Question
Problem 1.

Consider the built-in diamonds dataset, A data frame with 53940 rows and 10 variables:

price: price in US dollars (\$326–\$18,823) carat: weight of the diamond (0.2–5.01)
cut: quality of the cut (Fair, Good, Very Good, Premium, Ideal) color: diamond colour, from D (best) to J (worst)
clarity: a measurement of how clear the diamond is (I1 (worst), SI2, SI1, VS2, VS1, VVS2, VVS1, IF (best))
X:lengthinmm(0–10.74) Y: width in mm (0–58.9) Z: depth in mm (0–31.8)
depth: total depth percentage = z / mean(x, y) = 2 * z / (x + y) (43–79) table: width of top of diamond relative to widest point (43–95)

1. Summarize the data appropriately graphically and numerically and comment on that.

2. Fit a linear regression model to model price as a function of the given predictors

3. Briefly describe the steps of each of the following cross validation techniques:

The Validation set Approach, Leave one out cross validation – LOOCV, K-fold cross- validation, Repeated K-fold cross-validation

4. Use all the cross validation techniques mentioned above and discussed in class to validate your model and discuss your results.

Problem 2.

Consider the dataset plasma found in the "HSAUR", where plasma is a data frame with 32 observations on the following 3 variables.

fibrinogen: the fibrinogen level in the blood.
globulin: the globulin level in the blood.
ESR: the erythrocyte sedimentation rate, either less or greater 20 mm / hour.

The erythrocyte sedimentation rate (ESR) is the rate at which red blood cells (erythrocytes) settle out of suspension in blood plasma, when measured under standard conditions. If the ESR increases when the level of certain proteins in the blood plasma rise in association with conditions such as rheumatic diseases, chronic infections and malignant diseases, its determination might be useful in screening blood samples taken form people suspected to being suffering from one of the conditions mentioned. The absolute value of the ESR is not of great importance rather it is whether it is less than 20mm/hr since lower values indicate a healthy individual. Source: D. Collett and A. A. Jemain (1985), Residuals, outliers and influential observations in regression analysis. Sains Malaysiana, 4, 493–511.

The question of interest is whether there is any association between the probability of an ESR reading greater than 20mm/hr and the levels of the two plasma proteins. If there is not then the determination of ESR would not be useful for diagnostic purposes.

1. Summarize the data appropriately both numerically and graphically

2. Build the appropriate model to answer the research question

3. Comment on the model and interpret the coefficients

4. Find the 95 % CI and interpret it.
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# Problem 1

library(ggplot2)
diamonds
names(diamonds)
# [1] "carat"   "cut"    "color"   "clarity" "depth"
# [6] "table"   "price"   "x"       "y"       "z"      

# 1
summary(diamonds)
#    carat               cut       color       clarity          depth          table      
# Min.   :0.2000   Fair    : 1610   D: 6775   SI1    :13065   Min.   :43.00   Min.   :43.00
# 1st Qu.:0.4000   Good    : 4906   E: 9797   VS2    :12258   1st Qu.:61.00   1st Qu.:56.00
# Median :0.7000   Very Good:12082   F: 9542   SI2    : 9194   Median :61.80   Median :57.00
# Mean   :0.7979   Premium :13791   G:11292   VS1    : 8171   Mean   :61.75   Mean   :57.46
# 3rd Qu.:1.0400   Ideal    :21551   H: 8304   VVS2   : 5066   3rd Qu.:62.50   3rd Qu.:59.00
# Max.   :5.0100                     I: 5422   VVS1   : 3655   Max.   :79.00   Max.   :95.00
#                                    J: 2808   (Other): 2531                                 
#    price             x                y                z         
# Min.   : 326   Min.   : 0.000   Min.   : 0.000   Min.   : 0.000
# 1st Qu.: 950   1st Qu.: 4.710   1st Qu.: 4.720   1st Qu.: 2.910
# Median : 2401   Median : 5.700   Median : 5.710   Median : 3.530
# Mean   : 3933   Mean   : 5.731   Mean   : 5.735   Mean   : 3.539
# 3rd Qu.: 5324   3rd Qu.: 6.540   3rd Qu.: 6.540   3rd Qu.: 4.040
# Max.   :18823   Max.   :10.740   Max.   :58.900   Max.   :31.800

cor(diamonds[c("carat", "depth", "table", "price", "x", "y", "z")])
#          carat       depth      table      price          x          y          z
# carat 1.00000000 0.02822431 0.1816175 0.9215913 0.97509423 0.95172220 0.95338738
# depth 0.02822431 1.00000000 -0.2957785 -0.0106474 -0.02528925 -0.02934067 0.09492388
# table 0.18161755 -0.29577852 1.0000000 0.1271339 0.19534428 0.18376015 0.15092869
# price 0.92159130 -0.01064740 0.1271339 1.0000000 0.88443516 0.86542090 0.86124944
# x    0.97509423 -0.02528925 0.1953443 0.8844352 1.00000000 0.97470148 0.97077180
# y    0.95172220 -0.02934067 0.1837601 0.8654209 0.97470148 1.00000000 0.95200572
# z    0.95338738 0.09492388 0.1509287 0.8612494 0.97077180 0.95200572 1.00000000

ggplot(diamonds, aes(x=carat, y=price, col=color)) + geom_point()
# color: diamond colour, from D (best) to J (worst)
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      • eloquent.retrieved: App\Models\SubjectCat (73μs)
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      • Illuminate\Cache\Events\CacheHit (127μs)
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      • Illuminate\Cache\Events\CacheHit (117μs)
      • Illuminate\Cache\Events\CacheHit (107μs)
      • Illuminate\Cache\Events\CacheHit (121μs)
      • Illuminate\Cache\Events\CacheHit (112μs)
      • Illuminate\Cache\Events\CacheHit (138μs)
      • Illuminate\Cache\Events\CacheHit (105μs)
      • Illuminate\Cache\Events\CacheHit (115μs)
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      • Illuminate\Cache\Events\CacheHit (134μs)
      • Illuminate\Cache\Events\CacheHit (105μs)
      • Illuminate\Cache\Events\CacheHit (123μs)
      • Illuminate\Cache\Events\CacheHit (104μs)
      • Illuminate\Cache\Events\CacheHit (147μs)
      • Illuminate\Cache\Events\CacheHit (130μs)
      • Illuminate\Cache\Events\CacheHit (130μs)
      • Illuminate\Cache\Events\CacheHit (108μs)
      • Illuminate\Cache\Events\CacheHit (122μs)
      • Illuminate\Cache\Events\CacheHit (107μs)
      • Illuminate\Cache\Events\CacheHit (121μs)
      • Illuminate\Cache\Events\CacheHit (107μs)
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      • Illuminate\Cache\Events\CacheHit (104μs)
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      • Illuminate\Cache\Events\CacheHit (127μs)
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      • Illuminate\Cache\Events\CacheHit (173μs)
      • Illuminate\Cache\Events\CacheHit (162μs)
      • Illuminate\Cache\Events\CacheHit (153μs)
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      • Illuminate\Cache\Events\CacheHit (117μs)
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      • Illuminate\Cache\Events\CacheHit (152μs)
      • Illuminate\Cache\Events\CacheHit (115μs)
      • Illuminate\Cache\Events\CacheHit (124μs)
      • Illuminate\Cache\Events\CacheHit (105μs)
      • Illuminate\Cache\Events\CacheHit (117μs)
      • Illuminate\Cache\Events\CacheHit (178μs)
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      • Illuminate\Cache\Events\CacheHit (122μs)
      • Illuminate\Cache\Events\CacheHit (149μs)
      • Illuminate\Cache\Events\CacheHit (109μs)
      • Illuminate\Cache\Events\CacheHit (130μs)
      • Illuminate\Cache\Events\CacheHit (117μs)
      • Illuminate\Cache\Events\CacheHit (143μs)
      • Illuminate\Cache\Events\CacheHit (116μs)
      • Illuminate\Cache\Events\CacheHit (150μs)
      • Illuminate\Cache\Events\CacheHit (127μs)
      • Illuminate\Cache\Events\CacheHit (159μs)
      • Illuminate\Cache\Events\CacheHit (124μs)
      • Illuminate\Cache\Events\CacheMissed (223μs)
      • Illuminate\Database\Events\StatementPrepared (827μs)
      • Illuminate\Database\Events\QueryExecuted (993μs)
      • eloquent.retrieved: App\Models\SubjectCat (106μs)
      • Illuminate\Cache\Events\KeyWritten (1.2ms)
      • Illuminate\Cache\Events\CacheHit (244μs)
      • Illuminate\Cache\Events\CacheHit (312μs)
      • Illuminate\Cache\Events\CacheHit (181μs)
      • Illuminate\Cache\Events\CacheHit (172μs)
      • Illuminate\Cache\Events\CacheHit (120μs)
      • Illuminate\Cache\Events\CacheHit (125μs)
      • Illuminate\Cache\Events\CacheHit (106μs)
      • Illuminate\Cache\Events\CacheHit (137μs)
      • Illuminate\Cache\Events\CacheHit (103μs)
      • Illuminate\Cache\Events\CacheHit (127μs)
      • Illuminate\Cache\Events\CacheHit (110μs)
      • Illuminate\Cache\Events\CacheHit (126μs)
      • Illuminate\Cache\Events\CacheHit (104μs)
      • Illuminate\Cache\Events\CacheHit (123μs)
      • Illuminate\Cache\Events\CacheHit (103μs)
      • Illuminate\Cache\Events\CacheHit (115μs)
      • Illuminate\Cache\Events\CacheHit (101μs)
      • creating: site.layouts.app (481μs)
      • composing: site.layouts.app (19μs)
      • creating: components.canonical (417μs)
      • composing: components.canonical (76μs)
      • creating: components.open-graph (148μs)
      • composing: components.open-graph (49μs)
      • creating: site.headers.header (223μs)
      • composing: site.headers.header (49μs)
      • Illuminate\Cache\Events\CacheHit (1.29ms)
      • creating: components.footer (71μs)
      • composing: components.footer (73μs)
      • Illuminate\Cache\Events\CacheHit (641μs)
      • Illuminate\Cache\Events\CacheMissed (269μs)
      • Illuminate\Database\Events\StatementPrepared (896μs)
      • Illuminate\Database\Events\QueryExecuted (980μs)
      • eloquent.retrieved: App\Models\SubjectCat (69μs)
      • Illuminate\Cache\Events\KeyWritten (1.44ms)
      • Illuminate\Cache\Events\CacheHit (284μs)
      • Illuminate\Cache\Events\CacheHit (148μs)
      • Illuminate\Cache\Events\CacheHit (128μs)
      • Illuminate\Cache\Events\CacheHit (138μs)
      • Illuminate\Cache\Events\CacheHit (128μs)
      • Illuminate\Cache\Events\CacheHit (239μs)
      • Illuminate\Cache\Events\CacheHit (265μs)
      • Illuminate\Cache\Events\CacheHit (130μs)
      • Illuminate\Cache\Events\CacheHit (134μs)
      • Illuminate\Cache\Events\CacheHit (126μs)
      • Illuminate\Cache\Events\CacheHit (129μs)
      • Illuminate\Cache\Events\CacheHit (116μs)
      • creating: components.forms.contact-us (168μs)
      • composing: components.forms.contact-us (113μs)
      • creating: components.forms.get-started (109μs)
      • composing: components.forms.get-started (47μs)
      • creating: components.forms.free-tool-download (72μs)
      • composing: components.forms.free-tool-download (41μs)
      • creating: components.forms.claim-free-worksheet (67μs)
      • composing: components.forms.claim-free-worksheet (40μs)
      • creating: components.forms.tutor-subscription-waitlist (64μs)
      • composing: components.forms.tutor-subscription-waitlist (39μs)
      • creating: components.forms.tutor-subscription-join (63μs)
      • composing: components.forms.tutor-subscription-join (38μs)
      • creating: components.forms.tutor-support (162μs)
      • composing: components.forms.tutor-support (47μs)
      • 311 x Illuminate\Cache\Events\CacheHit (15.59%)
        65.51ms
        20 x Illuminate\Database\Events\QueryExecuted (10.28%)
        43.17ms
        20 x Illuminate\Database\Events\StatementPrepared (6.55%)
        27.52ms
        11 x Illuminate\Cache\Events\KeyWritten (2.39%)
        10.05ms
        11 x Illuminate\Cache\Events\CacheMissed (1.72%)
        7.23ms
        1 x Illuminate\Foundation\Events\LocaleUpdated (1.09%)
        4.58ms
        1 x Illuminate\Routing\Events\Routing (0.32%)
        1.32ms
        1 x Illuminate\Database\Events\ConnectionEstablished (0.25%)
        1.07ms
        12 x eloquent.retrieved: App\Models\SubjectCat (0.23%)
        983μs
        1 x Illuminate\Routing\Events\RouteMatched (0.14%)
        596μs
        1 x eloquent.booting: App\Models\SubjectCat (0.13%)
        532μs
        1 x creating: site.layouts.app (0.11%)
        481μs
        1 x creating: components.canonical (0.1%)
        417μs
        1 x creating: homework.show (0.07%)
        288μs
        1 x creating: components.breadcrumbs (0.07%)
        286μs
        7 x eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibrary (0.07%)
        275μs
        2 x eloquent.retrieved: App\Models\Subject (0.06%)
        271μs
        15 x eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibraryFile (0.06%)
        242μs
        1 x eloquent.booting: App\Models\HomeworkLibrary\HomeworkLibrary (0.06%)
        237μs
        1 x creating: site.headers.header (0.05%)
        223μs
        1 x eloquent.booted: App\Models\HomeworkLibrary\HomeworkLibrary (0.05%)
        206μs
        1 x creating: components.forms.contact-us (0.04%)
        168μs
        1 x creating: components.forms.tutor-support (0.04%)
        162μs
        1 x eloquent.booting: App\Models\HomeworkLibrary\HomeworkLibraryFile (0.04%)
        154μs
        1 x creating: components.open-graph (0.04%)
        148μs
        1 x composing: components.breadcrumbs (0.03%)
        131μs
        1 x eloquent.booting: App\Models\Subject (0.03%)
        130μs
        1 x composing: homework.show (0.03%)
        120μs
        1 x composing: components.forms.contact-us (0.03%)
        113μs
        1 x creating: components.forms.get-started (0.03%)
        109μs
        1 x composing: components.canonical (0.02%)
        76μs
        1 x composing: components.footer (0.02%)
        73μs
        1 x creating: components.forms.free-tool-download (0.02%)
        72μs
        1 x creating: components.footer (0.02%)
        71μs
        1 x creating: components.forms.claim-free-worksheet (0.02%)
        67μs
        1 x creating: components.forms.tutor-subscription-waitlist (0.02%)
        64μs
        1 x creating: components.forms.tutor-subscription-join (0.01%)
        63μs
        1 x eloquent.booted: App\Models\Subject (0.01%)
        59μs
        1 x eloquent.booted: App\Models\HomeworkLibrary\HomeworkLibraryFile (0.01%)
        59μs
        1 x composing: components.open-graph (0.01%)
        49μs
        1 x composing: site.headers.header (0.01%)
        49μs
        1 x eloquent.booted: App\Models\SubjectCat (0.01%)
        48μs
        1 x composing: components.forms.get-started (0.01%)
        47μs
        1 x composing: components.forms.tutor-support (0.01%)
        47μs
        1 x composing: components.forms.free-tool-download (0.01%)
        41μs
        1 x composing: components.forms.claim-free-worksheet (0.01%)
        40μs
        1 x composing: components.forms.tutor-subscription-waitlist (0.01%)
        39μs
        1 x composing: components.forms.tutor-subscription-join (0.01%)
        38μs
        1 x composing: site.layouts.app (0%)
        19μs
      14 templates were rendered
      • 1x homework.showshow.blade.phpblade
      • 1x components.breadcrumbsbreadcrumbs.blade.phpblade
      • 1x site.layouts.appapp.blade.phpblade
      • 1x components.canonicalcanonical.blade.phpblade
      • 1x components.open-graphopen-graph.blade.phpblade
      • 1x site.headers.headerheader.blade.phpblade
      • 1x components.footerfooter.blade.phpblade
      • 1x components.forms.contact-uscontact-us.blade.phpblade
      • 1x components.forms.get-startedget-started.blade.phpblade
      • 1x components.forms.free-tool-downloadfree-tool-download.blade.phpblade
      • 1x components.forms.claim-free-worksheetclaim-free-worksheet.blade.phpblade
      • 1x components.forms.tutor-subscription-waitlisttutor-subscription-waitlist.blade.phpblade
      • 1x components.forms.tutor-subscription-jointutor-subscription-join.blade.phpblade
      • 1x components.forms.tutor-supporttutor-support.blade.phpblade
      uri
      GET college-homework-library/{category}/{subject}/{id}
      middleware
      web, utm.parameters
      controller
      App\Http\Controllers\HomeworkLibraryController@show
      namespace
      where
      as
      homework.show
      file
      app/Http/Controllers/HomeworkLibraryController.php:79-176
      20 statements were executed, 5 of which were duplicates, 15 unique. Show only duplicated54.86ms
      • 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` = '53993' limit 1
        9.13mstwenty4_siteHomeworkLibraryController.php#97
        Bindings
        • 0: published
        • 1: 0
        • 2: 53993
        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 (60)
        1.19mstwenty4_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 (53993)
        3.26mstwenty4_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
        1.12mstwenty4_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` <> 53993 and `subject` = 60 and `status` = 'published' and `price` > 0 order by RAND() limit 6
        20.62mstwenty4_siteHomeworkLibraryRepository.php#30
        Bindings
        • 0: 53993
        • 1: 60
        • 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 (60)
        1.17mstwenty4_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` = 53993 and `solutionslibrary_files`.`solutionlib_id` is not null and `publish` = 'question' order by `order` asc, `id` asc
        1.56mstwenty4_siteHomeworkLibrary.php#260
        Bindings
        • 0: 53993
        • 1: question
        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
      • select * from `solutionslibrary_files` where `solutionslibrary_files`.`solutionlib_id` = 53993 and `solutionslibrary_files`.`solutionlib_id` is not null and `publish` = 'teaser' order by `order` asc, `id` asc
        1.48mstwenty4_siteHomeworkLibrary.php#260
        Bindings
        • 0: 53993
        • 1: teaser
        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` = 53993 and `solutionslibrary_files`.`solutionlib_id` is not null and `publish` = 'solution' order by `order` asc, `id` asc
        1.2mstwenty4_siteHomeworkLibrary.php#260
        Bindings
        • 0: 53993
        • 1: solution
        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
        1.1mstwenty4_siteHomeworkLibrary.php#201
        Bindings
        • 0: 1
        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` = 1 limit 1
        1.23mstwenty4_siteSubject.php#100
        Bindings
        • 0: 1
        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` = 3 limit 1
        1.32mstwenty4_siteSubject.php#100
        Bindings
        • 0: 3
        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` = 4 limit 1
        1.36mstwenty4_siteSubject.php#100
        Bindings
        • 0: 4
        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` = 10 limit 1
        1.31mstwenty4_siteSubject.php#100
        Bindings
        • 0: 10
        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
        1.34mstwenty4_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
        1.29mstwenty4_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
        1.22mstwenty4_siteSubject.php#100
        Bindings
        • 0: 5
        Backtrace
        • 18. app/Models/Subject.php:100
        • 19. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397
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