data yukle

data olusturum

x <- c(3,6,4,9,1,3,4,7,3,7)  
 y <- c(6,5,2,4,8,6,7,9,5,8) 
data <- data.frame(x, y)

ortalama bulun

ortalama formuller

\[ \bar{x} = \frac{\sum_{i = 1}^n x_i}{n} \]

x <- c(3,6,4,9,1,3,4,7,3,7)
mean(x)
## [1] 4.7

\[ \bar{y} = \frac{\sum_{i = 1}^n y_i}{n} \]

y <- c(6,5,2,4,8,6,7,9,5,8)
mean(y)
## [1] 6

##v varyanlar bulun

varyans formuller

\[ var{x}=\frac{\sum_{x=1}^{n}(x_i-\bar{x})^2}{n-1} \]

x <- c(3,6,4,9,1,3,4,7,3,7)

`

var(x)
## [1] 6.011111

\[ var{y}=\frac{\sum_{x=1}^{n}(y_i-\bar{y})^2}{n-1} \]

y <- c(6,5,2,4,8,6,7,9,5,8)
var(y)
## [1] 4.444444

standart sapmalari bulun

formuller bulun

\[ sd{x}=\sqrt{\frac{\sum_{i=1}^{n}(x_i-\bar{x})^2}{n-1}} \]

x <- c(3,6,4,9,1,3,4,7,3,7)
sd(x)
## [1] 2.451757

\[ sd{y}=\sqrt{\frac{\sum_{i=1}^{n}(y_i-\bar{y})^2}{n-1}} \]

y <- c(6,5,2,4,8,6,7,9,5,8)
sd(y)
## [1] 2.108185

kovaryanslar bulun

formuller

\[ cov(x,y)=\frac{\sum_{i=1}^{n}(x_i-\bar{x})(y_i-\bar{y})}{n-1} \]

x <- c(3,6,4,9,1,3,4,7,3,7)  
 y <- c(6,5,2,4,8,6,7,9,5,8) 
data <- data.frame(x, y)
cov(x,y)
## [1] -0.2222222

##korelasyonlar bulun formüller \[ cor(x,y)=\frac{\sum_{i=1}^{n}(x_i-\bar{x})(y_i-\bar{y})} {\sqrt{\sum_{i=1}^{n}(x_i-\bar{x})^2}\sqrt{\sum_{i=1}^{n}(y_i-\bar{y})^2}} \]

x <- c(3,6,4,9,1,3,4,7,3,7)  
 y <- c(6,5,2,4,8,6,7,9,5,8) 
data <- data.frame(x, y)
cor(x,y)
## [1] -0.04299336

regresyon model

model<-lm(y~x)
summary(model)
## 
## Call:
## lm(formula = y ~ x)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -4.0259 -1.0351 -0.0628  1.6409  3.0850 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)   
## (Intercept)  6.17375    1.59276   3.876   0.0047 **
## x           -0.03697    0.30373  -0.122   0.9061   
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 2.234 on 8 degrees of freedom
## Multiple R-squared:  0.001848,   Adjusted R-squared:  -0.1229 
## F-statistic: 0.01481 on 1 and 8 DF,  p-value: 0.9061
plot(x,y)