{"id":2460,"date":"2023-07-22T04:29:06","date_gmt":"2023-07-22T04:29:06","guid":{"rendered":"https:\/\/statorials.org\/tr\/pythonda-iki-degiskenli-analiz\/"},"modified":"2023-07-22T04:29:06","modified_gmt":"2023-07-22T04:29:06","slug":"pythonda-iki-degiskenli-analiz","status":"publish","type":"post","link":"https:\/\/statorials.org\/tr\/pythonda-iki-degiskenli-analiz\/","title":{"rendered":"Python'da 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 pandalar DataFrame’i kullanarak Python’da 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 al\u0131nan s\u0131nav puan\u0131:<\/span><\/p>\n

 import<\/span> pandas as<\/span> pd\n\n#createDataFrame<\/span>\ndf = pd. DataFrame<\/span> ({' hours<\/span> ': [1, 1, 1, 2, 2, 2, 3, 3, 3, 3,\n                             3, 4, 4, 5, 5, 6, 6, 6, 7, 8],\n                   ' score<\/span> ': [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 five rows of DataFrame\n<\/span>df. head<\/span> ()\n\n\thours score\n0 1 75\n1 1 66\n2 1 68\n3 2 74\n4 2 78<\/strong><\/pre>\n
 1. Nokta bulutlar\u0131<\/strong><\/span><\/h3>\n
 S\u0131nav sonu\u00e7lar\u0131na kar\u015f\u0131 \u00e7al\u0131\u015f\u0131lan saatlerin da\u011f\u0131l\u0131m grafi\u011fini olu\u015fturmak i\u00e7in a\u015fa\u011f\u0131daki s\u00f6zdizimini kullanabiliriz:<\/span> <\/p>\n
 import<\/span> matplotlib. pyplot<\/span> as<\/span> plt\n\n#create scatterplot of hours vs. score<\/span>\nplt. scatter<\/span> (df. hours<\/span> , df. score<\/span> )\nplt. title<\/span> (' Hours Studied vs. Exam Score<\/span> ')\nplt. xlabel<\/span> (' Hours Studied<\/span> ')\nplt. ylabel<\/span> (' 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
 Korelasyon matrisi olu\u015fturmak i\u00e7in pandalarda corr()<\/strong> fonksiyonunu kullanabiliriz:<\/span><\/p>\n
 #create correlation matrix\n<\/span>df. corr<\/span> ()\n\n\thours score\nhours 1.000000 0.891306\nscore 0.891306 1.000000<\/strong><\/pre>\n
 Korelasyon katsay\u0131s\u0131 0,891<\/strong> olarak \u00e7\u0131k\u0131yor. Bu,<\/span> \u00e7al\u0131\u015f\u0131lan saat ile s\u0131nav notu aras\u0131nda g\u00fc\u00e7l\u00fc bir pozitif korelasyon oldu\u011funu g\u00f6sterir.<\/span><\/p>\n
 3. Basit do\u011frusal regresyon<\/strong><\/span><\/h3>\n
 Basit do\u011frusal regresyon, iki de\u011fi\u015fken aras\u0131ndaki ili\u015fkiyi \u00f6l\u00e7mek i\u00e7in kullanabilece\u011fimiz istatistiksel bir y\u00f6ntemdir.<\/span><\/p>\n
 \u00c7al\u0131\u015f\u0131lan saatler ve al\u0131nan s\u0131nav sonu\u00e7lar\u0131 i\u00e7in basit bir do\u011frusal regresyon modelini<\/a> h\u0131zl\u0131 bir \u015fekilde uyarlamak amac\u0131yla statsmodels paketindeki OLS()<\/strong> i\u015flevini kullanabiliriz:<\/span><\/p>\n
 import<\/span> statsmodels. api<\/span> as<\/span> sm\n\n#define response variable\n<\/span>y = df[' score<\/span> ']\n\n#define explanatory variable\n<\/span>x = df[[' hours<\/span> ']]\n\n#add constant to predictor variables\n<\/span>x = sm. add_constant<\/span> (x)\n\n#fit linear regression model\n<\/span>model = sm. OLS<\/span> (y,x). fit<\/span> ()\n\n#view model summary\n<\/span>print<\/span> ( model.summary<\/span> ())\n\n                            OLS Regression Results                            \n==================================================== ============================\nDept. Variable: R-squared score: 0.794\nModel: OLS Adj. R-squared: 0.783\nMethod: Least Squares F-statistic: 69.56\nDate: Mon, 22 Nov 2021 Prob (F-statistic): 1.35e-07\nTime: 16:15:52 Log-Likelihood: -55,886\nNo. Observations: 20 AIC: 115.8\nDf Residuals: 18 BIC: 117.8\nModel: 1                                         \nCovariance Type: non-robust                                         \n==================================================== ============================\n                 coef std err t P>|t| [0.025 0.975]\n-------------------------------------------------- ----------------------------\nconst 69.0734 1.965 35.149 0.000 64.945 73.202\nhours 3.8471 0.461 8.340 0.000 2.878 4.816\n==================================================== ============================\nOmnibus: 0.171 Durbin-Watson: 1.404\nProb(Omnibus): 0.918 Jarque-Bera (JB): 0.177\nSkew: 0.165 Prob(JB): 0.915\nKurtosis: 2.679 Cond. No. 9.37\n==================================================== ============================\n<\/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