Worksheets/Week9

Part 1

Description here

center = 36 range = 24 rw.x <- c(24, 48) coded.x <- (rw.x - center)/(0.5*range) y0 <- c(28, 63) model.0 <- lm(y0 ~ coded.x) summary(model.0) # What is the interpretation of the # * slope? # * intercept # * why are R2 and SE where they are? # Basic plot of everything so far: raw_data <- data.frame(coded.x = coded.x, y = y0) library(ggplot2) p <- ggplot(data=raw_data, aes(x=coded.x, y=y)) + geom_point(size=5) + xlab("Coded value for x_A") + scale_x_continuous(breaks=seq(-2, 5, 1)) + ylab("Outcome variable") + scale_y_continuous(breaks=seq(0, 150, 10)) + theme_bw() + theme(axis.text=element_text(size=18), legend.position = "none") + theme(axis.title=element_text(face="bold", size=14)) p # Run experiment at center point: predict it first rw.x <- c(24, 48, 36) coded.x <- (rw.x - center)/(0.5*range) x.test <- data.frame(coded.x=coded.x) predict(model.0, newdata=x.test) # Expect a predicted value of 45.5 in the output. Actual: 54 and 55. So about # 10 units difference. # Add the linear fit: through the 2 points plot_data <- data.frame(coded.x = seq(-2, +5, 0.1)) plot_data$y <- predict(model.0, newdata=plot_data) p <- p + geom_line(data=plot_data, color="blue", size=1) p # Try fitting a linear model now through all the data points: rw.x <- c(24, 48, 36, 36) y1 <- c(28, 63, 55, 54) coded.x <- (rw.x - center)/(0.5*range) model.1 <- lm(y1 ~ coded.x) summary(model.1) # Show the linear fit with the extra data point (center points) raw_data <- data.frame(coded.x = coded.x, y = y1) plot_data$y <- predict(model.1, newdata=plot_data) p <- p + geom_point(aes(x=coded.x, y=y, color='darkgreen', size=5), data=raw_data) p <- p + geom_line(data=plot_data, color="darkgreen", size=1) p # A a quadratic component through all the data points: rw.x <- c(24, 48, 36, 36) y1 <- c(28, 63, 55, 54) coded.x <- (rw.x - center)/(0.5*range) model.1.quad <- lm(y1 ~ coded.x + I(coded.x^2)) summary(model.1.quad) # Show the quadratic fit between -2 and +2 in coded units # In real-world units this corresonds to _____ and _____ plot_data <- data.frame(coded.x = seq(-2, +3, 0.1)) plot_data$y <- predict(model.1.quad, newdata=plot_data) p <- p + geom_line(data=plot_data, color="red", size=1) p # Try a new point at +2: that is RW = coded * 0.5 * range + center; 60 hours # y = 66. y0 <- c(28, 63) rw.x <- c(24, 48, 36, 36, 60) y2 <- c(28, 63, 55, 54, 66) coded.x <- (rw.x - center)/(0.5*range) model.2.quad <- lm(y2 ~ coded.x + I(coded.x^2)) summary(model.2.quad) # Plot it again: DO: add the new point and response here plot_data <- data.frame(coded.x = seq(-2, +3, 0.1)) plot_data$y <- predict(model.2.quad, newdata=plot_data) p <- p + geom_line(data=plot_data, color="purple", size=1) p