Question
Investigating Relationships in Baseball
What is a better predictor of the number of wins for a baseball team, the number of runs scored by the team or the number of runs they allow the other team to score? What variables can we use to predict the number of runs a team scores? To predict the number of runs it allows the other team to score? In this project, you will use technology to help answer these questions by exploring a large set of data from Major League Baseball.
PART 1
1. Refer to the “MLB Team Data 2012-2016” Excel file, along with the “Glossary for MLB Team Data sheet,” which explains each of the variables included in the data set.
2. Create a scatterplot to investigate the relationship between runs scored per game (R/G) and wins (W). Then calculate the equation of the least-squares regression line, the standard deviation of the residuals, and .
Note: R/G is in the section for hitting statistics and W is in the section for pitching statistics
3. Create a scatterplot to investigate the relationship between runs allowed per game (RA/G) and wins (W). Then calculate the equation of the least-squares regression line, the standard deviation of the residuals, and .
Note: Both of these variables may be found in the section for pitching statistics.
4. Compare the two associations, is runs scored or runs allowed a better predictor of wins? Explain your reasoning.
5. Because the number of wins a team has is dependent on both how many runs they score and how many runs they allow, we can use a combination of both variables to predict the number of wins. Add a column in your data table for a new variable, run differential. Fill in the values using the formula:
R/G – RA/G
6. Create a scatterplot to investigate the relationship between run differential and wins. Then calculate the equation of the least-squares regression line, the standard deviation of the residuals, and .
7. Is run differential a better predictor than the variable you chose in Question 4? Explain your reasoning.

PART 2
It is fairly clear that the number of games a team wins is dependent on both runs scored and runs allowed. But what variables help predict runs scored? Or runs allowed?
1. Choose either runs scored (R) or runs allowed (RA) as the response variable you will try to model.
2. Choose at least three different explanatory variables (or combinations of explanatory variables) that might help predict the response variable you chose in Question 1. Create a scatterplot using each explanatory variable. Then calculate the equation of the least-squares regression line, the standard deviation of the residuals, and for each relationship.
3. Which explanatory variable from Question 2 is the best? Explain your reasoning.
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      • Illuminate\Cache\Events\CacheHit (96μs)
      • Illuminate\Cache\Events\CacheHit (292μs)
      • Illuminate\Cache\Events\CacheHit (142μs)
      • Illuminate\Cache\Events\CacheHit (129μs)
      • Illuminate\Cache\Events\CacheHit (99μs)
      • Illuminate\Cache\Events\CacheHit (125μs)
      • Illuminate\Cache\Events\CacheHit (95μs)
      • Illuminate\Cache\Events\CacheHit (109μs)
      • Illuminate\Cache\Events\CacheHit (94μs)
      • Illuminate\Cache\Events\CacheHit (114μs)
      • Illuminate\Cache\Events\CacheHit (97μs)
      • Illuminate\Cache\Events\CacheHit (218μs)
      • Illuminate\Cache\Events\CacheHit (116μs)
      • Illuminate\Cache\Events\CacheHit (115μs)
      • Illuminate\Cache\Events\CacheHit (95μs)
      • Illuminate\Cache\Events\CacheMissed (284μs)
      • Illuminate\Database\Events\StatementPrepared (772μs)
      • Illuminate\Database\Events\QueryExecuted (6.38ms)
      • eloquent.retrieved: App\Models\SubjectCat (996μs)
      • Illuminate\Cache\Events\KeyWritten (301μs)
      • Illuminate\Cache\Events\CacheHit (193μs)
      • Illuminate\Cache\Events\CacheHit (353μs)
      • Illuminate\Cache\Events\CacheHit (133μs)
      • Illuminate\Cache\Events\CacheHit (127μs)
      • Illuminate\Cache\Events\CacheHit (170μs)
      • Illuminate\Cache\Events\CacheHit (128μs)
      • Illuminate\Cache\Events\CacheHit (102μs)
      • Illuminate\Cache\Events\CacheHit (149μs)
      • Illuminate\Cache\Events\CacheHit (102μs)
      • Illuminate\Cache\Events\CacheHit (122μs)
      • Illuminate\Cache\Events\CacheHit (128μs)
      • Illuminate\Cache\Events\CacheHit (929μs)
      • Illuminate\Cache\Events\CacheHit (139μs)
      • Illuminate\Cache\Events\CacheHit (260μs)
      • Illuminate\Cache\Events\CacheHit (1.02ms)
      • Illuminate\Cache\Events\CacheHit (169μs)
      • Illuminate\Cache\Events\CacheHit (114μs)
      • creating: site.layouts.app (332μs)
      • composing: site.layouts.app (16μs)
      • creating: components.canonical (366μs)
      • composing: components.canonical (73μs)
      • creating: components.open-graph (150μs)
      • composing: components.open-graph (48μs)
      • creating: site.headers.header (208μs)
      • composing: site.headers.header (48μs)
      • Illuminate\Cache\Events\CacheHit (1.58ms)
      • creating: components.footer (69μs)
      • composing: components.footer (67μs)
      • Illuminate\Cache\Events\CacheHit (728μs)
      • Illuminate\Cache\Events\CacheMissed (389μs)
      • Illuminate\Database\Events\StatementPrepared (798μs)
      • Illuminate\Database\Events\QueryExecuted (8.83ms)
      • eloquent.retrieved: App\Models\SubjectCat (86μs)
      • Illuminate\Cache\Events\KeyWritten (307μs)
      • Illuminate\Cache\Events\CacheHit (279μs)
      • Illuminate\Cache\Events\CacheHit (336μs)
      • Illuminate\Cache\Events\CacheHit (167μs)
      • Illuminate\Cache\Events\CacheHit (116μs)
      • Illuminate\Cache\Events\CacheHit (1.91ms)
      • Illuminate\Cache\Events\CacheHit (260μs)
      • Illuminate\Cache\Events\CacheHit (222μs)
      • Illuminate\Cache\Events\CacheHit (168μs)
      • Illuminate\Cache\Events\CacheHit (712μs)
      • Illuminate\Cache\Events\CacheHit (167μs)
      • Illuminate\Cache\Events\CacheHit (515μs)
      • Illuminate\Cache\Events\CacheHit (229μs)
      • creating: components.forms.contact-us (252μs)
      • composing: components.forms.contact-us (117μs)
      • creating: components.forms.get-started (126μs)
      • composing: components.forms.get-started (46μs)
      • creating: components.forms.free-tool-download (83μs)
      • composing: components.forms.free-tool-download (40μs)
      • creating: components.forms.claim-free-worksheet (89μs)
      • composing: components.forms.claim-free-worksheet (39μs)
      • creating: components.forms.tutor-subscription-waitlist (74μs)
      • composing: components.forms.tutor-subscription-waitlist (36μs)
      • creating: components.forms.tutor-subscription-join (73μs)
      • composing: components.forms.tutor-subscription-join (37μs)
      • creating: components.forms.tutor-support (91μs)
      • composing: components.forms.tutor-support (117μs)
      • 311 x Illuminate\Cache\Events\CacheHit (21.64%)
        98.72ms
        20 x Illuminate\Database\Events\QueryExecuted (11.97%)
        54.63ms
        20 x Illuminate\Database\Events\StatementPrepared (8.69%)
        39.65ms
        11 x Illuminate\Cache\Events\CacheMissed (2.77%)
        12.62ms
        11 x Illuminate\Cache\Events\KeyWritten (1.85%)
        8.45ms
        1 x Illuminate\Foundation\Events\LocaleUpdated (0.94%)
        4.30ms
        12 x eloquent.retrieved: App\Models\SubjectCat (0.41%)
        1.87ms
        1 x Illuminate\Routing\Events\Routing (0.3%)
        1.38ms
        1 x Illuminate\Database\Events\ConnectionEstablished (0.18%)
        835μs
        1 x Illuminate\Routing\Events\RouteMatched (0.1%)
        438μs
        1 x creating: components.canonical (0.08%)
        366μs
        1 x eloquent.booting: App\Models\SubjectCat (0.08%)
        344μs
        1 x creating: site.layouts.app (0.07%)
        332μs
        1 x creating: homework.show (0.06%)
        273μs
        7 x eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibrary (0.06%)
        262μs
        1 x creating: components.forms.contact-us (0.06%)
        252μs
        1 x creating: components.breadcrumbs (0.05%)
        248μs
        1 x creating: site.headers.header (0.05%)
        208μs
        1 x eloquent.booting: App\Models\HomeworkLibrary\HomeworkLibrary (0.04%)
        198μs
        8 x eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibraryFile (0.04%)
        198μs
        1 x eloquent.booted: App\Models\HomeworkLibrary\HomeworkLibrary (0.04%)
        173μs
        2 x eloquent.retrieved: App\Models\Subject (0.04%)
        171μs
        1 x creating: components.open-graph (0.03%)
        150μs
        1 x creating: components.forms.get-started (0.03%)
        126μs
        1 x composing: components.breadcrumbs (0.03%)
        118μs
        1 x composing: components.forms.contact-us (0.03%)
        117μs
        1 x composing: components.forms.tutor-support (0.03%)
        117μs
        1 x composing: homework.show (0.02%)
        113μs
        1 x eloquent.booting: App\Models\HomeworkLibrary\HomeworkLibraryFile (0.02%)
        108μs
        1 x eloquent.booting: App\Models\Subject (0.02%)
        96μs
        1 x creating: components.forms.tutor-support (0.02%)
        91μs
        1 x creating: components.forms.claim-free-worksheet (0.02%)
        89μs
        1 x creating: components.forms.free-tool-download (0.02%)
        83μs
        1 x creating: components.forms.tutor-subscription-waitlist (0.02%)
        74μs
        1 x creating: components.forms.tutor-subscription-join (0.02%)
        73μs
        1 x composing: components.canonical (0.02%)
        73μs
        1 x creating: components.footer (0.02%)
        69μs
        1 x composing: components.footer (0.01%)
        67μs
        1 x composing: site.headers.header (0.01%)
        48μs
        1 x composing: components.open-graph (0.01%)
        48μs
        1 x composing: components.forms.get-started (0.01%)
        46μs
        1 x eloquent.booted: App\Models\Subject (0.01%)
        44μs
        1 x eloquent.booted: App\Models\HomeworkLibrary\HomeworkLibraryFile (0.01%)
        42μs
        1 x eloquent.booted: App\Models\SubjectCat (0.01%)
        41μs
        1 x composing: components.forms.free-tool-download (0.01%)
        40μs
        1 x composing: components.forms.claim-free-worksheet (0.01%)
        39μs
        1 x composing: components.forms.tutor-subscription-join (0.01%)
        37μs
        1 x composing: components.forms.tutor-subscription-waitlist (0.01%)
        36μs
        1 x composing: site.layouts.app (0%)
        16μs
      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 duplicated61.77ms
      • 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` = '42907' limit 1
        16.86mstwenty4_siteHomeworkLibraryController.php#97
        Bindings
        • 0: published
        • 1: 0
        • 2: 42907
        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 (240)
        2.49mstwenty4_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 (42907)
        5.1mstwenty4_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` = 31 limit 1
        1.07mstwenty4_siteHomeworkLibrary.php#201
        Bindings
        • 0: 31
        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` <> 42907 and `subject` = 240 and `status` = 'published' and `price` > 0 order by RAND() limit 6
        2.96mstwenty4_siteHomeworkLibraryRepository.php#30
        Bindings
        • 0: 42907
        • 1: 240
        • 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 (240)
        1.4mstwenty4_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` = 42907 and `solutionslibrary_files`.`solutionlib_id` is not null and `publish` = 'question' order by `order` asc, `id` asc
        1.02mstwenty4_siteHomeworkLibrary.php#260
        Bindings
        • 0: 42907
        • 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` = 42907 and `solutionslibrary_files`.`solutionlib_id` is not null and `publish` = 'teaser' order by `order` asc, `id` asc
        910μstwenty4_siteHomeworkLibrary.php#260
        Bindings
        • 0: 42907
        • 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` = 42907 and `solutionslibrary_files`.`solutionlib_id` is not null and `publish` = 'solution' order by `order` asc, `id` asc
        880μstwenty4_siteHomeworkLibrary.php#260
        Bindings
        • 0: 42907
        • 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` = 31 limit 1
        2.38mstwenty4_siteHomeworkLibrary.php#201
        Bindings
        • 0: 31
        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
        2.27mstwenty4_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
        3.42mstwenty4_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
        2mstwenty4_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
        2.39mstwenty4_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
        2.17mstwenty4_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
        3.46mstwenty4_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
        2.84mstwenty4_siteSubject.php#100
        Bindings
        • 0: 5
        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
        1.19mstwenty4_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
        1.07mstwenty4_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
        5.89mstwenty4_siteSubject.php#100
        Bindings
        • 0: 36
        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\SubjectCat
      12SubjectCat.php
      App\Models\HomeworkLibrary\HomeworkLibraryFile
      8HomeworkLibraryFile.php
      App\Models\HomeworkLibrary\HomeworkLibrary
      7HomeworkLibrary.php
      App\Models\Subject
      2Subject.php
          _token
          xccYiPwp6feoOpEiUz60so6hGS0Luv4q36dN5ZtP
          utm_source
          direct
          redirectUrl
          /college-homework-library/High-School-Subjects/High-School-Math/42907
          _previous
          array:1 [ "url" => "https://staging.dev.24houranswers.com/college-homework-library/High-School-Sub...
          _flash
          array:2 [ "old" => [] "new" => [] ]
          PHPDEBUGBAR_STACK_DATA
          []
          path_info
          /college-homework-library/High-School-Subjects/High-School-Math/42907
          status_code
          200
          
          status_text
          OK
          format
          html
          content_type
          text/html; charset=UTF-8
          request_query
          []
          
          request_request
          []
          
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