DS7310 Assignment 4

Author

Ariel Ganoe

Assignment Guideline (20 Points)

  1. Create a folder for this project and call it as DS7310_Assignment4_YourFullName.

  2. Create a project file in the folder.

  3. Change the name of author in YAML.

  4. Save this file as you lastname_firstname_Assignment4.qmd

  5. Add a table of content

  6. Add your code to the R code chunkes.

  7. Compress (zip) the DS7310_Assignment4_YourFullName folder.

  8. After upload the compress folder, download it, and make sure it is the correct one.

Question 1 (50 points)

  • Import the Data_Health_Ass4, remove incomplete rows, and create an interactive table for that.
library(readxl)
library(dplyr)
library(DT)

setwd("C:/Users/ajgan/downloads")

Data_Health_Ass4 <- read_excel("Data_Health_Ass4.xlsx")

# Remove incomplete rows
Data_Health_Ass4_clean <- Data_Health_Ass4 %>% 
  na.omit()

# Interactive table
datatable(Data_Health_Ass4_clean,
          options = list(pagelength = 10,
                         scrollX = TRUE))
  • Create an interactive histogram for Stroke variable.
#create an interactive histogram
library(ggplot2)

ggplot(
  data = Data_Health_Ass4_clean,
  aes(x = Stroke))+
  geom_histogram(fill = "red", color = "white", bins = 30) +
    labs(title = "Histogram of Stroke Rates",
         x = "Stroke Rate",
         y = "Count")

  • Get a subset of data for “Stroke”,“BloodPressure”,“Depression”, and “HighCholesterol,”

  • Make stroke prediction models based on different combinations of selecting 2 or 3 variables from BloodPressure, Depression, and HighCholesterol. Call each model from 1 to 4, like Model1, Model3, Model3, and Model4.

  • Make sure to use as.numeric for the variables, like as.numeric(Stroke), to convert the four variables to a numeric data, such as Data_Health_Ass4_subset$Stroke <- as.numeric(Data_Health_Ass4_subset$Stroke)

#create subset: "Stroke, blood pressure, depression  and high cholesterol
Data_Health_Ass4_subset <- Data_Health_Ass4_clean %>%
select(Stroke, BloodPressure, Depression, HighCholesterol)

#as.numeric for variables
Data_Health_Ass4_subset <- Data_Health_Ass4_subset %>%
  mutate(
    Stroke = as.numeric(Stroke),
    BloodPressure = as.numeric(BloodPressure),
    Depression = as.numeric(Depression),
    HighCholesterol = as.numeric(HighCholesterol))

#model 1:
model1 <- lm(Stroke ~ BloodPressure + Depression, data = Data_Health_Ass4_subset)
summary(model1)

Call:
lm(formula = Stroke ~ BloodPressure + Depression, data = Data_Health_Ass4_subset)

Residuals:
    Min      1Q  Median      3Q     Max 
-1.4076 -0.3004 -0.0246  0.2566  3.2568 

Coefficients:
               Estimate Std. Error t value Pr(>|t|)    
(Intercept)   -1.097974   0.083547 -13.142   <2e-16 ***
BloodPressure  0.143544   0.001607  89.342   <2e-16 ***
Depression    -0.003436   0.002960  -1.161    0.246    
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 0.4498 on 2476 degrees of freedom
Multiple R-squared:  0.7696,    Adjusted R-squared:  0.7694 
F-statistic:  4135 on 2 and 2476 DF,  p-value: < 2.2e-16
#model 2:
model2 <- lm(Stroke ~ BloodPressure + HighCholesterol, data = Data_Health_Ass4_subset)
summary(model2)

Call:
lm(formula = Stroke ~ BloodPressure + HighCholesterol, data = Data_Health_Ass4_subset)

Residuals:
    Min      1Q  Median      3Q     Max 
-1.3969 -0.2976 -0.0283  0.2517  3.2461 

Coefficients:
                 Estimate Std. Error t value Pr(>|t|)    
(Intercept)     -1.103410   0.107445 -10.269   <2e-16 ***
BloodPressure    0.144481   0.002450  58.982   <2e-16 ***
HighCholesterol -0.003030   0.004347  -0.697    0.486    
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 0.4499 on 2476 degrees of freedom
Multiple R-squared:  0.7695,    Adjusted R-squared:  0.7693 
F-statistic:  4133 on 2 and 2476 DF,  p-value: < 2.2e-16
#model 3:
model3 <- lm(Stroke ~ Depression + HighCholesterol, data = Data_Health_Ass4_subset)
summary(model3)

Call:
lm(formula = Stroke ~ Depression + HighCholesterol, data = Data_Health_Ass4_subset)

Residuals:
    Min      1Q  Median      3Q     Max 
-2.0490 -0.4289 -0.0697  0.3168  3.7800 

Coefficients:
                 Estimate Std. Error t value Pr(>|t|)    
(Intercept)     -3.089804   0.177777 -17.380  < 2e-16 ***
Depression       0.011876   0.004575   2.596  0.00949 ** 
HighCholesterol  0.191201   0.004407  43.390  < 2e-16 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 0.6968 on 2476 degrees of freedom
Multiple R-squared:  0.4471,    Adjusted R-squared:  0.4467 
F-statistic:  1001 on 2 and 2476 DF,  p-value: < 2.2e-16
#model 4:
model4 <- lm(Stroke ~ BloodPressure + Depression + HighCholesterol, data = Data_Health_Ass4_subset)
summary(model4)

Call:
lm(formula = Stroke ~ BloodPressure + Depression + HighCholesterol, 
    data = Data_Health_Ass4_subset)

Residuals:
    Min      1Q  Median      3Q     Max 
-1.4133 -0.2995 -0.0251  0.2525  3.2495 

Coefficients:
                 Estimate Std. Error t value Pr(>|t|)    
(Intercept)     -1.043555   0.119934  -8.701   <2e-16 ***
BloodPressure    0.144722   0.002459  58.858   <2e-16 ***
Depression      -0.003330   0.002965  -1.123    0.262    
HighCholesterol -0.002754   0.004354  -0.633    0.527    
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 0.4499 on 2475 degrees of freedom
Multiple R-squared:  0.7696,    Adjusted R-squared:  0.7693 
F-statistic:  2756 on 3 and 2475 DF,  p-value: < 2.2e-16

  • Report the evaluation results of the four combinations in a table, with three columns of of Model variables (e.g., BloodPressure + Depression), model number from 1 to 4, and adjusted RSquared.

  • Show the report_lm_results with knitr::kable.

  • First create the empty table using the following code. Add your code to the following code.

report_lm_results <- data.frame(
  Variables = character(),
  Model = integer(),
  Adj_R_squared = numeric(),
  stringsAsFactors = FALSE
)

#Example: report_lm_results[1,1] <- "BloodPressure + Depression"
# report_lm_results[1,2] <- 1
# report_lm_results[1,3] <- summary(Model1)$adj.r.squared

#fill in the results for each model
#model_1
report_lm_results[1,1] <- "BloodPressure + Pressure"
report_lm_results[1,2] <- 1 
report_lm_results[1,3] <- summary(model1)$adj.r.squared

#model_2
report_lm_results[2,1] <- "BloodPressure + HighCholesterol"
report_lm_results[2,2] <- 2
report_lm_results[2,3] <- summary(model2)$adj.r.squared

#model_3
report_lm_results[3,1] <- "Depression + HighCholesterol"
report_lm_results[3,2] <- 3
report_lm_results[3,3] <- summary(model3)$adj.r.squared

#model_4
report_lm_results[4,1] <- "BloodPressure + Depression + HighCholesterol"
report_lm_results[4,2] <- 4
report_lm_results[4,3] <- summary(model4)$adj.r.squared

#results
knitr:: kable(report_lm_results)
Variables Model Adj_R_squared
BloodPressure + Pressure 1 0.7693899
BloodPressure + HighCholesterol 2 0.7693097
Depression + HighCholesterol 3 0.4466909
BloodPressure + Depression + HighCholesterol 4 0.7693340
  • Find the summary of the best model.
models <- list(
  model1 = model1,
  model2 = model2,
  model3 = model3,
  model4 = model4
)

adj_r2_values <- sapply(models, function(m) summary(m)$adj.r.squared)
adj_r2_values
   model1    model2    model3    model4 
0.7693899 0.7693097 0.4466909 0.7693340 
best_model <- names(which.max(adj_r2_values))
best_model
[1] "model1"
summary(models[[best_model]])

Call:
lm(formula = Stroke ~ BloodPressure + Depression, data = Data_Health_Ass4_subset)

Residuals:
    Min      1Q  Median      3Q     Max 
-1.4076 -0.3004 -0.0246  0.2566  3.2568 

Coefficients:
               Estimate Std. Error t value Pr(>|t|)    
(Intercept)   -1.097974   0.083547 -13.142   <2e-16 ***
BloodPressure  0.143544   0.001607  89.342   <2e-16 ***
Depression    -0.003436   0.002960  -1.161    0.246    
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 0.4498 on 2476 degrees of freedom
Multiple R-squared:  0.7696,    Adjusted R-squared:  0.7694 
F-statistic:  4135 on 2 and 2476 DF,  p-value: < 2.2e-16

  • Write the regression formula for the best model in bold format.

Type the formula here:

Stroke ~ Blood Pressure + Depression + High Cholesterol

Stroke = \(\beta_0\) + \(\beta_1\)(BloodPressure) + \(\beta_2\)(Depression) + \(\beta_3\)(highCholesterol) + \(\epsilon\)

Question 2 (30 points)

  • Cluster the data using k-means.

  • Select the best estimate number of clusters other than min.nc and max.nc.

set.seed(123)

#cluster the data
data_kmeans <- Data_Health_Ass4_subset

#scale the data
scaled_data <- scale(data_kmeans)

#Try k = 2 to 5 
set.seed(123)
wss <- sapply(2:5, function(k) {
  kmeans(scaled_data, centers = k, nstart = 25)$tot.withinss})
best_k <- which.min(wss) + 1
best_k
[1] 5
set.seed(123)
kmeans_results <- kmeans(scaled_data, centers = best_k, nstart = 25)
kmeans_results
K-means clustering with 5 clusters of sizes 854, 417, 349, 437, 422

Cluster means:
       Stroke BloodPressure  Depression HighCholesterol
1 -0.07891134    -0.0120943  0.07622062       0.1274650
2 -1.02793486    -1.2096735  0.18460734      -1.4544704
3  1.50488683     1.4175571 -0.58091886       0.8902141
4 -0.76757364    -0.7793328 -1.18769930      -0.4591696
5  0.72574243     0.8545104  1.37367678       0.9185577

Clustering vector:
   [1] 1 1 3 5 5 3 3 1 3 5 1 3 3 5 5 1 1 3 3 5 5 5 5 3 5 1 3 5 5 5 5 3 3 3 1 5 1
  [38] 5 1 5 2 1 3 3 1 3 5 1 1 3 1 5 3 3 1 5 3 1 4 3 3 3 1 5 3 3 5 3 1 2 1 2 2 3
  [75] 4 3 1 2 1 4 1 4 5 3 5 2 5 3 1 5 3 2 5 5 5 1 5 1 5 5 5 3 5 2 5 5 5 1 5 5 5
 [112] 1 5 5 5 3 5 3 5 3 1 5 5 1 5 5 5 5 3 3 5 3 5 3 5 5 5 5 5 1 5 3 1 5 5 1 5 5
 [149] 1 5 2 5 3 5 4 1 2 1 4 4 1 4 2 1 1 4 4 4 2 1 2 4 2 4 3 1 2 2 4 4 1 4 4 1 4
 [186] 2 2 2 2 4 4 2 4 2 4 2 1 1 4 4 2 4 1 3 4 1 4 2 2 2 2 2 4 2 2 4 2 4 3 2 1 2
 [223] 2 2 2 2 4 2 2 2 2 1 2 4 2 2 2 1 2 2 2 2 1 4 2 1 4 2 2 4 4 2 1 2 2 4 2 2 4
 [260] 4 4 2 2 4 2 2 4 4 4 3 2 3 3 5 3 1 1 4 4 3 3 3 1 5 3 2 2 3 1 3 1 3 4 1 3 4
 [297] 2 3 1 2 3 4 3 4 3 1 4 3 4 3 3 1 1 3 4 3 3 3 4 3 1 4 3 3 3 3 4 1 4 1 4 3 1
 [334] 1 1 3 3 4 1 1 3 1 1 3 1 4 4 3 1 1 5 3 3 3 1 1 3 3 4 2 3 4 4 1 3 3 3 1 3 3
 [371] 3 3 1 3 1 1 1 1 4 1 4 1 1 1 1 1 3 3 3 3 3 1 1 1 3 3 1 1 4 3 3 1 3 3 3 3 1
 [408] 1 3 3 1 3 3 3 3 1 1 3 3 3 3 3 1 1 3 3 3 3 4 4 4 2 2 2 1 2 4 2 1 2 4 2 2 2
 [445] 4 3 1 4 4 1 4 4 4 2 4 4 4 2 4 4 1 2 4 4 1 4 4 1 1 4 4 1 2 1 4 1 4 4 4 2 1
 [482] 4 4 1 1 4 4 2 4 2 4 1 4 1 1 4 1 4 1 1 1 4 1 4 3 1 4 4 1 4 1 4 1 1 1 4 4 4
 [519] 4 1 2 2 1 2 1 1 1 2 1 1 5 1 1 1 2 1 1 2 5 1 1 1 1 1 1 1 2 2 1 2 1 1 1 1 1
 [556] 1 1 1 2 1 2 1 4 1 1 1 2 1 1 1 2 1 1 1 1 1 1 1 1 1 4 1 1 1 1 1 2 1 1 1 1 1
 [593] 1 2 1 1 1 1 1 4 1 1 1 1 1 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4
 [630] 4 4 4 4 4 4 4 4 4 4 4 4 2 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 2 4 4
 [667] 4 4 4 4 4 4 4 1 1 1 4 1 1 4 3 1 1 4 4 1 2 4 3 4 4 4 2 4 1 4 4 1 4 1 4 4 1
 [704] 1 4 3 1 4 4 1 4 2 1 4 4 1 4 4 5 5 1 5 5 5 2 5 5 1 5 5 5 1 5 5 1 2 5 5 5 2
 [741] 1 5 5 5 1 5 5 2 5 5 1 5 1 5 5 5 5 1 1 5 1 5 1 5 5 5 1 1 5 1 5 5 5 5 5 5 5
 [778] 5 1 5 5 5 2 5 5 5 5 5 1 5 1 5 5 5 1 5 2 5 5 5 5 5 5 5 2 5 2 1 1 1 1 5 5 5
 [815] 2 5 5 5 5 1 5 5 1 5 5 5 3 1 3 5 5 5 3 5 5 1 3 1 5 5 5 5 5 5 5 5 1 5 1 2 1
 [852] 3 3 5 1 1 1 5 5 5 5 5 5 1 3 5 3 5 5 5 5 5 5 5 5 2 5 5 1 5 1 5 1 5 1 1 1 1
 [889] 1 1 1 1 5 1 5 1 5 1 1 4 4 4 1 4 1 4 3 4 1 4 4 1 4 4 4 4 1 1 1 1 3 2 1 1 1
 [926] 4 4 2 1 2 2 2 4 4 2 2 3 1 1 1 1 5 1 1 1 1 1 1 1 1 1 5 1 5 2 5 1 1 1 1 1 5
 [963] 5 2 2 1 2 1 2 2 5 3 2 1 2 5 2 3 1 1 1 1 3 3 1 1 2 1 1 1 4 1 1 1 3 1 1 4 1
[1000] 5 5 3 1 2 3 1 1 1 1 1 1 1 2 1 1 1 2 1 2 2 2 2 2 2 1 2 2 1 1 2 2 2 2 1 1 1
[1037] 2 1 2 2 1 2 1 2 1 2 1 2 1 2 2 1 2 2 1 2 2 2 2 2 1 2 1 1 1 1 2 2 1 2 2 2 2
[1074] 2 2 2 1 1 2 1 2 2 2 2 2 3 1 3 3 3 3 3 3 3 3 3 3 3 3 3 3 4 4 3 1 1 3 3 1 3
[1111] 3 3 1 1 3 3 3 3 3 2 4 3 3 3 1 3 3 3 4 3 3 3 3 3 3 3 2 3 1 3 3 1 1 3 4 3 3
[1148] 3 1 3 3 1 1 1 3 1 3 3 3 3 1 3 3 3 3 2 1 1 1 5 1 3 5 2 1 1 1 1 1 2 1 5 1 3
[1185] 1 1 5 4 1 1 1 5 3 5 5 5 3 5 1 1 1 2 1 3 1 3 1 5 1 4 1 1 2 1 1 1 1 1 1 1 1
[1222] 1 1 1 1 3 1 3 1 3 3 1 2 3 3 3 1 1 1 4 1 2 1 1 2 3 1 1 4 1 1 1 3 1 1 3 1 1
[1259] 1 3 1 5 2 2 1 1 1 4 2 2 2 1 4 2 2 2 1 2 1 4 2 2 2 2 3 2 4 2 4 4 4 4 4 4 4
[1296] 4 4 4 4 4 1 4 4 4 4 1 1 1 3 4 4 4 4 2 1 2 1 2 2 2 2 2 2 4 4 4 4 4 4 4 4 4
[1333] 4 4 4 4 4 4 4 4 4 4 4 4 4 1 1 1 2 4 2 1 4 2 3 3 1 3 2 3 4 2 2 1 4 4 3 1 4
[1370] 1 4 4 1 4 4 1 1 1 1 1 2 4 2 1 4 4 1 1 1 4 4 4 2 4 1 2 1 2 1 4 4 1 4 2 2 4
[1407] 1 2 2 4 4 4 4 4 4 2 4 1 1 1 4 4 4 2 4 1 1 1 4 4 1 1 1 3 3 1 1 3 3 3 3 4 1
[1444] 4 1 1 1 3 1 1 3 3 3 1 3 1 2 1 1 1 1 3 2 3 1 1 1 3 1 1 2 3 2 1 1 3 2 3 1 1
[1481] 2 3 1 3 1 1 3 1 3 2 1 3 4 1 1 3 2 2 3 1 1 3 3 2 3 1 3 3 1 1 5 3 3 1 1 5 1
[1518] 1 4 3 4 3 3 2 1 5 3 1 3 4 4 4 2 4 2 2 2 4 4 4 2 4 1 2 2 5 1 1 5 2 2 1 1 2
[1555] 5 1 1 2 1 1 5 5 1 1 1 4 1 2 5 2 1 5 1 2 5 2 2 1 1 1 5 5 1 1 5 1 2 1 5 1 1
[1592] 1 1 1 1 1 2 5 1 1 5 1 5 1 1 3 1 1 1 1 5 2 1 1 1 1 1 5 1 1 1 1 5 1 2 1 5 2
[1629] 5 1 1 2 1 5 1 5 5 5 5 5 2 5 5 5 2 1 5 5 2 5 1 5 1 1 5 5 1 5 5 1 5 5 5 1 1
[1666] 1 5 5 5 5 5 5 5 5 5 1 5 5 5 5 2 5 5 5 5 2 5 5 5 1 1 1 5 5 2 1 1 2 2 2 2 1
[1703] 1 3 2 1 1 2 2 2 1 1 1 2 1 2 2 2 2 2 2 1 2 2 2 2 2 1 2 1 1 1 2 1 1 2 2 1 1
[1740] 2 4 1 1 2 2 1 2 2 4 1 1 1 1 1 1 1 1 1 1 2 2 1 1 2 2 1 1 1 1 4 4 1 4 1 1 2
[1777] 1 1 1 1 1 1 1 2 1 1 2 1 4 1 2 4 4 4 2 4 3 1 3 1 3 3 4 4 3 4 1 1 3 3 3 3 3
[1814] 4 3 3 1 3 4 1 3 1 3 1 1 1 3 4 3 3 3 1 3 3 2 4 3 1 1 3 3 4 4 4 2 4 4 2 4 3
[1851] 4 4 4 3 4 4 4 4 3 4 3 4 4 5 5 5 5 5 5 5 5 5 5 1 5 5 5 5 5 5 2 5 5 5 5 5 5
[1888] 5 5 5 5 5 5 5 1 5 5 5 5 5 5 5 5 5 5 5 1 5 5 5 5 5 5 5 5 5 5 5 5 1 5 5 2 5
[1925] 5 5 5 5 5 5 5 1 2 5 5 5 1 5 5 1 5 2 5 5 5 5 5 5 5 5 2 1 1 2 1 3 4 1 4 3 1
[1962] 4 2 2 1 4 3 1 4 2 1 1 1 1 1 1 4 1 4 1 5 4 2 1 4 1 3 4 1 1 3 3 1 2 1 1 4 1
[1999] 1 1 4 1 3 1 1 1 2 4 4 2 1 1 1 1 4 1 1 4 2 2 4 1 1 1 1 1 1 1 4 1 5 1 4 1 1
[2036] 2 5 1 1 1 1 1 3 4 4 1 1 1 1 5 1 3 1 4 1 4 2 4 3 1 4 1 1 1 4 1 1 3 1 3 1 3
[2073] 2 1 1 4 3 1 4 4 2 1 4 1 2 1 3 1 1 3 1 1 4 1 1 1 4 1 4 1 1 3 5 2 3 4 1 4 1
[2110] 1 3 3 3 1 1 1 1 5 1 1 1 1 1 4 2 1 1 1 2 3 1 1 4 4 5 1 1 2 1 1 4 1 1 1 1 4
[2147] 4 4 1 3 4 1 1 1 2 2 1 2 2 1 2 1 2 2 2 1 2 2 2 2 2 4 2 2 2 2 2 2 2 2 2 2 2
[2184] 2 3 4 5 3 1 5 2 1 1 1 1 3 5 3 1 1 5 3 3 4 1 1 3 5 1 3 4 4 1 1 3 1 1 1 1 5
[2221] 1 3 3 1 1 3 1 4 3 4 1 3 5 4 1 3 1 3 3 3 2 5 4 3 3 3 1 5 3 3 1 2 2 4 5 1 3
[2258] 1 1 1 5 5 1 5 3 1 4 3 3 5 1 5 3 5 5 4 2 5 2 2 1 5 3 3 4 4 3 2 5 1 2 5 2 4
[2295] 4 3 1 2 3 4 1 2 2 1 1 1 1 4 1 2 1 2 1 2 2 1 2 2 2 5 2 2 5 1 1 2 2 2 1 1 1
[2332] 1 5 5 1 2 1 2 1 2 2 1 2 2 2 2 2 5 1 5 5 5 5 5 5 5 1 5 5 5 5 5 5 5 1 5 5 5
[2369] 5 5 5 5 5 5 5 2 5 5 5 1 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 3 1 1 1 2 1 4 4
[2406] 1 2 1 2 1 1 2 2 2 1 1 2 1 1 4 3 1 2 1 2 1 2 1 1 1 1 1 1 1 1 2 4 1 1 2 4 2
[2443] 1 2 4 1 2 2 1 1 1 4 1 4 1 3 4 1 4 4 1 1 2 1 2 4 2 4 4 4 4 2 4 2 4 4 2 2 2

Within cluster sum of squares by cluster:
[1] 867.4192 572.0308 649.0868 518.2114 533.5076
 (between_SS / total_SS =  68.3 %)

Available components:

[1] "cluster"      "centers"      "totss"        "withinss"     "tot.withinss"
[6] "betweenss"    "size"         "iter"         "ifault"      
Data_Health_Ass4_subset$cluster <- kmeans_results$cluster

table(Data_Health_Ass4_subset$cluster)

  1   2   3   4   5 
854 417 349 437 422 
kmeans_results$centers
       Stroke BloodPressure  Depression HighCholesterol
1 -0.07891134    -0.0120943  0.07622062       0.1274650
2 -1.02793486    -1.2096735  0.18460734      -1.4544704
3  1.50488683     1.4175571 -0.58091886       0.8902141
4 -0.76757364    -0.7793328 -1.18769930      -0.4591696
5  0.72574243     0.8545104  1.37367678       0.9185577
  • Run the model with the best estimate number number of clusters.
#Type your code here
  • Show the average summary of variables in each cluster.
#Type your code here
  • Show the states in the healthiest cluster.
#Type your code here