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--- c:ma:regression_lecture_note [2023/10/27 22:18] – created hkimscil
+++ c:ma:regression_lecture_note [2023/10/27 22:19] (current) – hkimscil
@@ Line 1: / Line 1: @@
 {{regression.lecturenote.r}}
+<code>
+set.seed(401)
+sn <- 25
+x <- rnorm(sn, 100, 10)
+x
+y <- 1.4 * x + 2 + rnorm(sn, 0, 10)
+y
+df <- data.frame(x, y)
+# density graph
+install.packages("ggplot2")
+library(ggplot2)
+ggplot(data=df, aes(y)) +
+  geom_histogram() +
+  geom_vline(aes(xintercept=mean(y)),
+             color="red", linetype="dashed", size=1) +
+  coord_flip()
+ggplot(data=df, aes(y)) +
+  geom_density(color="blue", size=1.5) +
+  geom_vline(aes(xintercept=mean(y)),
+             color="red", linetype="dashed", size=1) +
+  coord_flip()
+lm.mod <- lm(y~x, data=df)
+summary(lm.mod)
+str(lm.mod)
+inc.y <- lm.mod$coefficients[1]
+slope.x <- lm.mod$coefficients[2]
+inc.y
+slope.x
+ggplot(data=df, aes(x,y)) +
+  geom_point(color="blue", size=1.5, pch=1.5) +
+  geom_hline(aes(yintercept=mean(y))) +
+  geom_abline(intercept=inc.y, slope=slope.x)
+ggplot(data=df, aes(x,y)) +
+  geom_point(color="blue", size=2.5, pch=2) +
+  geom_hline(aes(yintercept=mean(y)), size=1.5, color="red") +
+  geom_abline(intercept=inc.y, slope=slope.x, size=1.5, color="darkgreen")
+################################
+################################
+################################
+################################
+set.seed(101)
+sn <- 400
+x <- rnorm(sn, 100, 10)
+x
+y <- 1.4*x + 2 + rnorm(sn, 0, 16)
+y
+df <- data.frame(x,y)
+# density graph
+ggplot(data=df, aes(y)) +
+  geom_histogram() +
+  geom_vline(aes(xintercept=mean(y)),
+             color="red", linetype="dashed", size=1) +
+  coord_flip()
+ggplot(data=df, aes(y)) +
+  geom_density(color="blue", size=1.5) +
+  geom_vline(aes(xintercept=mean(y)),
+             color="red", linetype="dashed", size=1) +
+  coord_flip()
+ggplot(data=df, aes(x,y)) +
+  geom_point(color="blue", size=1.5, pch=2) +
+  geom_hline(aes(yintercept=mean(y)), size=1, color="darkgreen") +
+  geom_abline(intercept=10, slope=1.5, size=1.5, color="red")
+lm.mod2 <- lm(y~x, data=df)
+sum.lm.mod2 <- summary(lm.mod2)
+sum.lm.mod2
+lm.mod2$coefficients[2]
+lm.mod2$coefficients[1]
+b <- lm.mod2$coefficients[2]
+a <- lm.mod2$coefficients[1]
+ggplot(data=df, aes(x,y)) +
+  geom_point(color="blue", size=1.5, pch=2) +
+  geom_hline(aes(yintercept=mean(y)), size=1, color="darkgreen") +
+  geom_abline(intercept=a, slope=b, size=1.5, color="red")
+lm.mod2$residuals
+sum(lm.mod2$residuals^2)
+ss.res <- sum(lm.mod2$residuals^2)
+mean.y <- mean(df$y)
+var.tot <- var(df$y)
+df.tot <- length(df$y)-1
+ss.tot <- var.tot*df.tot
+ss.tot
+y.hat <- lm.mod2$fitted.values
+y.hat - mean(df$y)
+explained <- y.hat - mean(df$y)
+ss.exp <- sum(explained^2)
+ss.exp
+ss.res
+ss.exp + ss.res
+ss.tot
+r.square <- ss.exp / ss.tot
+r.square
+sum.lm.mod2
+r.coeff <- sqrt(r.square)
+r.coeff
+cor(x,y)
+###
+ggplot(data=df, aes(x,y)) +
+  geom_point(color="blue", size=1.5, pch=1.5) +
+  geom_hline(aes(yintercept=mean(y)), size=1, color="darkgreen") +
+  stat_smooth(method = "lm",
+              formula = y ~ x,
+              geom = "smooth", color="red", size=1)
+</code>