{"id":2458,"date":"2023-07-22T04:43:11","date_gmt":"2023-07-22T04:43:11","guid":{"rendered":"https:\/\/statorials.org\/tr\/rde-iki-degiskenli-analiz\/"},"modified":"2023-07-22T04:43:11","modified_gmt":"2023-07-22T04:43:11","slug":"rde-iki-degiskenli-analiz","status":"publish","type":"post","link":"https:\/\/statorials.org\/tr\/rde-iki-degiskenli-analiz\/","title":{"rendered":"R'de i\u0307ki de\u011fi\u015fkenli analiz nas\u0131l ger\u00e7ekle\u015ftirilir (\u00f6rneklerle)"},"content":{"rendered":"

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\u0130ki de\u011fi\u015fkenli analiz<\/strong> terimi, iki de\u011fi\u015fkenin analizini ifade eder. Bunu \u201cbi\u201d \u00f6n ekinin \u201ciki\u201d anlam\u0131na gelmesinden dolay\u0131 hat\u0131rlayabilirsiniz.<\/span><\/p>\n

\u0130ki de\u011fi\u015fkenli analizin amac\u0131 iki de\u011fi\u015fken aras\u0131ndaki ili\u015fkiyi anlamakt\u0131r.<\/span><\/p>\n

\u0130ki de\u011fi\u015fkenli analiz ger\u00e7ekle\u015ftirmenin \u00fc\u00e7 yayg\u0131n yolu vard\u0131r:<\/span><\/p>\n

1.<\/strong> Nokta bulutlar\u0131<\/span><\/p>\n

2.<\/strong> Korelasyon katsay\u0131lar\u0131<\/span><\/p>\n

3.<\/strong> Basit do\u011frusal regresyon<\/span><\/p>\n

A\u015fa\u011f\u0131daki \u00f6rnek, iki de\u011fi\u015fken hakk\u0131nda bilgi i\u00e7eren a\u015fa\u011f\u0131daki veri k\u00fcmesini kullanarak bu iki de\u011fi\u015fkenli analiz t\u00fcrlerinin her birinin nas\u0131l ger\u00e7ekle\u015ftirilece\u011fini g\u00f6sterir: (1)<\/strong> \u00c7al\u0131\u015fmak i\u00e7in harcanan saatler ve (2)<\/strong> 20 farkl\u0131 \u00f6\u011frenci taraf\u0131ndan kazan\u0131lan test puanlar\u0131:<\/span><\/p>\n

 #create data frame<\/span>\ndf <- data. frame<\/span> (hours=c(1, 1, 1, 2, 2, 2, 3, 3, 3, 3,\n                         3, 4, 4, 5, 5, 6, 6, 6, 7, 8),\n                 score=c(75, 66, 68, 74, 78, 72, 85, 82, 90, 82,\n                         80, 88, 85, 90, 92, 94, 94, 88, 91, 96))\n\n#view first six rows of data frame\n<\/span>head(df)\n\n  hours score\n1 1 75\n2 1 66\n3 1 68\n4 2 74\n5 2 78\n6 2 72<\/strong><\/pre>\n
 1. Nokta bulutlar\u0131<\/strong><\/span><\/h3>\n
 R’de \u00e7al\u0131\u015f\u0131lan saatlerin s\u0131nav notlar\u0131na g\u00f6re da\u011f\u0131l\u0131m grafi\u011fini olu\u015fturmak i\u00e7in a\u015fa\u011f\u0131daki s\u00f6zdizimini kullanabiliriz:<\/span> <\/p>\n
 #create scatterplot of hours studied vs. exam score<\/span>\nplot(df$hours, df$score, pch= 16<\/span> , col=' steelblue<\/span> ',\n     main=' Hours Studied vs. Exam Score<\/span> ',\n     xlab=' Hours Studied<\/span> ', ylab=' Exam Score<\/span> ')\n<\/strong><\/pre>\n
\"\"<\/p>\n
 X ekseni \u00e7al\u0131\u015f\u0131lan saatleri, y ekseni ise s\u0131navda al\u0131nan notu g\u00f6sterir.<\/span><\/p>\n
 Grafik, iki de\u011fi\u015fken aras\u0131nda pozitif bir ili\u015fki oldu\u011funu g\u00f6stermektedir: \u00c7al\u0131\u015fma saati artt\u0131k\u00e7a s\u0131nav puanlar\u0131 da artma e\u011filimindedir.<\/span><\/p>\n
 2. Korelasyon katsay\u0131lar\u0131<\/strong><\/span><\/h3>\n
 Pearson korelasyon katsay\u0131s\u0131, iki de\u011fi\u015fken aras\u0131ndaki do\u011frusal ili\u015fkiyi \u00f6l\u00e7menin bir yoludur.<\/span><\/p>\n
 \u0130ki de\u011fi\u015fken aras\u0131ndaki Pearson korelasyon katsay\u0131s\u0131n\u0131 hesaplamak i\u00e7in R’deki cor()<\/strong> fonksiyonunu kullanabiliriz:<\/span><\/p>\n
 #calculate correlation between hours studied and exam score received\n<\/span>cor(df$hours, df$score)\n\n[1] 0.891306\n<\/strong><\/pre>\n
 Korelasyon katsay\u0131s\u0131 0,891<\/strong> olarak \u00e7\u0131k\u0131yor.<\/span><\/p>\n
 Bu de\u011ferin 1’e yak\u0131n olmas\u0131 \u00e7al\u0131\u015f\u0131lan saat ile s\u0131nav notu aras\u0131nda g\u00fc\u00e7l\u00fc bir pozitif korelasyon oldu\u011funu g\u00f6stermektedir.<\/span><\/p>\n
 3. Basit do\u011frusal regresyon<\/strong><\/span><\/h3>\n
 Basit do\u011frusal regresyon, bir veri k\u00fcmesine en iyi “uyan” do\u011frunun denklemini bulmak i\u00e7in kullanabilece\u011fimiz istatistiksel bir y\u00f6ntemdir ve bunu daha sonra iki de\u011fi\u015fken aras\u0131ndaki kesin ili\u015fkiyi anlamak i\u00e7in kullanabiliriz.<\/span><\/p>\n
 \u00c7al\u0131\u015f\u0131lan saatler ve al\u0131nan s\u0131nav sonu\u00e7lar\u0131 i\u00e7in basit bir do\u011frusal regresyon modeline<\/a> uyacak \u015fekilde R’deki lm()<\/strong> i\u015flevini kullanabiliriz:<\/span><\/p>\n
 #fit simple linear regression model\n<\/span>fit <- lm(score ~ hours, data=df)\n\n#view summary of model\n<\/span>summary(fit)\n\nCall:\nlm(formula = score ~ hours, data = df)\n\nResiduals:\n   Min 1Q Median 3Q Max \n-6,920 -3,927 1,309 1,903 9,385 \n\nCoefficients:\n            Estimate Std. Error t value Pr(>|t|)    \n(Intercept) 69.0734 1.9651 35.15 < 2nd-16 ***\nhours 3.8471 0.4613 8.34 1.35e-07 ***\n---\nSignificant. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1\n\nResidual standard error: 4.171 on 18 degrees of freedom\nMultiple R-squared: 0.7944, Adjusted R-squared: 0.783 \nF-statistic: 69.56 on 1 and 18 DF, p-value: 1.347e-07<\/strong><\/pre>\n
 Uygun regresyon denklemi \u015fu \u015fekilde ortaya \u00e7\u0131k\u0131yor:<\/span><\/p>\n
 S\u0131nav puan\u0131 = 69.0734 + 3.8471*(\u00e7al\u0131\u015fma saati)<\/span><\/p>\n
 Bu bize, \u00e7al\u0131\u015f\u0131lan her ek saatin s\u0131nav puan\u0131nda ortalama 3,8471<\/strong> art\u0131\u015fla ili\u015fkili oldu\u011funu s\u00f6yl\u00fcyor.<\/span><\/p>\n
 Bir \u00f6\u011frencinin toplam ders saatine g\u00f6re alaca\u011f\u0131 puan\u0131 tahmin etmek i\u00e7in uygun regresyon denklemini de kullanabiliriz.<\/span><\/p>\n
 \u00d6rne\u011fin 3 saat ders \u00e7al\u0131\u015fan bir \u00f6\u011frencinin 81.6147<\/strong> puan almas\u0131 gerekir:<\/span><\/p>\n