Question
For each question, as needed, submit the clean R code, the appropriate R output, and interpret the results. Do not submit R markdown files, instead submit clean R codes.

The dataset for this assignment “Pima Indians Diabetes Database” contains information on 768 patients (females), with variables X1 (= Number of times pregnant), X2 (= Plasma glucose concentration a 2 hours in an oral glucose tolerance test), X3 (= Diastolic blood pressure (mm Hg)), X4 (= Triceps skin fold thickness (mm)), X5 (= 2-Hour serum insulin (mu U/ml)), X6 (= Body mass index (weight in kg/(height in m)^2)), X7 (= Diabetes pedigree function), X8 (= Age (years)) as independent predictors, and Y = Class variable (0 or 1)

Data Set Information:
Several constraints were placed on the selection of these instances from a larger database. In particular, all patients here are females at least 21 years old of Pima Indian heritage. ADAP is an adaptive learning routine that generates and executes digital analogs of perceptron-like devices. It is a unique algorithm; see the paper for details.

Attribute Information:
X1 = Number of times pregnant
X2 = Plasma glucose concentration a 2 hours in an oral glucose tolerance test
X3 = Diastolic blood pressure (mm Hg) X4 = Triceps skin fold thickness (mm) X5 = 2-Hour serum insulin (mu U/ml)
X6 = Body mass index (weight in kg/(height in m)^2)
X7 = Diabetes pedigree function
X8 = Age (years)
Y = Class variable (0 or 1)

The diagnostic, binary-valued variable investigated is whether the patient shows signs of diabetes. Class Distribution: class value 1 is interpreted as "tested positive for diabetes", and class value 0 is interpreted as "tested negative for diabetes"

Your task is to develop a classification rule to predict whether a patient (female) shows signs of diabetes or not [y = 1(diabetes) , y = 0 (no diabetes))].

For undergraduate students: Only use the logistic regression technique.

For graduate students: Try all the techniques we have discussed in class. Which is best?

To verify and test your models’ performance, split the data into training (train.data) and test data (test.data) sets. Split 80% of the data for training and the remaining 20% for testing. You can use the following R codes to split the original dataset or use your own.

##### Split the data into 80% training and 20% testing data

n.train <- as.integer(nrow(pima.indians.diabetes)*0.80) n.train

##### Randomly choose the rows of the training example

train.id <- sample(1:nrow(pima.indians.diabetes), n.train) head(train.id)

##### Now Split the data

train.data <- pima.indians.diabetes[train.id,] train.data

test.data <- pima.indians.diabetes[-train.id, colnames(pima.indians.diabetes) != "y"] length(test.data[,1])
test.data
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# read data from csv file
diabetes = read.csv("pima-indians-diabetes-data.txt", header = F)

# set names to columns
names(diabetes) = c("X1","X2","X3","X4","X5","X6","X7","X8","Y")

# create model using all columns
model = glm(formula = Y ~ ., family = binomial(link = "logit"),
            data = diabetes)
summary(model)
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      • Illuminate\Cache\Events\CacheHit (186μs)
      • Illuminate\Cache\Events\CacheHit (163μs)
      • Illuminate\Cache\Events\CacheHit (179μs)
      • Illuminate\Cache\Events\CacheHit (158μs)
      • Illuminate\Cache\Events\CacheHit (192μs)
      • Illuminate\Cache\Events\CacheHit (180μs)
      • Illuminate\Cache\Events\CacheHit (196μs)
      • Illuminate\Cache\Events\CacheHit (164μs)
      • Illuminate\Cache\Events\CacheHit (188μs)
      • Illuminate\Cache\Events\CacheHit (160μs)
      • Illuminate\Cache\Events\CacheHit (187μs)
      • Illuminate\Cache\Events\CacheHit (152μs)
      • Illuminate\Cache\Events\CacheHit (191μs)
      • Illuminate\Cache\Events\CacheHit (163μs)
      • Illuminate\Cache\Events\CacheHit (131μs)
      • Illuminate\Cache\Events\CacheHit (266μs)
      • Illuminate\Cache\Events\CacheMissed (233μs)
      • Illuminate\Database\Events\StatementPrepared (631μs)
      • Illuminate\Database\Events\QueryExecuted (864μs)
      • eloquent.retrieved: App\Models\SubjectCat (86μs)
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      • Illuminate\Cache\Events\CacheHit (190μs)
      • Illuminate\Cache\Events\CacheHit (161μs)
      • Illuminate\Cache\Events\CacheHit (191μs)
      • Illuminate\Cache\Events\CacheHit (172μs)
      • Illuminate\Cache\Events\CacheHit (223μs)
      • Illuminate\Cache\Events\CacheHit (149μs)
      • Illuminate\Cache\Events\CacheHit (256μs)
      • Illuminate\Cache\Events\CacheHit (172μs)
      • Illuminate\Cache\Events\CacheHit (187μs)
      • Illuminate\Cache\Events\CacheHit (166μs)
      • Illuminate\Cache\Events\CacheHit (187μs)
      • Illuminate\Cache\Events\CacheHit (164μs)
      • Illuminate\Cache\Events\CacheHit (183μs)
      • Illuminate\Cache\Events\CacheHit (163μs)
      • Illuminate\Cache\Events\CacheHit (195μs)
      • Illuminate\Cache\Events\CacheHit (167μs)
      • creating: site.layouts.app (473μs)
      • composing: site.layouts.app (22μs)
      • creating: components.canonical (438μs)
      • composing: components.canonical (82μs)
      • creating: components.open-graph (168μs)
      • composing: components.open-graph (71μs)
      • creating: site.headers.header (249μs)
      • composing: site.headers.header (79μs)
      • Illuminate\Cache\Events\CacheHit (1.69ms)
      • creating: components.footer (72μs)
      • composing: components.footer (88μs)
      • Illuminate\Cache\Events\CacheHit (820μs)
      • Illuminate\Cache\Events\CacheMissed (275μs)
      • Illuminate\Database\Events\StatementPrepared (818μs)
      • Illuminate\Database\Events\QueryExecuted (1.01ms)
      • eloquent.retrieved: App\Models\SubjectCat (81μs)
      • Illuminate\Cache\Events\KeyWritten (1.59ms)
      • Illuminate\Cache\Events\CacheHit (303μs)
      • Illuminate\Cache\Events\CacheHit (167μs)
      • Illuminate\Cache\Events\CacheHit (311μs)
      • Illuminate\Cache\Events\CacheHit (175μs)
      • Illuminate\Cache\Events\CacheHit (172μs)
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      • Illuminate\Cache\Events\CacheHit (116μs)
      • Illuminate\Cache\Events\CacheHit (125μs)
      • Illuminate\Cache\Events\CacheHit (115μs)
      • creating: components.forms.contact-us (222μs)
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      • creating: components.forms.get-started (108μs)
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      • creating: components.forms.free-tool-download (70μs)
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      • creating: components.forms.claim-free-worksheet (69μs)
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      • 314 x Illuminate\Cache\Events\CacheHit (20.1%)
        76.85ms
        17 x Illuminate\Database\Events\StatementPrepared (10.15%)
        38.81ms
        17 x Illuminate\Database\Events\QueryExecuted (9.47%)
        36.21ms
        8 x Illuminate\Cache\Events\KeyWritten (1.29%)
        4.91ms
        1 x Illuminate\Foundation\Events\LocaleUpdated (1.25%)
        4.78ms
        8 x Illuminate\Cache\Events\CacheMissed (1.06%)
        4.05ms
        1 x Illuminate\Routing\Events\Routing (0.49%)
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        1 x Illuminate\Database\Events\ConnectionEstablished (0.26%)
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        9 x eloquent.retrieved: App\Models\SubjectCat (0.21%)
        808μs
        1 x Illuminate\Routing\Events\RouteMatched (0.14%)
        553μs
        1 x creating: site.layouts.app (0.12%)
        473μs
        1 x creating: components.breadcrumbs (0.12%)
        454μs
        1 x creating: components.canonical (0.11%)
        438μs
        1 x eloquent.booting: App\Models\SubjectCat (0.1%)
        383μs
        1 x eloquent.booted: App\Models\HomeworkLibrary\HomeworkLibrary (0.08%)
        304μs
        1 x eloquent.booting: App\Models\HomeworkLibrary\HomeworkLibraryFile (0.08%)
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        7 x eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibrary (0.07%)
        276μs
        1 x creating: homework.show (0.07%)
        270μs
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        249μs
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        240μs
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        222μs
        2 x eloquent.retrieved: App\Models\Subject (0.06%)
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        1 x eloquent.booting: App\Models\HomeworkLibrary\HomeworkLibrary (0.05%)
        183μs
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        1 x composing: homework.show (0.03%)
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        119μs
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        108μs
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        104μs
        1 x composing: components.footer (0.02%)
        88μs
        1 x composing: components.canonical (0.02%)
        82μs
        1 x composing: site.headers.header (0.02%)
        79μs
        1 x creating: components.footer (0.02%)
        72μs
        1 x composing: components.open-graph (0.02%)
        71μs
        1 x creating: components.forms.free-tool-download (0.02%)
        70μs
        1 x creating: components.forms.claim-free-worksheet (0.02%)
        69μs
        1 x creating: components.forms.tutor-subscription-join (0.02%)
        66μs
        1 x creating: components.forms.tutor-subscription-waitlist (0.02%)
        65μs
        1 x creating: components.forms.tutor-support (0.02%)
        65μs
        1 x composing: components.forms.free-tool-download (0.01%)
        54μs
        1 x composing: components.forms.get-started (0.01%)
        49μs
        1 x eloquent.booted: App\Models\HomeworkLibrary\HomeworkLibraryFile (0.01%)
        45μs
        1 x eloquent.booted: App\Models\SubjectCat (0.01%)
        44μs
        1 x eloquent.booted: App\Models\Subject (0.01%)
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        1 x composing: components.forms.claim-free-worksheet (0.01%)
        40μs
        1 x composing: components.forms.tutor-subscription-join (0.01%)
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        1 x composing: components.forms.tutor-support (0.01%)
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        1 x composing: components.forms.tutor-subscription-waitlist (0.01%)
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      14 templates were rendered
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      • 1x components.forms.tutor-supporttutor-support.blade.phpblade
      uri
      GET college-homework-library/{category}/{subject}/{id}
      middleware
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      controller
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      where
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      homework.show
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      • Connection Establishedtwenty4_siteHomeworkLibraryController.php#91
        Backtrace
        • 13. app/Http/Controllers/HomeworkLibraryController.php:91
        • 14. vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
        • 15. vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:43
        • 16. vendor/laravel/framework/src/Illuminate/Routing/Route.php:260
        • 17. vendor/laravel/framework/src/Illuminate/Routing/Route.php:205
      • select * from `solutionslibrary` where `status` = 'published' and `price` > 0 and `solutionslibrary`.`id` = '35962' limit 1
        24.63mstwenty4_siteHomeworkLibraryController.php#97
        Bindings
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        • 1: 0
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        Backtrace
        • 16. app/Http/Controllers/HomeworkLibraryController.php:97
        • 17. vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
        • 18. vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:43
        • 19. vendor/laravel/framework/src/Illuminate/Routing/Route.php:260
        • 20. vendor/laravel/framework/src/Illuminate/Routing/Route.php:205
      • select * from `subjects` where `subjects`.`id` in (299)
        1.13mstwenty4_siteHomeworkLibraryController.php#97
        Backtrace
        • 21. app/Http/Controllers/HomeworkLibraryController.php:97
        • 22. vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
        • 23. vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:43
        • 24. vendor/laravel/framework/src/Illuminate/Routing/Route.php:260
        • 25. vendor/laravel/framework/src/Illuminate/Routing/Route.php:205
      • select * from `solutionslibrary_files` where `solutionslibrary_files`.`solutionlib_id` in (35962)
        6.05mstwenty4_siteHomeworkLibraryController.php#97
        Backtrace
        • 21. app/Http/Controllers/HomeworkLibraryController.php:97
        • 22. vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
        • 23. vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:43
        • 24. vendor/laravel/framework/src/Illuminate/Routing/Route.php:260
        • 25. vendor/laravel/framework/src/Illuminate/Routing/Route.php:205
      • select * from `subject_cats` where `subject_cats`.`id` = 1 limit 1
        1mstwenty4_siteHomeworkLibrary.php#201
        Bindings
        • 0: 1
        Backtrace
        • 20. app/Models/HomeworkLibrary/HomeworkLibrary.php:201
        • 26. app/Http/Controllers/HomeworkLibraryController.php:105
        • 27. vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
        • 28. vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:43
        • 29. vendor/laravel/framework/src/Illuminate/Routing/Route.php:260
      • select * from `solutionslibrary` where `id` <> 35962 and `subject` = 299 and `status` = 'published' and `price` > 0 order by RAND() limit 6
        13.6mstwenty4_siteHomeworkLibraryRepository.php#30
        Bindings
        • 0: 35962
        • 1: 299
        • 2: published
        • 3: 0
        Backtrace
        • 14. app/Repositories/HomeworkLibraryRepository.php:30
        • 15. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397
        • 16. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419
        • 18. app/Repositories/HomeworkLibraryRepository.php:39
        • 19. app/Http/Controllers/HomeworkLibraryController.php:139
      • select * from `subjects` where `subjects`.`id` in (299)
        940μstwenty4_siteHomeworkLibraryRepository.php#30
        Backtrace
        • 19. app/Repositories/HomeworkLibraryRepository.php:30
        • 20. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397
        • 21. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419
        • 23. app/Repositories/HomeworkLibraryRepository.php:39
        • 24. app/Http/Controllers/HomeworkLibraryController.php:139
      • select * from `solutionslibrary_files` where `solutionslibrary_files`.`solutionlib_id` = 35962 and `solutionslibrary_files`.`solutionlib_id` is not null and `publish` = 'question' order by `order` asc, `id` asc
        1.21mstwenty4_siteHomeworkLibrary.php#260
        Bindings
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        Backtrace
        • 15. app/Models/HomeworkLibrary/HomeworkLibrary.php:260
        • 16. app/Transformers/HomeworkLibrary/HomeworkLibraryTransformer.php:58
        • 19. vendor/league/fractal/src/TransformerAbstract.php:128
        • 20. vendor/league/fractal/src/TransformerAbstract.php:107
        • 21. vendor/league/fractal/src/Scope.php:383
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        1.13mstwenty4_siteHomeworkLibrary.php#260
        Bindings
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        Backtrace
        • 15. app/Models/HomeworkLibrary/HomeworkLibrary.php:260
        • 16. app/Transformers/HomeworkLibrary/HomeworkLibraryTransformer.php:69
        • 19. vendor/league/fractal/src/TransformerAbstract.php:128
        • 20. vendor/league/fractal/src/TransformerAbstract.php:107
        • 21. vendor/league/fractal/src/Scope.php:383
      • select * from `solutionslibrary_files` where `solutionslibrary_files`.`solutionlib_id` = 35962 and `solutionslibrary_files`.`solutionlib_id` is not null and `publish` = 'solution' order by `order` asc, `id` asc
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        Bindings
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        Backtrace
        • 15. app/Models/HomeworkLibrary/HomeworkLibrary.php:260
        • 16. app/Transformers/HomeworkLibrary/HomeworkLibraryTransformer.php:80
        • 19. vendor/league/fractal/src/TransformerAbstract.php:128
        • 20. vendor/league/fractal/src/TransformerAbstract.php:107
        • 21. vendor/league/fractal/src/Scope.php:383
      • select * from `subject_cats` where `subject_cats`.`id` = 1 limit 1
        1.05mstwenty4_siteHomeworkLibrary.php#201
        Bindings
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        Backtrace
        • 20. app/Models/HomeworkLibrary/HomeworkLibrary.php:201
        • 32. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
        • 33. vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
        • 34. vendor/livewire/livewire/src/ComponentConcerns/RendersLivewireComponents.php:69
        • 35. vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:70
      • select * from `subject_cats` where `subject_cats`.`id` = 10 limit 1
        1.7mstwenty4_siteSubject.php#100
        Bindings
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        Backtrace
        • 18. app/Models/Subject.php:100
        • 19. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397
        • 20. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419
        • 22. app/Models/Subject.php:101
        • 34. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
      • select * from `subject_cats` where `subject_cats`.`id` = 33 limit 1
        1.95mstwenty4_siteSubject.php#100
        Bindings
        • 0: 33
        Backtrace
        • 18. app/Models/Subject.php:100
        • 19. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397
        • 20. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419
        • 22. app/Models/Subject.php:101
        • 34. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
      • select * from `subject_cats` where `subject_cats`.`id` = 11 limit 1
        1.13mstwenty4_siteSubject.php#100
        Bindings
        • 0: 11
        Backtrace
        • 18. app/Models/Subject.php:100
        • 19. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397
        • 20. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419
        • 22. app/Models/Subject.php:101
        • 34. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
      • select * from `subject_cats` where `subject_cats`.`id` = 5 limit 1
        1.05mstwenty4_siteSubject.php#100
        Bindings
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        Backtrace
        • 18. app/Models/Subject.php:100
        • 19. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397
        • 20. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419
        • 22. app/Models/Subject.php:101
        • 34. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
      • select * from `subject_cats` where `subject_cats`.`id` = 34 limit 1
        1.1mstwenty4_siteSubject.php#100
        Bindings
        • 0: 34
        Backtrace
        • 18. app/Models/Subject.php:100
        • 19. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397
        • 20. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419
        • 22. app/Models/Subject.php:101
        • 34. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
      • select * from `subject_cats` where `subject_cats`.`id` = 31 limit 1
        990μstwenty4_siteSubject.php#100
        Bindings
        • 0: 31
        Backtrace
        • 18. app/Models/Subject.php:100
        • 19. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397
        • 20. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419
        • 22. app/Models/Subject.php:101
        • 34. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
      • select * from `subject_cats` where `subject_cats`.`id` = 36 limit 1
        1.3mstwenty4_siteSubject.php#100
        Bindings
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        Backtrace
        • 18. app/Models/Subject.php:100
        • 19. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397
        • 20. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419
        • 22. app/Models/Subject.php:101
        • 28. view::components.footer:170
      App\Models\HomeworkLibrary\HomeworkLibraryFile
      10HomeworkLibraryFile.php
      App\Models\SubjectCat
      9SubjectCat.php
      App\Models\HomeworkLibrary\HomeworkLibrary
      7HomeworkLibrary.php
      App\Models\Subject
      2Subject.php
          _token
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          status_text
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