17
## Corrections 0.27 0.35 0.20 0.15
## Public Safety 0.06 0.24 -0.03 -0.10
## Air & Water Quality -0.10 0.29 -0.08 0.13
## Pollution -0.01 0.18 0.04 0.24
## Pre-K-12 Energy Internet Access Transportation
## Health Care Access 0.67 -0.34 -0.03 -0.38
## Health Care Quality 0.33 -0.03 0.22 -0.06
## Public Health 0.58 0.02 0.36 -0.08
## Business Environment 0.36 -0.03 0.43 0.04
## Employment 0.47 0.36 0.42 0.27
## Growth 0.13 0.49 0.34 0.37
## Higher Education 0.12 0.46 0.53 0.43
## Pre-K-12 1.00 -0.09 0.18 -0.13
## Energy -0.09 1.00 0.09 0.64
## Internet Access 0.18 0.09 1.00 0.33
## Transportation -0.13 0.64 0.33 1.00
## Affordability -0.19 0.06 -0.22 0.03
## Economic Opportunity 0.54 0.08 0.35 0.13
## Equality 0.24 -0.39 -0.07 -0.22
## Long-Term 0.11 0.36 0.13 0.30
## Short-Term -0.36 0.35 0.08 0.43
## Corrections 0.30 -0.06 0.34 -0.05
## Public Safety 0.64 -0.10 -0.03 -0.11
## Air & Water Quality 0.34 -0.07 0.06 -0.10
## Pollution 0.17 0.22 0.00 -0.01
## Affordability Economic Opportunity Equality Long-Term
## Health Care Access -0.27 0.49 0.43 -0.16
## Health Care Quality -0.71 0.60 -0.02 0.10
## Public Health -0.72 0.73 -0.03 0.00
## Business Environment -0.37 0.30 0.00 0.26
## Employment -0.26 0.55 -0.16 0.35
## Growth -0.14 0.11 -0.06 0.49
## Higher Education -0.22 0.33 -0.28 0.42
## Pre-K-12 -0.19 0.54 0.24 0.11
## Energy 0.06 0.08 -0.39 0.36
## Internet Access -0.22 0.35 -0.07 0.13
## Transportation 0.03 0.13 -0.22 0.30
## Affordability 1.00 -0.56 -0.08 0.14
## Economic Opportunity -0.56 1.00 0.04 0.00
## Equality -0.08 0.04 1.00 0.10
## Long-Term 0.14 0.00 0.10 1.00
## Short-Term 0.09 -0.18 -0.39 0.33
## Corrections -0.57 0.33 0.24 -0.05
## Public Safety -0.10 0.41 0.17 -0.05
## Air & Water Quality -0.06 0.26 0.24 0.20
## Pollution -0.35 0.38 -0.13 -0.02
## Short-Term Corrections Public Safety Air & Water Quality
## Health Care Access -0.59 0.28 0.56 0.38
## Health Care Quality -0.12 0.40 0.10 -0.05
## Public Health -0.27 0.49 0.38 0.24
## Business Environment -0.06 0.27 0.06 -0.10
## Employment 0.14 0.35 0.24 0.29
## Growth 0.24 0.20 -0.03 -0.08
## Higher Education 0.17 0.15 -0.10 0.13
## Pre-K-12 -0.36 0.30 0.64 0.34
## Energy 0.35 -0.06 -0.10 -0.07
## Internet Access 0.08 0.34 -0.03 0.06
## Transportation 0.43 -0.05 -0.11 -0.10
## Affordability 0.09 -0.57 -0.10 -0.06
## Economic Opportunity -0.18 0.33 0.41 0.26
## Equality -0.39 0.24 0.17 0.24
## Long-Term 0.33 -0.05 -0.05 0.20
## Short-Term 1.00 -0.18 -0.24 -0.12
## Corrections -0.18 1.00 0.07 0.07
## Public Safety -0.24 0.07 1.00 0.29
## Air & Water Quality -0.12 0.07 0.29 1.00
## Pollution -0.05 0.25 0.30 0.25
## Pollution
## Health Care Access 0.17
## Health Care Quality 0.16
## Public Health 0.37
## Business Environment -0.01
## Employment 0.18
## Growth 0.04
## Higher Education 0.24
## Pre-K-12 0.17
## Energy 0.22
## Internet Access 0.00
## Transportation -0.01
## Affordability -0.35
## Economic Opportunity 0.38
## Equality -0.13
## Long-Term -0.02
## Short-Term -0.05
## Corrections 0.25
## Public Safety 0.30
## Air & Water Quality 0.25
## Pollution 1.00
## EDA Step 2B: Correlation Analysis # evaluate the entire dataset for
correlation # Objective: In order to further quantify the significance
of the major factors driving the living potential of the top/bottom 10
states, we have conducted this analysis.
# Results: - The dark blue circles indicate significant correlation
between factor-to-factor and factor-to-sub-factor. - From the plot, it
can be observed that five factors (Healthcare, Education, Economy, Crime
and Natural Environment) and their interaction with each other are
significant for living potential consideration. - Significant
factor-factor interactions (>0.5) are: Healthcare - Education: 0.63
Education - Crime: 0.59 Healthcare - Crime: 0.58 These results indicate
that the living potential of a state depends on providing Healthcare,
Education and reduction of crime.
#truncate data by dropping Rank and State columns
drop <- c("Rank","State")
states_trunk = states[,!(names(states) %in% drop)]
states_trunk # view the data## # A tibble: 50 × 8
## `Health Care` Education Economy Infrastructure Opportunity `Fiscal Stability`
## <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 8 4 4 3 25 6
## 2 16 17 15 9 2 21
## 3 11 10 1 5 30 5
## 4 13 13 11 34 3 33
## 5 24 29 3 10 24 4
## 6 28 9 20 6 10 17
## 7 12 12 13 39 8 18
## 8 15 8 26 24 9 9
## 9 2 2 5 42 36 43
## 10 25 3 8 20 33 8
## # … with 40 more rows, and 2 more variables: `Crime & Corrections` <dbl>,
## # `Natural Environment` <dbl># correlation matrix
res <- cor(states_trunk)
round(res,2)## Health Care Education Economy Infrastructure Opportunity
## Health Care 1.00 0.63 0.34 -0.06 -0.02
## Education 0.63 1.00 0.44 0.26 0.27
## Economy 0.34 0.44 1.00 0.50 0.05
## Infrastructure -0.06 0.26 0.50 1.00 0.12
## Opportunity -0.02 0.27 0.05 0.12 1.00
## Fiscal Stability -0.10 0.08 0.32 0.42 0.09
## Crime & Corrections 0.58 0.59 0.13 -0.03 0.27
## Natural Environment 0.33 0.43 0.03 0.09 0.15
## Fiscal Stability Crime & Corrections Natural Environment
## Health Care -0.10 0.58 0.33
## Education 0.08 0.59 0.43
## Economy 0.32 0.13 0.03
## Infrastructure 0.42 -0.03 0.09
## Opportunity 0.09 0.27 0.15
## Fiscal Stability 1.00 -0.24 -0.01
## Crime & Corrections -0.24 1.00 0.50
## Natural Environment -0.01 0.50 1.00# use Hmisc library to get further correlation data
res2 <- rcorr(as.matrix(states_trunk))
res2$r # display correlation coefficients## Health Care Education Economy Infrastructure Opportunity
## Health Care 1.00000000 0.6301561 0.3357983 -0.05805522 -0.02194478
## Education 0.63015606 1.0000000 0.4397119 0.26223289 0.26943577
## Economy 0.33579832 0.4397119 1.0000000 0.49771909 0.04749100
## Infrastructure -0.05805522 0.2622329 0.4977191 1.00000000 0.11529412
## Opportunity -0.02194478 0.2694358 0.0474910 0.11529412 1.00000000
## Fiscal Stability -0.10271309 0.0847539 0.3157263 0.42376951 0.09493397
## Crime & Corrections 0.57599040 0.5945258 0.1300840 -0.03068427 0.26780312
## Natural Environment 0.33243697 0.4339496 0.0337575 0.08993998 0.14545018
## Fiscal Stability Crime & Corrections Natural Environment
## Health Care -0.10271309 0.57599040 0.33243697
## Education 0.08475390 0.59452581 0.43394958
## Economy 0.31572629 0.13008403 0.03375750
## Infrastructure 0.42376951 -0.03068427 0.08993998
## Opportunity 0.09493397 0.26780312 0.14545018
## Fiscal Stability 1.00000000 -0.23822329 -0.01109244
## Crime & Corrections -0.23822329 1.00000000 0.49896759
## Natural Environment -0.01109244 0.49896759 1.00000000res2$P # display the p-values## Health Care Education Economy Infrastructure
## Health Care NA 9.401790e-07 0.0171219838 0.6888122563
## Education 9.401790e-07 NA 0.0013980313 0.0658110886
## Economy 1.712198e-02 1.398031e-03 NA 0.0002353927
## Infrastructure 6.888123e-01 6.581109e-02 0.0002353927 NA
## Opportunity 8.797656e-01 5.846856e-02 0.7432872647 0.4252788839
## Fiscal Stability 4.778270e-01 5.584152e-01 0.0255142955 0.0021647915
## Crime & Corrections 1.204713e-05 5.302387e-06 0.3679063788 0.8324717662
## Natural Environment 1.833668e-02 1.641386e-03 0.8159707474 0.5345029056
## Opportunity Fiscal Stability Crime & Corrections
## Health Care 0.87976559 0.477827006 1.204713e-05
## Education 0.05846856 0.558415202 5.302387e-06
## Economy 0.74328726 0.025514295 3.679064e-01
## Infrastructure 0.42527888 0.002164791 8.324718e-01
## Opportunity NA 0.511959606 6.007224e-02
## Fiscal Stability 0.51195961 NA 9.571981e-02
## Crime & Corrections 0.06007224 0.095719811 NA
## Natural Environment 0.31352789 0.939058053 2.257294e-04
## Natural Environment
## Health Care 0.0183366794
## Education 0.0016413862
## Economy 0.8159707474
## Infrastructure 0.5345029056
## Opportunity 0.3135278911
## Fiscal Stability 0.9390580534
## Crime & Corrections 0.0002257294
## Natural Environment NA#
# matrix of the p-value of the correlation
# computing correlogram with the significance test
cor.mtest <- function(mat, ...){
mat <- as.matrix(mat)
n <- ncol(mat)
p.mat<- matrix(NA, n, n)
diag(p.mat) <- 0
for (i in 1:(n - 1)) {
for (j in (i + 1):n) {
tmp <- cor.test(mat[, i], mat[, j], ...)
p.mat[i, j] <- p.mat[j, i] <- tmp$p.value
}
}
colnames(p.mat) <- rownames(p.mat) <- colnames(mat)
p.mat
}
p.mat <- cor.mtest(states_trunk)
# Insignificant correlation are crossed
corrplot(res, type="upper", order="hclust", p.mat = p.mat, sig.level = 0.01, insig = "blank")
col <- colorRampPalette(c("#BB4444", "#EE9988", "#FFFFFF", "#77AADD", "#4477AA"))
corrplot(res, method="color", col=col(50),
type="upper", order="hclust",
addCoef.col = "black", # Add coefficient of correlation
tl.col="black", tl.srt=25, #Text label color and rotation
# Combine with significance
p.mat = p.mat, sig.level = 0.01, insig = "blank",
# hide correlation coefficient on the principal diagonal
diag=FALSE
)
```