import numpy as np

import matplotlib.pyplot as plt

import pandas as pd

class LinearRegression:

def $\_\_$init$\_\_($self$,$X$,$Y$)$: # x ve y ayr$$l$$p verilecek

ones$=$np$.$ones$($X$.$shape$)$

X$=$np$.$append$($ones$,$X$,$axis$=1)$

self.X$=$X

self.Y$=$Y

self.m$=$X$.$shape$[0]$

self.n$=$X$.$shape$[1]$

self.theta$=$np$.$random.randn$($X$.$shape$[1])$

def computeCostFunction$($self$)$:

h$=$np$.$matmul$($self$.$X$,$self.theta$)$

self.J$=(1/(2*$self$.$m$))*$np$.$sum$(($h$-$self.Y$)**2)$

return self.J

def performGradientDescent$($self$,$num$\_$of$\_$iter,alpha$)$:# iterasyon say$$s$$

self.Cost$\_$history$=[]$

self.theta$\_$history$=[]$

for x in range$($num$\_$of$\_$iter$)$:

h$=$np$.$matmul$($self$.$X$,$self.theta$)$

J$=$self.computeCostFunction$()$

self.Cost$\_$history.append$($J$)$

self.theta$\_$history.append$($self$.$theta$)$

temp$=$h$-$self.Y

self.theta$=$self.theta$-($alpha$/$self$.$m$)*($self$.$X$.$T$.$dot$($temp$))$

return self.theta,self.Cost$\_$history,self.theta$\_$history

def predict$($self$,$X$\_$test,Y$\_$test$)$:

ones$=$np$.$ones$($X$\_$test.shape$)$

X$\_$test$=$np$.$append$($ones$,$X$\_$test,axis$=1)$

self.Y$\_$pred$=$np$.$matmul$($X$\_$test,self.theta$)$

self.error$\_$percentage$=($abs$($self$.$Y$\_$pred$-$Y$\_$test$)/$Y$\_$test$)*100$

return self.Y$\_$pred,self.error$\_$percentage

def predictUsingNormalEquation$($self$,$X$\_$test,Y$\_$test$)$:

ones$=$np$.$ones$($X$\_$test.shape$)$

X$\_$test$=$np$.$append$($ones$,$X$\_$test,axis$=1)$

inv$=$np$.$linalg.inv$($np$.$matmul$($self$.$X$.$T$,$self.X$))$

self.w$=$np$.$matmul$($np$.$matmul$($inv$,$self.X$.$T$),$self.Y$)$

y$\_$pred$=$np$.$matmul$($X$\_$test,self.w$)$

return y$\_$pred,$($abs$($Y$\_$test$-$y$\_$pred$)/$Y$\_$test$)*100$ bu kodu bir $$rnekte Bu $$al$$mada Python$$da Do$$rusal Regresyon $($Linear Regression$)$ s$$f$$rdan uygulayacaks$$n$$z$.$

Veri Seti $$znitelikleri:

$$ Kategori,

$$ Sayfa toplam be$$enisi: $$irketin sayfas$$n$$ be$$enen ki$$i say$$s$),$

$$ T$$r: $$erik t$$r$($Ba$$lant$,$ Foto$$raf$,$ Durum, Video$),$

$$ G$$nderi ay$$: G$$nderinin yay$$nland$$ ay $($Ocak$,$ubat$,$ Mart,..., Aral$$k$),$

$$ G$$nderim saati: G$$nderinin yay$$nland$$ saat $(0,1,2,3,4,...,23),$

$$ Hafta i$$i g$$nderi: G$$nderinin yay$$nland$$ hafta i$$i $($Pazar$,$ Pazartesi, $...,$ Cumartesi$),$

$$cretli: $$irketin reklam i$$in Facebook'a $$deme yapmas durumunda $($evet$,$ hay$$r$)$

Modellemek i$$in:

Modellemeye $$al$$abilece$$imiz bir$$ok olas$$zellik var ancak biz $$Total Interactions$$e

odaklanaca$$z$.$zellik alan$$m$$z $$unlar$$ i$$erecektir: $$Category$,$Page total likes$,$Post month$,$

$$Post hour$,$Post weekday$,$ ve $$Paid$.$n i$$lemeyi $$nlemek i$$in "Type" se$$ene$$ini b$$rak$$yoruz$.$

Veri Seti: Facebook Posts Metrics

Takip Edilmesi Gereken Ad$$mlar:

$$ Verinin indirilmesi

$$ Verinin okunmas$$

$$ Verileri B$$lme $($X ve Y $($X$\_$train, X$\_$Test ve y$\_$train, y$\_$test$))$

a$.$ Veri k$$mesini X ve Y'ye b$$l$$n$.$

b$.$ Sa$$lanan y$$zdesel b$$lmeyi kullanarak X ve Y'yi e$$itim ve test setlerine ay$$r$$n

$($varsay$$lan$,\%80$ e$$itim ve $\%20$ testtir$).$

$$ Modelin e$$itimi ve test edilmesi

a$.$ train$\_$test$\_$split$()$esini $$a$$rarak e$$itim ve test setini al$$n

b$.$ Bir a$$rl$$k $(\backslash$theta $)$ vekt$$r$$n$$ tan$$mlay$$n

c$.$ Yukar$$daki bilgileri kullanarak Gradyan $$ni$$ini $($Gradient Descent$)$ uygulay$$n

d$.$ E$$itim ve test verileri i$$in Toplam Kare Hatay$($Sum Squared Error$)$ kaydedin

e$.$ A$$rl$$k matrisini, e$$itim hatalar$$n$$ ve test hatalar$$n$$ d$$nd$$r$$n

f$.$ E$$itim ve test hatalar$$n$$izin ve grafik $$zerinde yorum yap$$n bu $$devi uygula