Create a dataframe
x <- c(0,1,1,2,2,2,2,3,3,4)
y <- c(0,3,1,3,3,2,4,2,5,4)
head(df <- data.frame(x,y))
## x y
## 1 0 0
## 2 1 3
## 3 1 1
## 4 2 3
## 5 2 3
## 6 2 2
Means, sd, variance, correlation, regression
# means
mean(df$x)
## [1] 2
mean(df$y)
## [1] 2.7
# sum of squares
sum((df$x - mean(df$x))^2)
## [1] 12
sum((df$y - mean(df$y))^2)
## [1] 20.1
# variance and sd
var(df$x)
## [1] 1.333333
sd(df$x)
## [1] 1.154701
var(df$y)
## [1] 2.233333
sd(df$y)
## [1] 1.494434
# correlation plot
library(ggpubr)
## Загрузка требуемого пакета: ggplot2
ggscatter(df, x = "x", y = "y",
add = "reg.line", conf.int = TRUE,
cor.coef = TRUE, cor.method = "pearson",
xlab = "x", ylab = "y")
## `geom_smooth()` using formula 'y ~ x'
# correlation analysis
test <- cor.test(df$x, df$y, method = c("pearson"))
test
##
## Pearson's product-moment correlation
##
## data: df$x and df$y
## t = 2.8378, df = 8, p-value = 0.02189
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## 0.1419588 0.9252769
## sample estimates:
## cor
## 0.7082785
# regression
summary(model <- lm(y ~ x, data = df))
##
## Call:
## lm(formula = y ~ x, data = df)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.6167 -0.7625 -0.1167 0.9875 1.3833
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.8667 0.7366 1.177 0.2732
## x 0.9167 0.3230 2.838 0.0219 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.119 on 8 degrees of freedom
## Multiple R-squared: 0.5017, Adjusted R-squared: 0.4394
## F-statistic: 8.053 on 1 and 8 DF, p-value: 0.02189