seed_value <- 19710822 set.seed(seed_value) x <- rnorm(100) y <- rnorm(100) plot(y ~ x) cor.test(x, y) x[101] = 30 y[101] = 29 plot(y ~ x) cor.test(x, y) x <- seq(0, 10, 0.1) y <- 2 * x + 3 + rnorm(x) plot(y ~ x) mymodel <- lm(y ~ x) plot(y ~ x) abline(mymodel, lwd = 2) summary(mymodel) cor.test(x,y)$estimate^2 x <- 0:100 y <- x + (1 / 400) * x ^ 2 + rnorm(x, sd = 3) plot(y ~ x) model1 <- lm(y ~ x) abline(model1, lwd = 2) summary(model1) model2 <- lm(y ~ x + I(x ^ 2)) plot(y ~ x) abline(model1, lwd = 2) lines(x, model2$fitted.values, col = "red", lwd = 4) summary(model2) model3 <- lm(y ~ x + I(x^2) - 1) plot(y ~ x) abline(model1, lwd = 2) lines(x, model2$fitted.values, col = "red", lwd = 4) lines(x, model3$fitted.values, col = "blue", lty = 4, lwd = 2) summary(model3) x <- 0:10 y <- 0:10 mydata <- merge(x, y) mydata$z <- 2 * mydata$x + 3 * mydata$y + mydata$x * mydata$y + rnorm(mydata$x) model1 <- lm(z ~ x + y, data = mydata) model2 <- lm(z ~ x * y, data = mydata) model3 <- lm(z ~ x * y - 1, data = mydata)