Difference between revisions of "Worksheets/Week9"

Latest revision as of 04:51, 6 May 2019

Part 1

The aim is to find the duration [hours] of the experiments to maximize the yield of a biological product. If you operate the reactor too long some side reactions start to occur which consume your product. If you operate for too short a time, then you miss out on the opportunity of creating more product.

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 === Part 1 ===
-Description here
-<html><div data-datacamp-exercise data-lang="r" data-height="auto">
+The aim is to find the duration [hours] of the experiments to maximize the yield of a biological product. If you operate the reactor too long some side reactions start to occur which consume your product. If you operate for too short a time, then you miss out on the opportunity of creating more product.
-    <code data-type="sample-code">
-center = 36
-range = 24
-rw.x <- c(24, 48)
+<html><div data-datacamp-exercise data-lang="r" data-height="500">
-coded.x <- (rw.x - center)/(0.5*range)
+    <code data-type="sample-code">
-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
      </code>
 </div></html>

Difference between revisions of "Worksheets/Week9"

Latest revision as of 04:51, 6 May 2019

Part 1

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