Exploratory Data Analysis

Choonghyun Ryu

2021-03-19

Preface

After you have acquired the data, you should do the following:

The dlookr package makes these steps fast and easy:

This document introduces EDA(Exploratory Data Analysis) methods provided by the dlookr package. You will learn how to EDA of tbl_df data that inherits from data.frame and data.frame with functions provided by dlookr.

dlookr increases synergy with dplyr. Particularly in data exploration and data wrangle, it increases the efficiency of the tidyverse package group.

Supported data structures

Data diagnosis supports the following data structures.

datasets

To illustrate the basic use of EDA in the dlookr package, I use a Carseats dataset. Carseats in the ISLR package is a simulated data set containing sales of child car seats at 400 different stores. This data is a data.frame created for the purpose of predicting sales volume.

library(ISLR)
str(Carseats)
'data.frame':   400 obs. of  11 variables:
 $ Sales      : num  9.5 11.22 10.06 7.4 4.15 ...
 $ CompPrice  : num  138 111 113 117 141 124 115 136 132 132 ...
 $ Income     : num  73 48 35 100 64 113 105 81 110 113 ...
 $ Advertising: num  11 16 10 4 3 13 0 15 0 0 ...
 $ Population : num  276 260 269 466 340 501 45 425 108 131 ...
 $ Price      : num  120 83 80 97 128 72 108 120 124 124 ...
 $ ShelveLoc  : Factor w/ 3 levels "Bad","Good","Medium": 1 2 3 3 1 1 3 2 3 3 ...
 $ Age        : num  42 65 59 55 38 78 71 67 76 76 ...
 $ Education  : num  17 10 12 14 13 16 15 10 10 17 ...
 $ Urban      : Factor w/ 2 levels "No","Yes": 2 2 2 2 2 1 2 2 1 1 ...
 $ US         : Factor w/ 2 levels "No","Yes": 2 2 2 2 1 2 1 2 1 2 ...

The contents of individual variables are as follows. (Refer to ISLR::Carseats Man page)

When data analysis is performed, data containing missing values is frequently encountered. However, ‘Carseats’ is complete data without missing values. So the following script created the missing values and saved them as carseats.

carseats <- ISLR::Carseats

suppressWarnings(RNGversion("3.5.0"))
set.seed(123)
carseats[sample(seq(NROW(carseats)), 20), "Income"] <- NA

suppressWarnings(RNGversion("3.5.0"))
set.seed(456)
carseats[sample(seq(NROW(carseats)), 10), "Urban"] <- NA

Exploratory Data Analysis

dlookr can help to understand the distribution of data by calculating descriptive statistics of numerical data. In addition, correlation between variables is identified and normality test is performed. It also identifies the relationship between target variables and independent variables.:

The following is a list of the EDA functions included in the dlookr package.:

Univariate data EDA

Calculating descriptive statistics using describe()

describe() computes descriptive statistics for numerical data. The descriptive statistics help determine the distribution of numerical variables. Like function of dplyr, the first argument is the tibble (or data frame). The second and subsequent arguments refer to variables within that data frame.

The variables of the tbl_df object returned by describe() are as follows.

For example, describe() can computes the statistics of all numerical variables in carseats:

describe(carseats)
# A tibble: 8 x 26
  variable     n    na   mean    sd se_mean   IQR skewness kurtosis   p00    p01
  <chr>    <int> <int>  <dbl> <dbl>   <dbl> <dbl>    <dbl>    <dbl> <dbl>  <dbl>
1 Sales      400     0   7.50  2.82   0.141  3.93   0.186   -0.0809     0  0.906
2 CompPri…   400     0 125.   15.3    0.767 20     -0.0428   0.0417    77 89.0  
3 Income     380    20  68.9  28.1    1.44  48.2    0.0449  -1.09      21 21.8  
4 Adverti…   400     0   6.64  6.65   0.333 12      0.640   -0.545      0  0    
# … with 4 more rows, and 15 more variables: p05 <dbl>, p10 <dbl>, p20 <dbl>,
#   p25 <dbl>, p30 <dbl>, p40 <dbl>, p50 <dbl>, p60 <dbl>, p70 <dbl>,
#   p75 <dbl>, p80 <dbl>, p90 <dbl>, p95 <dbl>, p99 <dbl>, p100 <dbl>

The following explains the descriptive statistics only for a few selected variables.:

# Select columns by name
describe(carseats, Sales, CompPrice, Income)
# A tibble: 3 x 26
  variable     n    na   mean    sd se_mean   IQR skewness kurtosis   p00    p01
  <chr>    <int> <int>  <dbl> <dbl>   <dbl> <dbl>    <dbl>    <dbl> <dbl>  <dbl>
1 Sales      400     0   7.50  2.82   0.141  3.93   0.186   -0.0809     0  0.906
2 CompPri…   400     0 125.   15.3    0.767 20     -0.0428   0.0417    77 89.0  
3 Income     380    20  68.9  28.1    1.44  48.2    0.0449  -1.09      21 21.8  
# … with 15 more variables: p05 <dbl>, p10 <dbl>, p20 <dbl>, p25 <dbl>,
#   p30 <dbl>, p40 <dbl>, p50 <dbl>, p60 <dbl>, p70 <dbl>, p75 <dbl>,
#   p80 <dbl>, p90 <dbl>, p95 <dbl>, p99 <dbl>, p100 <dbl>
# Select all columns between year and day (include)
describe(carseats, Sales:Income)
# A tibble: 3 x 26
  variable     n    na   mean    sd se_mean   IQR skewness kurtosis   p00    p01
  <chr>    <int> <int>  <dbl> <dbl>   <dbl> <dbl>    <dbl>    <dbl> <dbl>  <dbl>
1 Sales      400     0   7.50  2.82   0.141  3.93   0.186   -0.0809     0  0.906
2 CompPri…   400     0 125.   15.3    0.767 20     -0.0428   0.0417    77 89.0  
3 Income     380    20  68.9  28.1    1.44  48.2    0.0449  -1.09      21 21.8  
# … with 15 more variables: p05 <dbl>, p10 <dbl>, p20 <dbl>, p25 <dbl>,
#   p30 <dbl>, p40 <dbl>, p50 <dbl>, p60 <dbl>, p70 <dbl>, p75 <dbl>,
#   p80 <dbl>, p90 <dbl>, p95 <dbl>, p99 <dbl>, p100 <dbl>
# Select all columns except those from year to day (exclude)
describe(carseats, -(Sales:Income))
# A tibble: 5 x 26
  variable     n    na   mean     sd se_mean   IQR skewness kurtosis   p00   p01
  <chr>    <int> <int>  <dbl>  <dbl>   <dbl> <dbl>    <dbl>    <dbl> <dbl> <dbl>
1 Adverti…   400     0   6.64   6.65   0.333  12     0.640    -0.545     0   0  
2 Populat…   400     0 265.   147.     7.37  260.   -0.0512   -1.20     10  16.0
3 Price      400     0 116.    23.7    1.18   31    -0.125     0.452    24  55.0
4 Age        400     0  53.3   16.2    0.810  26.2  -0.0772   -1.13     25  25  
# … with 1 more row, and 15 more variables: p05 <dbl>, p10 <dbl>, p20 <dbl>,
#   p25 <dbl>, p30 <dbl>, p40 <dbl>, p50 <dbl>, p60 <dbl>, p70 <dbl>,
#   p75 <dbl>, p80 <dbl>, p90 <dbl>, p95 <dbl>, p99 <dbl>, p100 <dbl>

The describe() function can be sorted by left or right skewed size(skewness) using dplyr.:

carseats %>%
  describe() %>%
  select(variable, skewness, mean, p25, p50, p75) %>% 
  filter(!is.na(skewness)) %>% 
  arrange(desc(abs(skewness)))
# A tibble: 8 x 6
  variable    skewness   mean    p25    p50    p75
  <chr>          <dbl>  <dbl>  <dbl>  <dbl>  <dbl>
1 Advertising   0.640    6.64   0      5     12   
2 Sales         0.186    7.50   5.39   7.49   9.32
3 Price        -0.125  116.   100    117    131   
4 Age          -0.0772  53.3   39.8   54.5   66   
# … with 4 more rows

The describe() function supports the group_by() function syntax of the dplyr package.

carseats %>%
  group_by(US) %>% 
  describe(Sales, Income) 
# A tibble: 4 x 27
  variable US        n    na  mean    sd se_mean   IQR skewness kurtosis   p00
  <chr>    <fct> <dbl> <dbl> <dbl> <dbl>   <dbl> <dbl>    <dbl>    <dbl> <dbl>
1 Sales    No      142     0  6.82  2.60   0.218  3.44   0.323     0.808  0   
2 Sales    Yes     258     0  7.87  2.88   0.179  4.23   0.0760   -0.326  0.37
3 Income   No      130    12 65.8  28.2    2.48  50      0.100    -1.14  22   
4 Income   Yes     250     8 70.4  27.9    1.77  48      0.0199   -1.06  21   
# … with 16 more variables: p01 <dbl>, p05 <dbl>, p10 <dbl>, p20 <dbl>,
#   p25 <dbl>, p30 <dbl>, p40 <dbl>, p50 <dbl>, p60 <dbl>, p70 <dbl>,
#   p75 <dbl>, p80 <dbl>, p90 <dbl>, p95 <dbl>, p99 <dbl>, p100 <dbl>
carseats %>%
  group_by(US, Urban) %>% 
  describe(Sales, Income) 
# A tibble: 12 x 28
  variable US    Urban     n    na  mean    sd se_mean   IQR skewness kurtosis
  <chr>    <fct> <fct> <dbl> <dbl> <dbl> <dbl>   <dbl> <dbl>    <dbl>    <dbl>
1 Sales    No    No       46     0  6.46  2.72   0.402 3.15    0.0889    1.53 
2 Sales    No    Yes      92     0  7.00  2.58   0.269 3.49    0.492     0.306
3 Sales    No    <NA>      4     0  6.99  1.28   0.639 0.827   1.69      3.16 
4 Sales    Yes   No       69     0  8.23  2.65   0.319 4.1    -0.0212   -0.777
# … with 8 more rows, and 17 more variables: p00 <dbl>, p01 <dbl>, p05 <dbl>,
#   p10 <dbl>, p20 <dbl>, p25 <dbl>, p30 <dbl>, p40 <dbl>, p50 <dbl>,
#   p60 <dbl>, p70 <dbl>, p75 <dbl>, p80 <dbl>, p90 <dbl>, p95 <dbl>,
#   p99 <dbl>, p100 <dbl>

Test of normality on numeric variables using normality()

normality() performs a normality test on numerical data. Shapiro-Wilk normality test is performed. When the number of observations is greater than 5000, it is tested after extracting 5000 samples by random simple sampling.

The variables of tbl_df object returned by normality() are as follows.

normality() performs the normality test for all numerical variables of carseats as follows.:

normality(carseats)
# A tibble: 8 x 4
  vars        statistic  p_value sample
  <chr>           <dbl>    <dbl>  <dbl>
1 Sales           0.995 2.54e- 1    400
2 CompPrice       0.998 9.77e- 1    400
3 Income          0.961 1.52e- 8    400
4 Advertising     0.874 1.49e-17    400
# … with 4 more rows

The following example performs a normality test on only a few selected variables.

# Select columns by name
normality(carseats, Sales, CompPrice, Income)
# A tibble: 3 x 4
  vars      statistic      p_value sample
  <chr>         <dbl>        <dbl>  <dbl>
1 Sales         0.995 0.254           400
2 CompPrice     0.998 0.977           400
3 Income        0.961 0.0000000152    400

# Select all columns between year and day (inclusive)
normality(carseats, Sales:Income)
# A tibble: 3 x 4
  vars      statistic      p_value sample
  <chr>         <dbl>        <dbl>  <dbl>
1 Sales         0.995 0.254           400
2 CompPrice     0.998 0.977           400
3 Income        0.961 0.0000000152    400

# Select all columns except those from year to day (inclusive)
normality(carseats, -(Sales:Income))
# A tibble: 5 x 4
  vars        statistic  p_value sample
  <chr>           <dbl>    <dbl>  <dbl>
1 Advertising     0.874 1.49e-17    400
2 Population      0.952 4.08e-10    400
3 Price           0.996 3.90e- 1    400
4 Age             0.957 1.86e- 9    400
# … with 1 more row

You can use dplyr to sort variables that do not follow a normal distribution in order of p_value:

library(dplyr)

carseats %>%
  normality() %>%
  filter(p_value <= 0.01) %>% 
  arrange(abs(p_value))
# A tibble: 5 x 4
  vars        statistic  p_value sample
  <chr>           <dbl>    <dbl>  <dbl>
1 Advertising     0.874 1.49e-17    400
2 Education       0.924 2.43e-13    400
3 Population      0.952 4.08e-10    400
4 Age             0.957 1.86e- 9    400
# … with 1 more row

In particular, the Advertising variable is considered to be the most out of the normal distribution.

The normality() function supports the group_by() function syntax in the dplyr package.

carseats %>%
  group_by(ShelveLoc, US) %>%
  normality(Income) %>% 
  arrange(desc(p_value))
# A tibble: 6 x 6
  variable ShelveLoc US    statistic p_value sample
  <chr>    <fct>     <fct>     <dbl>   <dbl>  <dbl>
1 Income   Bad       No        0.969  0.470      34
2 Income   Bad       Yes       0.958  0.0343     62
3 Income   Good      No        0.902  0.0328     24
4 Income   Good      Yes       0.955  0.0296     61
# … with 2 more rows

The Income variable does not follow the normal distribution. However, the case where US is No and ShelveLoc is Good and Bad at the significance level of 0.01, it follows the normal distribution.

The following example performs normality test of log(Income) for each combination of ShelveLoc and US categorical variables to search for variables that follow the normal distribution.

carseats %>%
  mutate(log_income = log(Income)) %>%
  group_by(ShelveLoc, US) %>%
  normality(log_income) %>%
  filter(p_value > 0.01)
# A tibble: 1 x 6
  variable   ShelveLoc US    statistic p_value sample
  <chr>      <fct>     <fct>     <dbl>   <dbl>  <dbl>
1 log_income Bad       No        0.940  0.0737     34

Visualization of normality of numerical variables using plot_normality()

plot_normality() visualizes the normality of numeric data.

The information visualized by plot_normality() is as follows.:

In the data analysis process, it often encounters numerical data that follows the power-law distribution. Since the numerical data that follows the power-law distribution is converted into a normal distribution by performing the log or sqrt transformation, so draw a histogram of the log and sqrt transformed data.

plot_normality() can also specify several variables like normality() function.

# Select columns by name
plot_normality(carseats, Sales, CompPrice)

The plot_normality() function also supports the group_by() function syntax in the dplyr package.

carseats %>%
  filter(ShelveLoc == "Good") %>%
  group_by(US) %>%
  plot_normality(Income)

EDA of bivariate data

Calculation of correlation coefficient using correlate()

correlate() calculates the correlation coefficient of all combinations of carseats numerical variables as follows:

correlate(carseats)
# A tibble: 56 x 3
  var1        var2  coef_corr
  <fct>       <fct>     <dbl>
1 CompPrice   Sales    0.0641
2 Income      Sales    0.151 
3 Advertising Sales    0.270 
4 Population  Sales    0.0505
# … with 52 more rows

The following example performs a normality test only on combinations that include several selected variables.

# Select columns by name
correlate(carseats, Sales, CompPrice, Income)
# A tibble: 21 x 3
  var1      var2      coef_corr
  <fct>     <fct>         <dbl>
1 CompPrice Sales        0.0641
2 Income    Sales        0.151 
3 Sales     CompPrice    0.0641
4 Income    CompPrice   -0.0761
# … with 17 more rows

# Select all columns between year and day (include)
correlate(carseats, Sales:Income)
# A tibble: 21 x 3
  var1      var2      coef_corr
  <fct>     <fct>         <dbl>
1 CompPrice Sales        0.0641
2 Income    Sales        0.151 
3 Sales     CompPrice    0.0641
4 Income    CompPrice   -0.0761
# … with 17 more rows

# Select all columns except those from year to day (exclude)
correlate(carseats, -(Sales:Income))
# A tibble: 35 x 3
  var1        var2  coef_corr
  <fct>       <fct>     <dbl>
1 Advertising Sales    0.270 
2 Population  Sales    0.0505
3 Price       Sales   -0.445 
4 Age         Sales   -0.232 
# … with 31 more rows

correlate() produces two pairs of variables. So the following example uses filter() to get the correlation coefficient for a pair of variable combinations:

carseats %>%
  correlate(Sales:Income) %>%
  filter(as.integer(var1) > as.integer(var2))
# A tibble: 3 x 3
  var1      var2      coef_corr
  <fct>     <fct>         <dbl>
1 CompPrice Sales        0.0641
2 Income    Sales        0.151 
3 Income    CompPrice   -0.0761

The correlate() also supports the group_by() function syntax in the dplyr package.

carseats %>%
  filter(ShelveLoc == "Good") %>%
  group_by(Urban, US) %>%
  correlate(Sales) %>%
  filter(abs(coef_corr) > 0.5)
# A tibble: 10 x 5
  Urban US    var1  var2       coef_corr
  <fct> <fct> <fct> <fct>          <dbl>
1 No    No    Sales Population    -0.530
2 No    No    Sales Price         -0.838
3 No    Yes   Sales Price         -0.630
4 Yes   No    Sales Price         -0.833
# … with 6 more rows

Visualization of the correlation matrix using plot_correlate()

plot_correlate() visualizes the correlation matrix.

plot_correlate(carseats)

plot_correlate() can also specify multiple variables, like the correlate() function. The following is a visualization of the correlation matrix including several selected variables.

# Select columns by name
plot_correlate(carseats, Sales, Price)

The plot_correlate() function also supports the group_by() function syntax in the dplyr package.

carseats %>%
  filter(ShelveLoc == "Good") %>%
  group_by(Urban) %>%
  plot_correlate(Sales)

EDA based on target variable

Definition of target variable

To perform EDA based on target variable, you need to create a target_by class object. target_by() creates a target_by class with an object inheriting data.frame or data.frame. target_by() is similar to group_by() in dplyr which creates grouped_df. The difference is that you specify only one variable.

The following is an example of specifying US as target variable in carseats data.frame.:

categ <- target_by(carseats, US)

EDA when target variable is categorical variable

Let’s perform EDA when the target variable is a categorical variable. When the categorical variable US is the target variable, we examine the relationship between the target variable and the predictor.

Cases where predictors are numeric variable

relate() shows the relationship between the target variable and the predictor. The following example shows the relationship between Sales and the target variable US. The predictor Sales is a numeric variable. In this case, the descriptive statistics are shown for each level of the target variable.

# If the variable of interest is a numerical variable
cat_num <- relate(categ, Sales)
cat_num
# A tibble: 3 x 27
  variable US        n    na  mean    sd se_mean   IQR skewness kurtosis   p00
  <chr>    <fct> <dbl> <dbl> <dbl> <dbl>   <dbl> <dbl>    <dbl>    <dbl> <dbl>
1 Sales    No      142     0  6.82  2.60   0.218  3.44   0.323    0.808   0   
2 Sales    Yes     258     0  7.87  2.88   0.179  4.23   0.0760  -0.326   0.37
3 Sales    total   400     0  7.50  2.82   0.141  3.93   0.186   -0.0809  0   
# … with 16 more variables: p01 <dbl>, p05 <dbl>, p10 <dbl>, p20 <dbl>,
#   p25 <dbl>, p30 <dbl>, p40 <dbl>, p50 <dbl>, p60 <dbl>, p70 <dbl>,
#   p75 <dbl>, p80 <dbl>, p90 <dbl>, p95 <dbl>, p99 <dbl>, p100 <dbl>
summary(cat_num)
   variable             US          n               na         mean      
 Length:3           No   :1   Min.   :142.0   Min.   :0   Min.   :6.823  
 Class :character   Yes  :1   1st Qu.:200.0   1st Qu.:0   1st Qu.:7.160  
 Mode  :character   total:1   Median :258.0   Median :0   Median :7.496  
                              Mean   :266.7   Mean   :0   Mean   :7.395  
                              3rd Qu.:329.0   3rd Qu.:0   3rd Qu.:7.682  
                              Max.   :400.0   Max.   :0   Max.   :7.867  
       sd           se_mean            IQR           skewness      
 Min.   :2.603   Min.   :0.1412   Min.   :3.442   Min.   :0.07603  
 1st Qu.:2.713   1st Qu.:0.1602   1st Qu.:3.686   1st Qu.:0.13080  
 Median :2.824   Median :0.1791   Median :3.930   Median :0.18556  
 Mean   :2.768   Mean   :0.1796   Mean   :3.866   Mean   :0.19489  
 3rd Qu.:2.851   3rd Qu.:0.1988   3rd Qu.:4.077   3rd Qu.:0.25432  
 Max.   :2.877   Max.   :0.2184   Max.   :4.225   Max.   :0.32308  
    kurtosis             p00              p01              p05       
 Min.   :-0.32638   Min.   :0.0000   Min.   :0.4675   Min.   :3.147  
 1st Qu.:-0.20363   1st Qu.:0.0000   1st Qu.:0.6868   1st Qu.:3.148  
 Median :-0.08088   Median :0.0000   Median :0.9062   Median :3.149  
 Mean   : 0.13350   Mean   :0.1233   Mean   :1.0072   Mean   :3.183  
 3rd Qu.: 0.36344   3rd Qu.:0.1850   3rd Qu.:1.2771   3rd Qu.:3.200  
 Max.   : 0.80776   Max.   :0.3700   Max.   :1.6480   Max.   :3.252  
      p10             p20             p25             p30       
 Min.   :3.917   Min.   :4.754   Min.   :5.080   Min.   :5.306  
 1st Qu.:4.018   1st Qu.:4.910   1st Qu.:5.235   1st Qu.:5.587  
 Median :4.119   Median :5.066   Median :5.390   Median :5.867  
 Mean   :4.073   Mean   :5.051   Mean   :5.411   Mean   :5.775  
 3rd Qu.:4.152   3rd Qu.:5.199   3rd Qu.:5.576   3rd Qu.:6.010  
 Max.   :4.184   Max.   :5.332   Max.   :5.763   Max.   :6.153  
      p40             p50             p60             p70       
 Min.   :5.994   Min.   :6.660   Min.   :7.496   Min.   :7.957  
 1st Qu.:6.301   1st Qu.:7.075   1st Qu.:7.787   1st Qu.:8.386  
 Median :6.608   Median :7.490   Median :8.078   Median :8.815  
 Mean   :6.506   Mean   :7.313   Mean   :8.076   Mean   :8.740  
 3rd Qu.:6.762   3rd Qu.:7.640   3rd Qu.:8.366   3rd Qu.:9.132  
 Max.   :6.916   Max.   :7.790   Max.   :8.654   Max.   :9.449  
      p75             p80              p90              p95       
 Min.   :8.523   Min.   : 8.772   Min.   : 9.349   Min.   :11.28  
 1st Qu.:8.921   1st Qu.: 9.265   1st Qu.:10.325   1st Qu.:11.86  
 Median :9.320   Median : 9.758   Median :11.300   Median :12.44  
 Mean   :9.277   Mean   : 9.665   Mean   :10.795   Mean   :12.08  
 3rd Qu.:9.654   3rd Qu.:10.111   3rd Qu.:11.518   3rd Qu.:12.49  
 Max.   :9.988   Max.   :10.464   Max.   :11.736   Max.   :12.54  
      p99             p100      
 Min.   :13.64   Min.   :14.90  
 1st Qu.:13.78   1st Qu.:15.59  
 Median :13.91   Median :16.27  
 Mean   :13.86   Mean   :15.81  
 3rd Qu.:13.97   3rd Qu.:16.27  
 Max.   :14.03   Max.   :16.27  

plot() visualizes the relate class object created by relate() as the relationship between the target variable and the predictor variable. The relationship between US and Sales is visualized by density plot.

plot(cat_num)

Cases where predictors are categorical variable

The following example shows the relationship between ShelveLoc and the target variable US. The predictor variable ShelveLoc is a categorical variable. In this case, it shows the contingency table of two variables. The summary() function performs independence test on the contingency table.

# If the variable of interest is a categorical variable
cat_cat <- relate(categ, ShelveLoc)
cat_cat
     ShelveLoc
US    Bad Good Medium
  No   34   24     84
  Yes  62   61    135
summary(cat_cat)
Call: xtabs(formula = formula_str, data = data, addNA = TRUE)
Number of cases in table: 400 
Number of factors: 2 
Test for independence of all factors:
    Chisq = 2.7397, df = 2, p-value = 0.2541

plot() visualizes the relationship between the target variable and the predictor. The relationship between US and ShelveLoc is represented by a mosaics plot.

plot(cat_cat)

EDA when target variable is numerical variable

Let’s perform EDA when the target variable is numeric. When the numeric variable Sales is the target variable, we examine the relationship between the target variable and the predictor.

# If the variable of interest is a numerical variable
num <- target_by(carseats, Sales)

Cases where predictors are numeric variable

The following example shows the relationship between Price and the target variable Sales. The predictor variable Price is a numeric variable. In this case, it shows the result of a simple linear model of the target ~ predictor formula. The summary() function expresses the details of the model.

# If the variable of interest is a numerical variable
num_num <- relate(num, Price)
num_num

Call:
lm(formula = formula_str, data = data)

Coefficients:
(Intercept)        Price  
   13.64192     -0.05307  
summary(num_num)

Call:
lm(formula = formula_str, data = data)

Residuals:
    Min      1Q  Median      3Q     Max 
-6.5224 -1.8442 -0.1459  1.6503  7.5108 

Coefficients:
             Estimate Std. Error t value Pr(>|t|)    
(Intercept) 13.641915   0.632812  21.558   <2e-16 ***
Price       -0.053073   0.005354  -9.912   <2e-16 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 2.532 on 398 degrees of freedom
Multiple R-squared:  0.198, Adjusted R-squared:  0.196 
F-statistic: 98.25 on 1 and 398 DF,  p-value: < 2.2e-16

plot() visualizes the relationship between the target and predictor variables. The relationship between Sales and Price is visualized with a scatter plot. The figure on the left shows the scatter plot of Sales and Price and the confidence interval of the regression line and regression line. The figure on the right shows the relationship between the original data and the predicted values of the linear model as a scatter plot. If there is a linear relationship between the two variables, the scatter plot of the observations converges on the red diagonal line.

plot(num_num)

The scatter plot of the data with a large number of observations is output as overlapping points. This makes it difficult to judge the relationship between the two variables. It also takes a long time to perform the visualization. In this case, the above problem can be solved by hexabin plot.

In plot(), the hex_thres argument provides a basis for drawing hexabin plot. If the number of observations is greater than hex_thres, draw a hexabin plot.

The following example visualizes the hexabin plot rather than the scatter plot by specifying 350 for the hex_thres argument. This is because the number of observations is 400.

plot(num_num, hex_thres = 350)

Cases where predictors are categorical variable

The following example shows the relationship between ShelveLoc and the target variable Sales. The predictor ShelveLoc is a categorical variable and shows the result of one-way ANOVA of target ~ predictor relationship. The results are expressed in terms of ANOVA. The summary() function shows the regression coefficients for each level of the predictor. In other words, it shows detailed information about simple regression analysis of target ~ predictor relationship.

# If the variable of interest is a categorical variable
num_cat <- relate(num, ShelveLoc)
num_cat
Analysis of Variance Table

Response: Sales
           Df Sum Sq Mean Sq F value    Pr(>F)    
ShelveLoc   2 1009.5  504.77   92.23 < 2.2e-16 ***
Residuals 397 2172.7    5.47                      
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
summary(num_cat)

Call:
lm(formula = formula(formula_str), data = data)

Residuals:
    Min      1Q  Median      3Q     Max 
-7.3066 -1.6282 -0.0416  1.5666  6.1471 

Coefficients:
                Estimate Std. Error t value Pr(>|t|)    
(Intercept)       5.5229     0.2388  23.131  < 2e-16 ***
ShelveLocGood     4.6911     0.3484  13.464  < 2e-16 ***
ShelveLocMedium   1.7837     0.2864   6.229  1.2e-09 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 2.339 on 397 degrees of freedom
Multiple R-squared:  0.3172,    Adjusted R-squared:  0.3138 
F-statistic: 92.23 on 2 and 397 DF,  p-value: < 2.2e-16

plot() visualizes the relationship between the target variable and the predictor. The relationship between Sales and ShelveLoc is represented by a box plot.

plot(num_cat)

Creating an EDA report using eda_report()

eda_report() performs EDA on all variables of the data frame or object (tbl_df,tbl, etc.) that inherits the data frame.

eda_report() creates an EDA report in two forms:

The contents of the report are as follows.:

The following example generates an EDA report for carseats. The file format is pdf, and the file name is EDA_Report.pdf.

carseats %>%
  eda_report(target = Sales)

The following example generates an HTML-formatted report named EDA_carseats.html.

carseats %>%
  eda_report(target = Sales, output_format = "html", output_file = "EDA_carseats.html")

The EDA report is an automated report to assist in the EDA process. Design the data analysis scenario with reference to the report results.

EDA report contents

Contents of pdf file

  • The cover of the report is shown in the following figure.
EDA report cover

EDA report cover

  • The report’s agenda is shown in the following figure.
EDA Report Contents

EDA Report Contents

  • Much information is represented in tables in the report. An example of the table is shown in the following figure.
Example EDA report table

Example EDA report table

  • In the EDA report, the normality test content includes visualization results. The result is shown in the following figure.