{"id":29712,"date":"2025-09-18T20:22:01","date_gmt":"2025-09-18T17:22:01","guid":{"rendered":"https:\/\/fatihsoysal.com\/blog\/dogrusal-olasilik-modeli-tanim-ornekler-ve-sinirlamalar\/"},"modified":"2025-09-18T20:22:01","modified_gmt":"2025-09-18T17:22:01","slug":"dogrusal-olasilik-modeli-tanim-ornekler-ve-sinirlamalar","status":"publish","type":"post","link":"https:\/\/fatihsoysal.com\/blog\/dogrusal-olasilik-modeli-tanim-ornekler-ve-sinirlamalar\/","title":{"rendered":"Do\u011frusal Olas\u0131l\u0131k Modeli: Tan\u0131m, \u00d6rnekler ve S\u0131n\u0131rlamalar"},"content":{"rendered":"

# Lineer Olas\u0131l\u0131k Modeli: Tan\u0131m, \u00d6rnekler ve S\u0131n\u0131rlamalar<\/p>\n

Meta A\u00e7\u0131klamas\u0131:<\/strong> Lineer olas\u0131l\u0131k modelini (LPM) anlamak i\u00e7in kapsaml\u0131 bir rehber. Tan\u0131mdan uygulamalara, s\u0131n\u0131rlamalardan performans optimizasyonuna kadar her \u015feyi bu makalede bulacaks\u0131n\u0131z. Ger\u00e7ek d\u00fcnya \u00f6rnekleri ve ad\u0131m ad\u0131m a\u00e7\u0131klamalar ile LPM’yi \u00f6\u011frenin.<\/p>\n

Bir \u015firketin yeni bir \u00fcr\u00fcn\u00fcn piyasaya s\u00fcr\u00fclmesinden sonraki sat\u0131\u015flar\u0131n\u0131 tahmin etmesi gerekti\u011fini d\u00fc\u015f\u00fcn\u00fcn. Ya da bir bankan\u0131n kredi ba\u015fvurusunda bulunan m\u00fc\u015fterilerin kredi risklerini de\u011ferlendirmesi gerekse? Bu gibi durumlarda, olaylar\u0131n olas\u0131l\u0131\u011f\u0131n\u0131 tahmin etmek i\u00e7in istatistiksel modeller kullanmak \u00e7ok \u00f6nemlidir. Lineer olas\u0131l\u0131k modeli (LPM), bu t\u00fcr ikili (0 veya 1) ba\u011f\u0131ml\u0131 de\u011fi\u015fkenleri tahmin etmek i\u00e7in kullan\u0131lan basit ancak g\u00fc\u00e7l\u00fc bir y\u00f6ntemdir. Bu makalede, lineer olas\u0131l\u0131k modelini detayl\u0131 bir \u015fekilde inceleyecek, \u00f6rnekler verecek ve s\u0131n\u0131rlamalar\u0131n\u0131 ele alaca\u011f\u0131z.<\/p>\n

Lineer Olas\u0131l\u0131k Modeli Nedir?<\/strong><\/p>\n

Lineer olas\u0131l\u0131k modeli, ba\u011f\u0131ml\u0131 de\u011fi\u015fkenin 0 veya 1 de\u011ferlerini (\u00f6rne\u011fin, evet\/hay\u0131r, ba\u015far\u0131\/ba\u015far\u0131s\u0131zl\u0131k) alan bir regresyon modelidir. Ba\u011f\u0131ms\u0131z de\u011fi\u015fkenler ile ba\u011f\u0131ml\u0131 de\u011fi\u015fken aras\u0131ndaki ili\u015fkiyi do\u011frusal bir denklemle modelleyerek, ba\u011f\u0131ms\u0131z de\u011fi\u015fkenlerin olas\u0131 de\u011ferleri verildi\u011finde ba\u011f\u0131ml\u0131 de\u011fi\u015fkenin 1 olma olas\u0131l\u0131\u011f\u0131n\u0131 tahmin eder. Basit\u00e7e ifade edersek, LPM, ba\u011f\u0131ms\u0131z de\u011fi\u015fkenlerdeki bir birimlik de\u011fi\u015fimin ba\u011f\u0131ml\u0131 de\u011fi\u015fkenin 1 olma olas\u0131l\u0131\u011f\u0131n\u0131 ne kadar etkiledi\u011fini tahmin etmeye \u00e7al\u0131\u015f\u0131r. Form\u00fcl \u015fu \u015fekildedir:<\/p>\n

P(Y=1|X) = \u03b2\u2080 + \u03b2\u2081X\u2081 + \u03b2\u2082X\u2082 + ... + \u03b2\u2099X\u2099<\/code><\/p>\n

Burada:<\/p>\n

* P(Y=1|X)<\/code>: Ba\u011f\u0131ms\u0131z de\u011fi\u015fkenler X<\/code> verildi\u011finde ba\u011f\u0131ml\u0131 de\u011fi\u015fken Y<\/code>‘nin 1 olma olas\u0131l\u0131\u011f\u0131d\u0131r.
\n* \u03b2\u2080<\/code>: Kesim noktas\u0131 (intercept)
\n* \u03b2\u1d62<\/code>: Ba\u011f\u0131ms\u0131z de\u011fi\u015fken X\u1d62<\/code>‘nin katsay\u0131s\u0131 (i = 1, 2, …, n)
\n* X\u1d62<\/code>: Ba\u011f\u0131ms\u0131z de\u011fi\u015fkenler<\/p>\n

Lineer Olas\u0131l\u0131k Modelini Nas\u0131l Uygulayabilirim? (Ad\u0131m Ad\u0131m K\u0131lavuz)<\/strong><\/p>\n

Yeni Ba\u015flayanlar i\u00e7in:<\/strong><\/p>\n

1. Veri Haz\u0131rl\u0131\u011f\u0131:<\/strong> \u0130lk ad\u0131m, ba\u011f\u0131ml\u0131 ve ba\u011f\u0131ms\u0131z de\u011fi\u015fkenlerinizi i\u00e7eren bir veri k\u00fcmesi olu\u015fturmakt\u0131r. Ba\u011f\u0131ml\u0131 de\u011fi\u015fkeniniz ikili (0 veya 1) olmal\u0131d\u0131r. \u00d6rne\u011fin, bir pazarlama kampanyas\u0131n\u0131n ba\u015far\u0131s\u0131n\u0131 tahmin etmek istiyorsan\u0131z, ba\u011f\u0131ml\u0131 de\u011fi\u015fkeniniz “kampanya ba\u015far\u0131l\u0131 m\u0131 (1=evet, 0=hay\u0131r)” olabilir. Ba\u011f\u0131ms\u0131z de\u011fi\u015fkenleriniz ise kampanya b\u00fct\u00e7esi, hedef kitle boyutu, reklam t\u00fcr\u00fc gibi fakt\u00f6rler olabilir.<\/p>\n

2. Model Kurulumu:<\/strong> Se\u00e7ti\u011finiz istatistiksel yaz\u0131l\u0131m (R, Python, SPSS vb.) kullanarak lineer regresyon modelini kurun. Ba\u011f\u0131ml\u0131 de\u011fi\u015fkeninizi ve ba\u011f\u0131ms\u0131z de\u011fi\u015fkenlerinizi modele ekleyin.<\/p>\n

3. Model Uydurma:<\/strong> Yaz\u0131l\u0131m, verilerinize en uygun parametreleri (\u03b2\u2080<\/code>, \u03b2\u2081<\/code>, \u03b2\u2082<\/code>, vb.) bulmak i\u00e7in modeli uyduracakt\u0131r.<\/p>\n

4. Tahmin:<\/strong> Model, yeni bir g\u00f6zlem i\u00e7in ba\u011f\u0131ms\u0131z de\u011fi\u015fken de\u011ferlerini kullanarak ba\u011f\u0131ml\u0131 de\u011fi\u015fkenin 1 olma olas\u0131l\u0131\u011f\u0131n\u0131 tahmin edecektir.<\/p>\n

Basit Python \u00d6rne\u011fi (statsmodels k\u00fct\u00fcphanesi):<\/strong><\/p>\n

import statsmodels.api as sm\nimport numpy as np\n\n# \u00d6rnek veri (ba\u011f\u0131ml\u0131 de\u011fi\u015fken: ba\u015far\u0131\/ba\u015far\u0131s\u0131zl\u0131k, ba\u011f\u0131ms\u0131z de\u011fi\u015fken: \u00e7al\u0131\u015fma saati)\nX = np.array([2, 4, 6, 8, 10]).reshape(-1, 1)  # Ba\u011f\u0131ms\u0131z de\u011fi\u015fken\ny = np.array([0, 0, 1, 1, 1])  # Ba\u011f\u0131ml\u0131 de\u011fi\u015fken\n\n# Sabit terim ekleme\nX = sm.add_constant(X)\n\n# Model kurma ve uydurma\nmodel = sm.OLS(y, X)\nresults = model.fit()\n\n# Sonu\u00e7lar\u0131 yazd\u0131rma\nprint(results.summary())<\/code><\/pre>\n
Ger\u00e7ek D\u00fcnya \u00d6rnekleri ve Vaka Analizleri<\/strong><\/p>\n
Orta Seviye:<\/strong><\/p>\n
\u00d6rnek 1: Kredi Riski De\u011ferlendirmesi:<\/strong> Bir banka, m\u00fc\u015fterilerin kredi ba\u015fvurular\u0131n\u0131 de\u011ferlendirmek i\u00e7in LPM kullanabilir.  Ba\u011f\u0131ms\u0131z de\u011fi\u015fkenler kredi puan\u0131, gelir, bor\u00e7 oran\u0131 gibi fakt\u00f6rler olabilirken, ba\u011f\u0131ml\u0131 de\u011fi\u015fken m\u00fc\u015fterinin kredinin geri \u00f6denip \u00f6denmeyece\u011fini g\u00f6sterir (1=\u00f6denir, 0=\u00f6denmez). Model, belirli bir m\u00fc\u015fterinin kredi ba\u015fvurusunun onaylanma olas\u0131l\u0131\u011f\u0131n\u0131 tahmin etmeye yard\u0131mc\u0131 olur.<\/p>\n
\u00d6rnek 2: M\u00fc\u015fteri Ayr\u0131lma Tahmini (Churn Prediction):<\/strong>  Bir telekom\u00fcnikasyon \u015firketi, m\u00fc\u015fterilerinin hizmetlerini iptal etme olas\u0131l\u0131\u011f\u0131n\u0131 (churn) tahmin etmek i\u00e7in LPM kullanabilir.  Ba\u011f\u0131ms\u0131z de\u011fi\u015fkenler olarak m\u00fc\u015fteri memnuniyeti puan\u0131, hizmet s\u00fcresi, kullan\u0131lan hizmet paketi gibi fakt\u00f6rler kullan\u0131labilir.  Model, churn riskini y\u00fcksek olan m\u00fc\u015fterileri belirlemek ve onlar\u0131 elde tutmak i\u00e7in proaktif \u00f6nlemler almak i\u00e7in kullan\u0131labilir.<\/p>\n
Optimizasyon \u0130pu\u00e7lar\u0131:<\/strong><\/p>\n
* Veri Temizli\u011fi:<\/strong>  Eksik verilerin d\u00fczg\u00fcn bir \u015fekilde ele al\u0131nmas\u0131 ve ayk\u0131r\u0131 de\u011ferlerin tespit edilmesi \u00f6nemlidir.
\n* De\u011fi\u015fken Se\u00e7imi:<\/strong>  Modelin performans\u0131n\u0131 art\u0131rmak i\u00e7in uygun ba\u011f\u0131ms\u0131z de\u011fi\u015fkenleri se\u00e7mek \u00f6nemlidir.  De\u011fi\u015fken se\u00e7imi teknikleri (\u00f6rne\u011fin, ad\u0131m ad\u0131m regresyon) kullan\u0131labilir.
\n* Model Do\u011frulamas\u0131:<\/strong>  Modelin performans\u0131n\u0131 de\u011ferlendirmek i\u00e7in farkl\u0131 veri k\u00fcmeleri \u00fczerinde do\u011frulama yapmak \u00f6nemlidir.  (E\u011fitim ve test k\u00fcmeleri)<\/p>\n
Lineer Olas\u0131l\u0131k Modelinin S\u0131n\u0131rlamalar\u0131 ve Performans Analizi<\/strong><\/p>\n
\u0130leri D\u00fczey:<\/strong><\/p>\n
LPM’nin en \u00f6nemli s\u0131n\u0131rlamas\u0131, tahmin edilen olas\u0131l\u0131klar\u0131n 0 ile 1 aras\u0131nda olma zorunlulu\u011funun olmamas\u0131d\u0131r.  Model, ba\u011f\u0131ms\u0131z de\u011fi\u015fkenlerin belirli kombinasyonlar\u0131 i\u00e7in 1’den b\u00fcy\u00fck veya 0’dan k\u00fc\u00e7\u00fck olas\u0131l\u0131klar \u00fcretebilir. Bu durum, olas\u0131l\u0131k yorumlamas\u0131n\u0131 zorla\u015ft\u0131r\u0131r ve modelin g\u00fcvenilirli\u011fini azalt\u0131r.  Ayr\u0131ca, LPM, ba\u011f\u0131ml\u0131 de\u011fi\u015fkenin olas\u0131l\u0131\u011f\u0131n\u0131 do\u011frusal olarak modelledi\u011fi i\u00e7in, ger\u00e7ek d\u00fcnyadaki bir\u00e7ok olayda g\u00f6r\u00fclen do\u011frusal olmayan ili\u015fkileri yakalayamayabilir.<\/p>\n
Performans Analizi:<\/strong><\/p>\n
Modelin performans\u0131n\u0131 de\u011ferlendirmek i\u00e7in \u00e7e\u015fitli metrikler kullan\u0131labilir:<\/p>\n
* Do\u011fruluk (Accuracy):<\/strong> Do\u011fru tahmin edilen g\u00f6zlemlerin toplam g\u00f6zlem say\u0131s\u0131na oran\u0131.
\n* Hassasiyet (Precision):<\/strong>  Pozitif olarak tahmin edilen g\u00f6zlemler aras\u0131nda ger\u00e7ekten pozitif olanlar\u0131n oran\u0131.
\n* Duyarl\u0131l\u0131k (Recall\/Sensitivity):<\/strong> Ger\u00e7ekte pozitif olan g\u00f6zlemler aras\u0131nda do\u011fru tahmin edilenlerin oran\u0131.
\n* F1 Skoru:<\/strong> Hassasiyet ve duyarl\u0131l\u0131\u011f\u0131n harmonik ortalamas\u0131.
\n* AUC (Alan Alt\u0131ndaki E\u011fri):<\/strong> ROC e\u011frisinin alt\u0131ndaki alan, modelin s\u0131n\u0131fland\u0131rma performans\u0131n\u0131 g\u00f6sterir.<\/p>\n
Edge Case’ler:<\/strong><\/p>\n
* \u00c7oklu do\u011frusal ba\u011f\u0131ml\u0131l\u0131k:<\/strong> Ba\u011f\u0131ms\u0131z de\u011fi\u015fkenler aras\u0131nda y\u00fcksek korelasyon olmas\u0131, modelin tahminlerinin g\u00fcvenilirli\u011fini azaltabilir.
\n* K\u00fc\u00e7\u00fck \u00f6rneklem boyutu:<\/strong> K\u00fc\u00e7\u00fck \u00f6rneklem boyutlar\u0131, modelin genelleme yetene\u011fini azaltabilir.
\n* Heterosedastisite:<\/strong> Hata terimlerinin varyans\u0131n\u0131n sabit olmamas\u0131, modelin tahminlerinin etkinli\u011fini azaltabilir.<\/p>\n
Lineer Olas\u0131l\u0131k Modelinin Alternatifleri<\/strong><\/p>\n
LPM’nin s\u0131n\u0131rlamalar\u0131 nedeniyle, ikili ba\u011f\u0131ml\u0131 de\u011fi\u015fkenli veriler i\u00e7in daha geli\u015fmi\u015f modeller tercih edilebilir.  Bunlara lojistik regresyon, probit regresyon ve daha geli\u015fmi\u015f makine \u00f6\u011frenmesi modelleri (\u00f6rne\u011fin, destek vekt\u00f6r makineleri, yapay sinir a\u011flar\u0131) \u00f6rnek verilebilir.  Bu modeller, olas\u0131l\u0131klar\u0131n 0 ile 1 aras\u0131nda kalmas\u0131n\u0131 sa\u011flar ve do\u011frusal olmayan ili\u015fkileri daha iyi yakalayabilir.  Hangi modelin en uygun olaca\u011f\u0131, veri setinin \u00f6zelliklerine ve ara\u015ft\u0131rma sorusuna ba\u011fl\u0131d\u0131r.  Daha detayl\u0131 bilgi i\u00e7in [Fatih Soysal’\u0131n istatistiksel modelleme \u00fczerine yaz\u0131lar\u0131n\u0131](https:\/\/fatihsoysal.com) inceleyebilirsiniz.<\/p>\n
Sonu\u00e7<\/strong><\/p>\n
Lineer olas\u0131l\u0131k modeli, ikili ba\u011f\u0131ml\u0131 de\u011fi\u015fkenleri modellemek i\u00e7in basit ve anla\u015f\u0131l\u0131r bir y\u00f6ntemdir.  Ancak, s\u0131n\u0131rlamalar\u0131n\u0131n fark\u0131nda olmak ve uygun alternatifleri de\u011ferlendirmek \u00f6nemlidir.  Uygun veri haz\u0131rlama, model do\u011frulama ve performans analizi, LPM’nin etkinli\u011fini art\u0131rmak i\u00e7in hayati \u00f6nem ta\u015f\u0131r.<\/p>\n
S\u0131k\u00e7a Sorulan Sorular:<\/strong><\/p>\n
1. LPM’nin lojistik regresyondan fark\u0131 nedir?<\/strong> LPM do\u011frusal bir model iken, lojistik regresyon olas\u0131l\u0131klar\u0131 lojistik bir fonksiyon kullanarak modelleyerek 0 ile 1 aras\u0131nda s\u0131n\u0131rland\u0131r\u0131r.<\/p>\n
2. LPM’de heterosedastisite nas\u0131l ele al\u0131n\u0131r?<\/strong>  A\u011f\u0131rl\u0131kl\u0131 en k\u00fc\u00e7\u00fck kareler y\u00f6ntemi (WLS) veya robust standart hatalar kullan\u0131labilir.<\/p>\n
3. LPM’nin performans\u0131n\u0131 nas\u0131l iyile\u015ftirebilirim?<\/strong>  Veri temizli\u011fi, de\u011fi\u015fken se\u00e7imi, model do\u011frulama ve uygun optimizasyon teknikleri kullan\u0131labilir.<\/p>\n
4. Hangi yaz\u0131l\u0131mlar LPM uygulanmas\u0131nda kullan\u0131labilir?<\/strong> R, Python (statsmodels, scikit-learn), SPSS gibi istatistiksel yaz\u0131l\u0131mlar kullan\u0131labilir.<\/p>\n
5. LPM hangi durumlarda uygun de\u011fildir?<\/strong>  Do\u011frusal olmayan ili\u015fkilerin bask\u0131n oldu\u011fu durumlarda veya olas\u0131l\u0131klar\u0131n 0 ile 1 aras\u0131nda s\u0131n\u0131rland\u0131r\u0131lmas\u0131 gerekti\u011finde LPM uygun olmayabilir.<\/p>\n
Yazar: Fatih Soysal<\/p>\n","protected":false},"excerpt":{"rendered":"# Lineer Olas\u0131l\u0131k Modeli: Tan\u0131m, \u00d6rnekler ve S\u0131n\u0131rlamalar Meta A\u00e7\u0131klamas\u0131: Lineer olas\u0131l\u0131k modelini (LPM) anlamak i\u00e7in kapsaml\u0131 bir…","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"csco_page_header_type":"","csco_page_load_nextpost":"","csco_page_subscribe_form":"","csco_page_contact_form":"","footnotes":""},"categories":[1],"tags":[],"class_list":{"0":"post-29712","1":"post","2":"type-post","3":"status-publish","4":"format-standard","6":"category-genel","7":"cs-entry","8":"cs-video-wrap"},"yoast_head":"\nDo\u011frusal Olas\u0131l\u0131k Modeli: Tan\u0131m, \u00d6rnekler ve S\u0131n\u0131rlamalar<\/title>\n<meta name=\"description\" content=\"Hi\u00e7bir etiketi bulunamad\u0131.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/fatihsoysal.com\/blog\/dogrusal-olasilik-modeli-tanim-ornekler-ve-sinirlamalar\/\" \/>\n<meta property=\"og:locale\" content=\"tr_TR\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Do\u011frusal Olas\u0131l\u0131k Modeli: Tan\u0131m, \u00d6rnekler ve S\u0131n\u0131rlamalar\" \/>\n<meta property=\"og:description\" content=\"Hi\u00e7bir etiketi bulunamad\u0131.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/fatihsoysal.com\/blog\/dogrusal-olasilik-modeli-tanim-ornekler-ve-sinirlamalar\/\" \/>\n<meta property=\"og:site_name\" content=\"Kodlar\u0131n Gizemli D\u00fcnyas\u0131\" \/>\n<meta property=\"article:published_time\" content=\"2025-09-18T17:22:01+00:00\" \/>\n<meta name=\"author\" content=\"Fatih Soysal\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Yazan:\" \/>\n\t<meta name=\"twitter:data1\" content=\"Fatih Soysal\" \/>\n\t<meta name=\"twitter:label2\" content=\"Tahmini okuma s\u00fcresi\" \/>\n\t<meta name=\"twitter:data2\" content=\"7 dakika\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"Article\",\"@id\":\"https:\/\/fatihsoysal.com\/blog\/dogrusal-olasilik-modeli-tanim-ornekler-ve-sinirlamalar\/#article\",\"isPartOf\":{\"@id\":\"https:\/\/fatihsoysal.com\/blog\/dogrusal-olasilik-modeli-tanim-ornekler-ve-sinirlamalar\/\"},\"author\":{\"name\":\"Fatih Soysal\",\"@id\":\"https:\/\/fatihsoysal.com\/blog\/#\/schema\/person\/002a254750921dcfd568a99e48240dd1\"},\"headline\":\"Do\u011frusal Olas\u0131l\u0131k Modeli: Tan\u0131m, \u00d6rnekler ve S\u0131n\u0131rlamalar\",\"datePublished\":\"2025-09-18T17:22:01+00:00\",\"mainEntityOfPage\":{\"@id\":\"https:\/\/fatihsoysal.com\/blog\/dogrusal-olasilik-modeli-tanim-ornekler-ve-sinirlamalar\/\"},\"wordCount\":1324,\"commentCount\":0,\"publisher\":{\"@id\":\"https:\/\/fatihsoysal.com\/blog\/#\/schema\/person\/002a254750921dcfd568a99e48240dd1\"},\"inLanguage\":\"tr\",\"potentialAction\":[{\"@type\":\"CommentAction\",\"name\":\"Comment\",\"target\":[\"https:\/\/fatihsoysal.com\/blog\/dogrusal-olasilik-modeli-tanim-ornekler-ve-sinirlamalar\/#respond\"]}],\"copyrightYear\":\"2025\",\"copyrightHolder\":{\"@id\":\"https:\/\/fatihsoysal.com\/blog\/#organization\"}},{\"@type\":\"WebPage\",\"@id\":\"https:\/\/fatihsoysal.com\/blog\/dogrusal-olasilik-modeli-tanim-ornekler-ve-sinirlamalar\/\",\"url\":\"https:\/\/fatihsoysal.com\/blog\/dogrusal-olasilik-modeli-tanim-ornekler-ve-sinirlamalar\/\",\"name\":\"Do\u011frusal Olas\u0131l\u0131k Modeli: Tan\u0131m, \u00d6rnekler ve S\u0131n\u0131rlamalar\",\"isPartOf\":{\"@id\":\"https:\/\/fatihsoysal.com\/blog\/#website\"},\"datePublished\":\"2025-09-18T17:22:01+00:00\",\"description\":\"Hi\u00e7bir etiketi bulunamad\u0131.\",\"breadcrumb\":{\"@id\":\"https:\/\/fatihsoysal.com\/blog\/dogrusal-olasilik-modeli-tanim-ornekler-ve-sinirlamalar\/#breadcrumb\"},\"inLanguage\":\"tr\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/fatihsoysal.com\/blog\/dogrusal-olasilik-modeli-tanim-ornekler-ve-sinirlamalar\/\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/fatihsoysal.com\/blog\/dogrusal-olasilik-modeli-tanim-ornekler-ve-sinirlamalar\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Anasayfa\",\"item\":\"https:\/\/fatihsoysal.com\/blog\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"Do\u011frusal Olas\u0131l\u0131k Modeli: Tan\u0131m, \u00d6rnekler ve S\u0131n\u0131rlamalar\"}]},{\"@type\":\"WebSite\",\"@id\":\"https:\/\/fatihsoysal.com\/blog\/#website\",\"url\":\"https:\/\/fatihsoysal.com\/blog\/\",\"name\":\"Fatihsoysal.com\",\"description\":\"Blog - 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