.Rhistory (1)

arrows(x0 = 3.5, x1 = 7.5, y0 = 7.5, y1 = 7.5, code = 0, lwd = 2, lty = 2)
text(4.5, 8, labels = expression(paste(Delta,"X")), cex = 1.5)
text(3.2, 5.75, labels = expression(paste(Delta,"Y")), cex = 1.5)
text(4, 0.35, expression(Y == beta[0] + beta[1]*X), cex = 2, col = "blue")
library(shape)
Arrows(3.5, 1.0, 3.1, 2.8, lwd = 1.5, col = "blue")
text(2.5, 8,expression(beta[1] == over(Delta*Y,Delta*X)), cex = 1.5)
lines(0:10, 5 + 0.9 * 0:10, lwd = 2, col = "blue")
points(11.03, 8.674, pch = 20)
set.seed(400)
x <- 1:1000/100
Y <- 5 + 0.9 * x +rnorm(1000)
plot(x, Y, pch = ".", # xaxt = "n", yaxt = "n",
xlab = "X", ylab = "Y",
xlim = c(0,10), ylim = c(0,10),
bty = "l", cex.lab = 1.5, cex = 1.75,
main = "Population line and X-Y values")
lines(x = c(6.03, 6.03), y = c(8.674, 11.03), col = "red", lty = 3, lwd = 2)
lines(0:10, 5 + 0.9 * 0:10, lwd = 2, col = "blue")
x <- 1:1000/100
Y <- 5 + 0.9 * x +rnorm(1000)
plot(x, Y, pch = ".", # xaxt = "n", yaxt = "n",
xlab = "X", ylab = "Y",
xlim = c(0,15), ylim = c(0,15),
bty = "l", cex.lab = 1.5, cex = 1.75,
main = "Population line and X-Y values")
plot(x, Y, pch = ".", # xaxt = "n", yaxt = "n",
xlab = "X", ylab = "Y",
xlim = c(0,10), ylim = c(0,15),
bty = "l", cex.lab = 1.5, cex = 1.75,
main = "Population line and X-Y values")
plot(x, Y, pch = ".", # xaxt = "n", yaxt = "n",
xlab = "X", ylab = "Y",
xlim = c(0,10), ylim = c(0,17),
bty = "l", cex.lab = 1.5, cex = 1.75,
main = "Population line and X-Y values")
lines(x = c(6.03, 6.03), y = c(8.674, 11.03), col = "red", lty = 3, lwd = 2)
lines(x = c(6.03, 6.03), y = c(8.674, 11.03), col = "red", lty = 3, lwd = 2)
lines(0:10, 5 + 0.9 * 0:10, lwd = 2, col = "blue")
set.seed(400)
x <- 1:1000/100
Y <- 5 + 0.9 * x +rnorm(1000)
plot(x, Y, pch = ".", # xaxt = "n", yaxt = "n",
xlab = "X", ylab = "Y",
xlim = c(0,10), ylim = c(0,17),
bty = "l", cex.lab = 1.5, cex = 1.75,
main = "Population line and X-Y values")
lines(x = c(6, 6), y = c(8, 10.4), col = "red", lty = 3, lwd = 2)
points(6, 10.4, pch = 20)
points(6, 8, pch = 20)
text(7, 4, labels = expression(Y[i] - Y == epsilon[i]),cex = 1.5, col = "red")
lines(x = c(6, 6), y = c(8, 10.4), col = "red", lty = 1, lwd = 2)
points(6, 8, pch = 20)
lines(0:10, 5 + 0.9 * 0:10, lwd = 2, col = "blue")
text(7, 9, labels = expression(Y[i] - Y == epsilon[i]),cex = 1.5, col = "red")
arrows(x0 = 3.5, y0 = 3.5, y1 = 7.5, code = 0, lwd = 2, lty = 2)
arrows(x0 = 1, y0 = 5.9, x1 = 3, y1 = 7.7, code = 0, lwd = 2, lty = 2)
arrows(x0 = 1, y0 = 5.9, x1 = 3, y1 = 3, code = 0, lwd = 2, lty = 2)
arrows(x0 = 1, y0 = 5.9, x1 = 3, y1 = 5.9, code = 0, lwd = 2, lty = 2)
arrows(x0 = 0.5, y0 = 5.45, x1 = 4, y1 = 5.45, code = 0, lwd = 2, lty = 2)
arrows(x0 = 4, x1 = 4, y0 = 5.45, y1 = 8.6, code = 0, lwd = 2, lty = 2)
text(2.5, 4, labels = expression(paste(Delta,"X")), cex = 1.5)
text(2.5, 4.5, labels = expression(paste(Delta,"X")), cex = 1.5)
text(4.5, 7, expression(Y == beta[0] + beta[1]*X), cex = 2, col = "blue")
text(3.2, 7, labels = expression(paste(Delta,"Y")), cex = 1.5)
text(4.5, 7, labels = expression(paste(Delta,"Y")), cex = 1.5)
text(4.3, 7, labels = expression(paste(Delta,"Y")), cex = 1.5)
text(2.5, 4.5,expression(beta[1] == over(Delta*Y,Delta*X)), cex = 1.5)
text(4.5, 4,expression(beta[1] == over(Delta*Y,Delta*X)), cex = 1.5)
text(4.2, 4,expression(beta[1] == over(Delta*Y,Delta*X)), cex = 1.5)
text(2, 13, expression(Y == beta[0] + beta[1]*X == 5 + 0.9 * X), cex = 2, col = "blue")
text(2, 13, expression(Y == beta[0] + beta[1]*X = 5 + 0.9 * X), cex = 2, col = "blue")
text(2, 13, expression(Y == beta[0] + beta[1]*X), cex = 2, col = "blue")
text(2, 13, expression(Y == 5 + 0.9*X), cex = 2, col = "blue")
text(2, 14, expression(Y == beta[0] + beta[1]*X =), cex = 2, col = "blue")
text(2, 14, expression(Y == beta[0] + beta[1]*X ==), cex = 2, col = "blue")
text(2, 14, paste(expression(Y == beta[0] + beta[1]*X), " = 5 + 0.9 * X"), cex = 2, col = "blue")
text(2, 14, paste(expression(Y == beta[0] + beta[1]*X), cex = 2, col = "blue")
########make a figure and label it slr#####
set.seed(400)
x <- 1:1000/100
Y <- 5 + 0.9 * x +rnorm(1000)
plot(x, Y, pch = ".", # xaxt = "n", yaxt = "n",
xlab = "X", ylab = "Y",
xlim = c(0,10), ylim = c(0,17),
bty = "l", cex.lab = 1.5, cex = 1.75,
main = "Population line and X-Y values")
lines(x = c(6, 6), y = c(8, 10.4), col = "red", lty = 1, lwd = 2)
points(6, 8, pch = 20)
lines(0:10, 5 + 0.9 * 0:10, lwd = 2, col = "blue")
text(7, 9, labels = expression(Y[i] - Y == epsilon[i]),cex = 1.5, col = "red")
arrows(x0 = 0.5, y0 = 5.45, x1 = 4, y1 = 5.45, code = 0, lwd = 2, lty = 2)
arrows(x0 = 4, x1 = 4, y0 = 5.45, y1 = 8.6, code = 0, lwd = 2, lty = 2)
text(2.5, 4.5, labels = expression(paste(Delta,"X")), cex = 1.5)
text(4.3, 7, labels = expression(paste(Delta,"Y")), cex = 1.5)
text(4.2, 4,expression(beta[1] == over(Delta*Y,Delta*X)), cex = 1.5)
text(2, 15, expression(Y == beta[0] + beta[1]*X), cex = 1.7, col = "blue")
text(2, 11, expression(Y == 5 + 0.9*X), cex = 1.7, col = "blue")
library(shape)
Arrows(3.5, 1.0, 3.1, 2.8, lwd = 1.5, col = "blue")
text(2, 14, expression(Y == beta[0] + beta[1]*X), cex = 1.7, col = "blue")
text(2, 12, expression(Y == 5 + 0.9*X), cex = 1.7, col = "blue")
########make a figure and label it slr#####
set.seed(400)
x <- 1:1000/100
Y <- 5 + 0.9 * x +rnorm(1000)
plot(x, Y, pch = ".", # xaxt = "n", yaxt = "n",
xlab = "X", ylab = "Y",
xlim = c(0,10), ylim = c(0,17),
bty = "l", cex.lab = 1.5, cex = 1.75,
main = "Population line and X-Y values")
lines(x = c(6, 6), y = c(8, 10.4), col = "red", lty = 1, lwd = 2)
points(6, 8, pch = 20)
lines(0:10, 5 + 0.9 * 0:10, lwd = 2, col = "blue")
text(7, 9, labels = expression(Y[i] - Y == epsilon[i]),cex = 1.5, col = "red")
arrows(x0 = 0.5, y0 = 5.45, x1 = 4, y1 = 5.45, code = 0, lwd = 2, lty = 2)
arrows(x0 = 4, x1 = 4, y0 = 5.45, y1 = 8.6, code = 0, lwd = 2, lty = 2)
text(2.5, 4.5, labels = expression(paste(Delta,"X")), cex = 1.5)
text(4.3, 7, labels = expression(paste(Delta,"Y")), cex = 1.5)
text(4.2, 4,expression(beta[1] == over(Delta*Y,Delta*X)), cex = 1.5)
text(2, 14, expression(Y == beta[0] + beta[1]*X), cex = 1.7, col = "blue")
text(2, 12.5, expression(Y == 5 + 0.9*X), cex = 1.6, col = "blue")
text(2, 14, expression(E{Y|X} == beta[0] + beta[1]*X), cex = 1.7, col = "blue")
text(2, 14, expression(E\{Y|X\} == beta[0] + beta[1]*X), cex = 1.7, col = "blue")
text(2, 14, expression(mu[Y|X] == beta[0] + beta[1]*X), cex = 1.7, col = "blue")
plot(x, Y, pch = ".", # xaxt = "n", yaxt = "n",
xlab = "X", ylab = "Y",
xlim = c(0,10), ylim = c(0,17),
bty = "l", cex.lab = 1.5, cex = 1.75,
main = "Population line and X-Y values")
text(2, 14, expression(mu[Y|X] == beta[0] + beta[1]*X), cex = 1.7, col = "blue")
text(2, 14, expression(mu[Y,X] == beta[0] + beta[1]*X), cex = 1.7, col = "blue")
plot(x, Y, pch = ".", # xaxt = "n", yaxt = "n",
xlab = "X", ylab = "Y",
xlim = c(0,10), ylim = c(0,17),
bty = "l", cex.lab = 1.5, cex = 1.75,
main = "Population line and X-Y values")
text(2, 14, expression(mu[Y,X] == beta[0] + beta[1]*X), cex = 1.7, col = "blue")
text(2, 14, expression(mu[Y]|[X] == beta[0] + beta[1]*X), cex = 1.7, col = "blue")
text(2, 14, expression(mu[YX] == beta[0] + beta[1]*X), cex = 1.7, col = "blue")
########make a figure and label it slr#####
z1 = xyz.tips[, 3],
xlim = c(0, 10),
ylim = c(0, 10),
zlim = c(0, 10),
phi = 35,
theta = 450,
lwd = 2,
d = 3,
bty = "g",
ticktype = "detailed")
bookdown:::serve_book()
install.packages("servr")
bookdown:::serve_book()
servr::daemon_stop("4747113896")
<<<<<<< HEAD
=======
mhGoats <- data.frame(Door1 = c("Car", "Aldebaran", "Casiopeia"),
Door2 = c("Aldebaran", "Car", "Casiopeia"),
Door3 = c("Aldebaran", "Casiopeia", "Car"))
mhGoats
mhGoats <- data.frame(Door1 = c("Car", "Aldebaran", "Casiopeia"),
Door2 = c("Aldebaran", "Car", "Casiopeia"),
Door3 = c( "Casiopeia", "Aldebaran","Car"),
ResultIfSwitch = c("Goat", "Car", "Car"))
mhGoats <- data.frame(Door1 = c("Car", "Aldebaran", "Casiopeia"),
Door2 = c("Aldebaran", "Car", "Casiopeia"),
Door3 = c( "Casiopeia", "Aldebaran","Car"),
ResultIfSwitch = c("Goat", "Car", "Car"))
mhGoats
mhGoats <- data.frame(Door1 = c("Car", "Aldebaran", "Casiopeia"),
Door2 = c("Casiopeia", "Car", "Aldebaran"),
Door3 = c( "Casiopeia", "Aldebaran","Car"),
ResultIfSwitch = c("Goat", "Car", "Car"))
mhGoats
mhGoats <- data.frame(Door1 = c("Car", "Aldebaran", "Casiopeia"),
Door2 = c("Casiopeia", "Car", "Aldebaran"),
Door3 = c("Aldebaran", "Casiopeia", "Car"),
ResultIfSwitch = c("Goat", "Car", "Car"))
mhGoats
mhGoats <- data.frame(Door1 = c("Car", "Goat", "Goat"),
Door2 = c("Goat", "Car", "Goat"),
Door3 = c("Goat", "Goat", "Car"),
ResultIfSwitch = c("Goat", "Car", "Car"))
mhGoats <- data.frame(Door1 = c("Car", "Goat", "Goat"),
Door2 = c("Goat", "Car", "Goat"),
Door3 = c("Goat", "Goat", "Car"),
ResultIfSwitch = c("Goat", "Car", "Car"))
mhGoats
mhGoats
knitr::include_graphics("images/CH2Windows.png")
knitr::include_graphics("images/CH2Windows.png")
knitr::include_graphics("images/CH2Windows.png")
knitr::include_graphics("images/CH2Console.png")
knitr::include_graphics("images/CH2Console2.png")
knitr::include_graphics("images/CH2IncompleteError.png")
knitr::include_graphics("images/CH2Error.png")
knitr::include_graphics("images/CH2RunChunk.png")
knitr::include_graphics("images/CH2RmdSave.png")
```{r BasicFunctions, echo=FALSE}
#two ways to calculate the sum of 1 and 5
1 + 5
sum(c(1,5))
#two ways to calculate the mean of 8, 4, and 6
(8 + 4 + 6) / 3
mean(c(8,4,6))
knitr::include_graphics("images/CH2RmdSave.png")
knitr::include_graphics("images/CH2htmlSave.png")
knitr::include_graphics("images/CH2WD.png")
knitr::include_graphics("images/CH2Plot.png")
knitr::include_graphics("images/CH2Packages.png")
mymatrix <- cbind(myvector, myvector2)
mymatrix
mymatrix <- cbind(myvector, myvector2)
myvector <- c(1,2,3)
myvector
myvector2 <- c("one","two","three")
myvector2
help(c) #help() allows you to search for a description of a given function
mymatrix <- cbind(myvector, myvector2)
mymatrix
help(cbind)
mydataframe <- as.data.frame(cbind(myvector, myvector2))
mydataframe
help(as.data.frame)
knitr::include_graphics("images/CH2Import2.png")
plotPoly <- function(b0, b1, b2, b3, xmin, xmax){ # name function and arguments
x <- seq(from = xmin, to = xmax, length.out = 100) # create x values
y <- b0 + b1 * x + b2 * x^2 + b3 * x^3 # calculate y values
plot(y ~ x, type = "l") # plot the results
}
plotPoly(b0 = 1, b1 = 0.5, b2 = 0.03, b3 = -0.01, xmin = -5, xmax = 10)
plotPoly(b0 = 1, b1 = 0.5, b2 = 0.03, b3 = -0.01, xmin = -10, xmax = 10)
a <- c(1, 2, 3, 4, 5)
b <- c(10, 20, 30, 40, 50)
a + 100
## [1] 101 102 103 104 105
a + b
## [1] 11 22 33 44 55
(a + b) / 10
a <- 1:5
b <- 1:5
ab.sum <- a + b
ab.diff <- a - b
ab.prod <- a * b
ab.sum
## [1]  2  4  6  8 10
ab.diff
## [1] 0 0 0 0 0
ab.prod
mydata <- data.frame(Y1 = c("treatment 1", "treatment 2", "treatment 3"), Y2 = c(35, 23, 30)) # Create data frame with 2 columns and 3 rows
mydata # see the contents of the data frame
str(mydata) # see the structure of the data frame
class(mydata) # see the class of the data frame
library(pander) # we need to install pander first
pander(mydata, caption = "Table showing my data.") #pander() creates a table for the data
clover <- read.csv("Datasets/Lab01clover.txt", header = TRUE) # read in data.
help(clover) # Read about the nature of the data set.
(avg.lnwt <- mean(clover$lnwt)) # obtain the average lnwtance; note the use of $ to select parts of an object and the outer parentheses to display the result.
(med.lnwt <- median(clover$lnwt)) # median or 50th percentile
quantile(clover$lnwt, 0.5) # 50th percentile is the same as the median
(var.lnwt <- var(clover$lnwt)) # variance
(std.lnwt <- sd(clover$lnwt)) # standard deviation
sum(clover$lnwt)/length(clover$lnwt) # manual calculation of average
sum( (clover$lnwt - avg.lnwt) ^ 2 ) / (length(clover$lnwt) - 1)
(rng.lnwt <- range(clover$lnwt)) # output is a vector of lenght 2
min(clover$lnwt) # minimum braking lnwtance
max(clover$lnwt) # maximum braking lnwtance
(cv.lnwt <- std.lnwt / avg.lnwt) # coefficient of variation
```{r ps freqhist, echo = TRUE, include = TRUE}
(sample.size <- length(clover$lnwt))
(nbins <- max(8, (1 + log(sample.size, 2)))) # we round down for bins
clover$bin <- cut(clover$lnwt, breaks = nbins) # create column with bin
(freq.table <- as.data.frame(xtabs( ~clover$bin))) # creates frequency table
pander(freq.table) # format the table a little better
plot(freq.table, xlim = c()) # make histogram "by hand"
hist(clover$lnwt) # by default it uses Sturges rule for bins.
summary(clover$lnwt) # summary of a numeric variable or vector
class(clover$lnwt) # a numeriv vector contains real numbers
summary(clover$bin) # this is a character variable coded as a factor
class(clover$bin)
summary(clover) # gives the summary for all variables
class(summary(clover)) # This is functional programming; nested functions
mode(summary(clover))
str(summary(clover)) # See the inside of an object!!
summary(clover)[1,1] # get the first element of the table
summary(clover)[1,] # get the first row of the summary table
summary(clover)[,1] #  get the first column of the summary table
myrange.factor = 1.5 # save number in a named object for later use
boxplot(clover$lnwt, range = myrange.factor)
text(x = 0.70, y = median(clover$lnwt), label = "Median")
boxplot(clover$lnwt, range = myrange.factor)
clover$lnwt
plot(clover$lnwt)
boxplot(clover$lnwt)
boxplot(clover$lnwt, range = 1)
boxplot(clover$lnwt, range = 1)
boxplot(clover$lnwt, range = 1.5)
boxplot(clover$lnwt, range = 1.5)
myrange.factor
boxplot(clover$lnwt, range = myrange.factor)
boxplot(clover$lnwt, range = myrange.factor)
boxplot(clover$lnwt, range = 1.5)
boxplot(clover$lnwt, range = 1.5)
boxplot(clover$lnwt, range = 1.5)
boxplot(clover$lnwt, range = 1.5)
boxplot(clover$lnwt, range = 1.5)
boxplot(clover$lnwt, range = 1.5)
myrange.factor <- 1.5
boxplot(clover$lnwt, range = myrange.factor)
text(x = 0.70, y = median(clover$lnwt), label = "Median")
boxplot(clover$lnwt, range = myrange.factor)
myrange.factor = 1.5 # save number in a named object for later use
boxplot(heifer$Birth_Wt, range = myrange.factor)
myrange.factor <- 1.5
boxplot(clover$lnwt, range = myrange.factor)
text(x = 0.70, y = median(clover$lnwt), label = "Median")
text(x = 0.65, y = quantile(clover$lnwt, 0.75), label = "3rd quartile or 75% quantile")
text(x = 1.30, y = quantile(clover$lnwt, 0.75), label = "Upper Hinge")
text(x = 0.65, y = quantile(clover$lnwt, 0.25), label = "1st quartile or 25% quantile")
text(x = 1.30, y = quantile(clover$lnwt, 0.25), label = "Lower Hinge")
myrange.factor = 0.5
boxplot(clover$lnwt, range = myrange.factor)
text(x = 0.70, y = median(clover$lnwt), label = "Median")
text(x = 0.65, y = quantile(clover$lnwt, 0.75), label = "3rd quartile or 75% quantile")
text(x = 1.30, y = quantile(clover$lnwt, 0.75), label = "Upper Hinge")
text(x = 0.65, y = quantile(clover$lnwt, 0.25), label = "1st quartile or 25% quantile")
text(x = 1.30, y = quantile(clover$lnwt, 0.25), label = "Lower Hinge")
(iqrange <- IQR(clover$lnwt)) # Calculate the interquartile range
(uplimit <- quantile(clover$lnwt, 0.75) + myrange.factor * iqrange)
(rows.where.lt.uplimit <- which(clover$lnwt <= uplimit)) # gives row numbers of those that are less than uplimit
clover$lnwt[rows.where.lt.uplimit] # gives lnwt in those rows
(up.fence <- max(clover$lnwt[rows.where.lt.uplimit])) # gives the value we seek
(outl <- clover$lnwt[clover$lnwt > up.fence]) # We have outliers!
text(x = 0.65, y = up.fence, label = "Upper Fence")
sumry.by.temp
sumry.by.temp <- by(data = clover$lnwt, INDICES = clover$temp, FUN = summary
)
sumry.by.temp
pander(sumry.by.temp)
class(sumry.by.temp)
str(sumry.by.temp)
bookdown:::serve_book()
servr::daemon_stop("4559906504")
pander(freq.table) # format the table a little better
set.seed(1221) # To always make the same random sample.
set.seed(1221) # To always make the same random sample.
smpl <- rchisq(n = 100, df = 2)
smpl
mean(c(smpl, 200))
smpl <- rchisq(n = 100, df = 2)
(avg <- mean(smpl))
mean(c(smpl, 200))
plot(sapply(sort(c(-20:80/10, mean(smpl))), FUN = function(i) sum((smpl - i)^2)) ~
sort(c(-20:80/10, mean(smpl))),
type = "l",
lwd = 4,
col = "chocolate",
ylab = "Sum of squared deviations",
xlab = "Value to calculate deviation to")
arrows(x0 = mean(smpl) , y0 = 1500,
x1 = mean(smpl), y1 = sum((smpl - mean(smpl))^2),
angle = 25, length = 0.2,
lwd = 2)
text(x = mean(smpl) , y = 1900 ,
labels = c("Sum of squared deviations \n is minimized when \n X equals the average"))
median(smpl)
median(c(smpl, 200))
plot(sapply(sort(c(-20:80/10, median(smpl))), FUN = function(i) sum(abs(smpl - i))) ~
sort(c(-20:80/10, median(smpl))),
type = "l",
lwd = 4,
col = "chocolate",
ylab = "Sum of absolute deviations",
xlab = "Value to calculate deviation to")
arrows(x0 = median(smpl) , y0 = 350,
x1 = median(smpl), y1 = sum(abs(smpl - median(smpl))),
angle = 25, length = 0.2,
lwd = 2)
text(x = median(smpl) , y = 400 ,
labels = c("Sum of absolute deviations \n is minimized when \n X equals the median"))
```{r Bimodal, message=FALSE, echo=FALSE, out.width='70%', fig.align='center', fig.cap="Example of bimodal distribution. A single central confidence interval would not be very useful. These data should be explored to find a way to stratify into groups."}
set.seed(1333)
smpl2 <- c(rnorm(n = 50, mean = 10, sd = 1), rnorm(n = 50, mean = 20, sd = 2))
plot(density(smpl2, adjust = 0.5),
type = "l",
lwd = 4,
col = "chocolate",
ylab = "Probability density",
xlab = "Random variable value",
main = "")
var(c(1, 2, 3))
mean(c(1, 2, 3))
hvirus <- expand.grid(marker = c("-M", "+M"), Hanta = c("-H", "+H"))
hvirus
str(cards)
str(S)
ProbH <- 0.17
ProbNoH <- 1 - ProbH
ProbM <- 0.63
ProbNoM <- 1 - ProbM
ProbHM <- 0.05
ProbHNoM <- ProbH - ProbHM
ProbHNoM
ProbNoHM <- ProbM - ProbHM
ProbNoHM
P.H <- 0.17
P.h <- 1 - P.H
P.M <- 0.63
P.m <- 1 - P.M
P.HM <- 0.05
P.Hm <- P.H - P.HM
P.hM <- P.M - P.HM
P.hm <- 1 - P.h - P.Hm - P.hM
hvirus
# Create a data frame with the probabilities for each event
hvirus <- expand.grid(marker = c("m", "M"), Hanta = c("h", "H"))
# Create a data frame with the probabilities for each event
hvirus <- expand.grid(Hanta = c("h", "H"), marker = c("m", "M"))
hvirus
hvirus$probs <- c(P.hm, P.Hm, P.hM, P.HM)
hvirus
P.hm <- 1 - P.HM - P.Hm - P.hM
hvirus$probs <- c(P.hm, P.Hm, P.hM, P.HM)
hvirus
sum(hvirus$probs)
install.packages("prob")
library(prob)
marginal(hvirus, vars = "marker")
marginal(hvirus, vars = "Hanta")
P.H * P.M == P.HM
P.h * P.m == P.hm
hvirus
hv.event <- subset(hvirus, Hanta = "H")
M.event <- subset(hvirus, marker = "M")
Prob(hvirus, given = M.event)
M.event
H.event
# Create events for virus and marker
H.event <- subset(hvirus, Hanta = "H")
H.event
# Create events for virus and marker
H.event <- subset(hvirus, Hanta == "H")
M.event <- subset(hvirus, marker == "M")
H.event
M.event
Prob(hvirus, given = M.event)
H.event
M.event
Prob(H.event, given = M.event)
Prob(!H.event, given = M.event)
m.event <- subset(hvirus, marker == "m")
Prob(H.event, given = m.event)
m.event
h.event <- subset(hvirus, Hanta == "h")
Prob(h.event, given = m.event)
Prob(H.event, given = M.event) + Prob(h.event, given = m.event)
Prob(h.event, given = M.event)
Prob(H.event, given = M.event) + Prob(h.event, given = M.event)
Prob(h.event, given = M.event)
P.H <- 0.30
?pbinom # lower.tail = FALSE, q = 9, size = 30, prob = 0.10
Prob(H) * Prob(M, given = H)/(Prob(H) * Prob(M, given = H) + Prob(h) * Prob(M, given = h))
library(prob)
P.H <- 0.17
P.h <- 1 - P.H
P.M <- 0.63
P.m <- 1 - P.M
P.HM <- 0.05
P.Hm <- P.H - P.HM
P.hM <- P.M - P.HM
P.hm <- 1 - P.HM - P.Hm - P.hM
hvirus$probs <- c(P.hm, P.Hm, P.hM, P.HM)
marginal(hvirus, vars = "marker")
marginal(hvirus, vars = "Hanta")
# Is the product of the marginals equal to the joint probability?
P.H * P.M == P.HM
P.h * P.m == P.hm
# Create events for virus and marker
H <- subset(hvirus, Hanta == "H")
M <- subset(hvirus, marker == "M")
Prob(H, given = M)
h <- subset(hvirus, Hanta == "h")
Prob(h, given = M)
Prob(H, given = M) + Prob(h, given = M)
P.H <- 0.30 # New prior probability
P.H * Prob(M, given = H)/(P.H * Prob(M, given = H) + (1 - P.H) * Prob(M, given = h))
pbinom(q = 9, size = 30, prob = 0.10, lower.tail = FALSE)
pbinom(q = 9, size = 50, prob = 0.20, lower.tail = FALSE)
plot(dbinom, x = 0:50, size = 50, prob = 0.20)
plot(dbinom(x = 0:50, size = 50, prob = 0.20) ~ 0:50)
plot(dbinom(x = 0:50, size = 50, prob = 0.20) ~ c(0:50))
plot(dbinom(x = 0:50, size = 50, prob = 0.20) ~ c(0:50), type = "h")
plot(pbinom(q = 9, size = 60:80, prob = 0.20, lower.tail = FALSE) ~ c(60:80))
plot(pbinom(q = 9, size = 60:80, prob = 0.20, lower.tail = FALSE) ~ c(60:80), type = "v")
plot(pbinom(q = 9, size = 60:80, prob = 0.20, lower.tail = FALSE) ~ c(60:80), type = "S")
c(60:80)[which(pbinom(q = 9, size = 60:80, prob = 0.20, lower.tail = FALSE) >= 0.95)]
# Graphical solution
plot(
pbinom(q = 9,
size = 60:80,
prob = 0.20,
lower.tail = FALSE) ~
c(60:80),
type = "S",
ylab = "P(10 or more seeds germinating)")
rate <- 0.0001 # per foot
lambda <- 1000 * rate # per roll
dpois(q = 0, lambda = lambda)
dpois(x = 0, lambda = lambda)
lambda <- 0.0001 # per foot
s = 1000 # feet per roll
rate <- s * lambda # per roll
dpois(x = 0, lambda = rate)
-log(0.999)
-log(0.99)
-log(0.99)/s
-log(0.95)/s
lambda <- 0.00015 # per foot
s = 1000 # feet per roll
rate <- s * lambda # per roll
dpois(x = 0, lambda = rate)
-log(0.95)/s
-log(0.95)
rate
dpois(x = 0, lambda = 100:1/200)
c(100:1/200)[which(dpois(x = 0, lambda = 100:1/200) <= 0.95)]
c(100:1/200)[which(dpois(x = 0, lambda = 100:1/200) >= 0.95)]
0.050/1000
max(c(100:1/200)[which(dpois(x = 0, lambda = 100:1/200) >= 0.95)])
0.05*100
max(c(100:1/200)[which(dpois(x = 0, lambda = seq(from = 0.05, to = 0.045, by = 0.001)) >= 0.95)])
max(c(100:1/200)[which(dpois(x = 0, lambda = seq(from = 0.05, to = 0.045, by = -0.001)) >= 0.95)])
max(c(100:1/200)[which(dpois(x = 0, lambda = seq(from = 0.05, to = 0.055, by = 0.001)) >= 0.95)])
-log(0.95)/s
max(c(seq(from = 0.05, to = 0.055, by = 0.001))[which(dpois(x = 0, lambda = seq(from = 0.05, to = 0.055, by = 0.001)) >= 0.95)])
max(c(guesses)[which(dpois(x = 0, lambda = guesses) >= 0.95)])
guesses <- seq(from = 0.05, to = 0.055, by = 0.001)
max(c(guesses)[which(dpois(x = 0, lambda = guesses) >= 0.95)])
-log(0.95)/s
max(c(guesses)[which(dpois(x = 0, lambda = guesses) >= 0.95)])
max(c(guesses)[which(dpois(x = 0, lambda = guesses) >= 0.95)])/s
curve(dnorm, from = -3.5, to = 4.5)
curve(dnorm(x, sd = 2), from = -3.5, to = 4.5, add = TRUE, col = "chocolate", lwd = 2)
curve(dnorm, from = -5.5, to = 5.5)
curve(dnorm(x, sd = 2), from = -3.5, to = 4.5, add = TRUE, col = "chocolate", lwd = 2)
curve(dnorm(x, sd = 2), from = -5.5, to = 5.5, add = TRUE, col = "chocolate", lwd = 2)
curve(dnorm(x, mean = 1), from = -5.5, to = 5.5, add = TRUE, col = "skyblue", lwd = 2)
# Mutually exclusive events. Add the separate probabilities.
pnorm(q = 1, mean = 5, sd = sqrt(2))
# Mutually exclusive events. Add the separate probabilities.
pnorm(q = 2, mean = 5, sd = sqrt(2))
pnorm(q = 7, mean = 5, sd = sqrt(2), lower.tail = FALSE)
# Mutually exclusive events. Add the separate probabilities.
left.area <- pnorm(q = 2, mean = 5, sd = sqrt(2))
right.area <- pnorm(q = 7, mean = 5, sd = sqrt(2), lower.tail = FALSE)
left.area + right.area
zTable <- matrix(NA, nrow = 33, ncol = 10)
for (j in 0:9) {
zTable[i, j] <- 1 - pnorm(q = 1/10 + j/100)
}
zTable[i, j+1] <- 1 - pnorm(q = 1/10 + j/100)
zTable[i, j] <- 1 - pnorm(q = 1/10 + (j - 1)/100)
str(zTable)
for (i in 1:33) {
for (j in 1:10) {
print(zTable[i, j])
}
}
for (i in 1:33) {
for (j in 1:10) {
zTable[i, j]  <- 1 - pnorm(q = i/10 + (j - 1)/100)
}
}
zTable
row.names(zTable)
row.names(zTable) <- 1:33
row.names(zTable)
colnames(zTable) <- 0:9/10
colnames(zTable)
print(zTable, digits = 7)
kable(zTable, digits = 7)
library(knitr)
kable(zTable, digits = 7)
library(knitr)
library(kableExtra)
kable(zTable, digits = 7, caption = "Right tail areas under the standard normal distribution. For left-tail areas and other calculations consider that the function is symmetric about 0.") %>%
kable_styling(full_width = TRUE, )
zTable <- matrix(NA, nrow = 34, ncol = 10)
for (i in 1:34) {
for (j in 1:10) {
zTable[i, j]  <- 1 - pnorm(q = (i - 1)/10 + (j - 1)/100)
}
}
row.names(zTable) <- 1:33
row.names(zTable) <- 0:33/10
colnames(zTable) <- 0:9/10
kable(zTable, digits = 7, caption = "Right tail areas under the standard normal distribution. For left-tail areas and other calculations consider that the function is symmetric about 0.") %>%
kable_styling(full_width = TRUE, )
colnames(zTable) <- 0:9/100
kable(zTable, digits = 7, caption = "Right tail areas under the standard normal distribution. For left-tail areas and other calculations consider that the function is symmetric about 0.") %>%
kable_styling(full_width = TRUE, )
p.values <- c(0.15, 0.10, 0.05, 0.025, 0.01, 0.005)
df <- c(1:30, 16:21*2)
df
tTable <- matrix(nrow = length(df), ncol = length(p.values))
length(p.values)
length(df)
tTable[i, j] <- qt(p = p.values[j], df = df[i])
for (i in 1:36) {
for (j in 1:6) {
tTable[i, j] <- qt(p = p.values[j], df = df[i])
}
}
row.names(tTable) <- p.values
colnames(tTable) <- df
row.names(tTable) <- df
colnames(tTable) <- p.values
kable(tTable, digits = 5, caption = "Values of Student's t with row degrees of freedom that have th eolumn probability under the right tail. For left-tail areas and other calculations consider that the function is symmetric about 0.") %>%
kable_styling(full_width = TRUE, )
install.packages("arrangements")
5 +20+10+15+10+10+30
# Cumulative distribution function for number of 5's in 10 die rolls
(df <- data.frame(k = 0:10, P = pbinom(q = 0:10, size = 10, prob = 1/6)))
plot(df, type = "S", col = "skyblue", lwd = 4)
plot(0:20 + 0.05, dpois(x = 0:20, lambda = 1.5), type = "h", lwd = 4, col = "orange", ylab = "PROBABILITY", xlab = "NUMBER OF PLANTS IN QUADRAT")
points(0:20 - 0.05, dpois(x = 0:20, lambda = 6), type = "h", lwd = 4, col = "black")
# Probability of y crossovers
(df <- data.frame(y = 0:7, P = dpois(x = 0:7, lambda = 0.8)))
plot(df, type = "h", lwd = 4)
plot(df, type = "S", col = "skyblue", lwd = 4)
# Cumulative distribution function for number of crossovers
(df <- data.frame(y = 0:7, P = ppois(q = 0:7, lambda = 0.8)))
plot(df, type = "S", col = "skyblue", lwd = 4)
# Cumulative distribution function for number of 5's in 10 die rolls
(df <- data.frame(k = 0:10, P = pbinom(q = 0:10, size = 10, prob = 1/6)))
plot(df, type = "S", col = "skyblue", lwd = 4)
# Probability of k heads in 5 tosses
(df <- data.frame(k = 0:5, P = dbinom(x = 0:5, size = 5, prob = 0.5)))
plot(df, type = "h", col = "skyblue", lwd = 4)
# Probability of k heads in 5 tosses
(df <- data.frame(k = 0:5, P = pbinom(x = 0:5, size = 5, prob = 0.5)))
# Probability of k heads in 5 tosses
(df <- data.frame(k = 0:5, P = pbinom(q = 0:5, size = 5, prob = 0.5)))
plot(df, type = "h", col = "skyblue", lwd = 4)
plot(df, type = "S", col = "skyblue", lwd = 4)
curve(pnorm(x),
from = -3.5,
to = 3.5,
lwd = 2,
xlab = "Y",
ylab = "")
lwd = 2.5,
xlab = "",
ylab = "")
# Two tails
curve(df(x, df1 = 5, df2 = 15),
from = 0,
to = 6,
lwd = 2.5,
xlab = "",
ylab = "")
abline(h = 0)
# Two tails
curve(df(x, df1 = 5, df2 = 15),
from = 0,
to = 5,
lwd = 2.5,
xlab = "",
ylab = "")
abline(h = 0)
cord.x <- c(qf(0.975, df1 = 5, df2 = 15), seq(qf(0.975, df1 = 5, df2 = 15), 35, 0.01), qf(0.975, df1 = 5, df2 = 15))
cord.y <- c(0, qf(seq(qf(0.975, df1 = 5, df2 = 15), 35, 0.01), df = 15), 0)
cord.y <- c(0, qf(seq(qf(0.975, df1 = 5, df2 = 15), 35, 0.01) df1 = 5, df2 = 15), 0)
cord.y <- c(0, qf(seq(qf(0.975, df1 = 5, df2 = 15), 35, 0.01), df1 = 5, df2 = 15), 0)
cord.x <- c(qf(0.975, df1 = 5, df2 = 15), seq(qf(0.975, df1 = 5, df2 = 15), 6, 0.01), qf(0.975, df1 = 5, df2 = 15))
cord.y <- c(0, qf(seq(qf(0.975, df1 = 5, df2 = 15), 6, 0.01), df1 = 5, df2 = 15), 0)
qf(0.975, df1 = 5, df2 = 15)
seq(qf(0.975, df1 = 5, df2 = 15), 6, 0.01)
cord.y <- c(0, pf(seq(qf(0.975, df1 = 5, df2 = 15), 6, 0.01), df1 = 5, df2 = 15), 0)
polygon(cord.x, cord.y, col = "orange")
qf(0.975, df1 = 5, df2 = 15)
qf(0.95, df1 = 5, df2 = 15)
qf(0.95, df1 = 5, df2 = 15), 5, 0.01)
qf(0.95, df1 = 5, df2 = 15)
seq(qf(0.95, df1 = 5, df2 = 15), 5, 0.01)
qf(0.95, df1 = 5, df2 = 15)
cord.x <- c(qf(0.95, df1 = 5, df2 = 15), seq(qf(0.95, df1 = 5, df2 = 15), 5, 0.02), qf(0.95, df1 = 5, df2 = 15))
cord.y <- c(0, pf(seq(qf(0.95, df1 = 5, df2 = 15), 5, 0.02), df1 = 5, df2 = 15), 0)
polygon(cord.x, cord.y, col = "orange")
pf(seq(qf(0.95, df1 = 5, df2 = 15), 5, 0.02), df1 = 5, df2 = 15)
cord.y <- c(0, df(seq(qf(0.95, df1 = 5, df2 = 15), 5, 0.02), df1 = 5, df2 = 15), 0)
polygon(cord.x, cord.y, col = "orange")
polygon(cord.x, cord.y, col = "skyblue")
curve(df(x, df1 = 5, df2 = 15),
from = 0,
to = 5,
lwd = 2.5,
xlab = "",
ylab = "")
curve(df(x, df1 = 5, df2 = 15),
from = 0,
to = 5,
lwd = 2.5,
xlab = "",
ylab = "")
abline(h = 0)
# Add the shaded area.
cord.x <- c(qf(0.95, df1 = 5, df2 = 15), seq(qf(0.95, df1 = 5, df2 = 15), 5, 0.02), qf(0.95, df1 = 5, df2 = 15))
cord.y <- c(0, df(seq(qf(0.95, df1 = 5, df2 = 15), 5, 0.02), df1 = 5, df2 = 15), 0)
polygon(cord.x, cord.y, col = "skyblue")
curve(df(x, df1 = 5, df2 = 15),
from = 0,
to = 5,
lwd = 2.5,
xlab = "",
ylab = "",
add = TRUE)
### F()
df1 <- 15
df2 <- 15
# Two tails on the right
curve(df(x, df1 = df1, df2 = df2),
from = 0,
to = 5,
lwd = 2.5,
xlab = "",
ylab = "")
abline(h = 0)
cord.x <- c(qf(0.95, df1 = df1, df2 = df2),
seq(qf(0.95, df1 = df1, df2 = df2), 5, 0.02),
qf(0.95, df1 = df1, df2 = df2))
cord.y <- c(0,
df(seq(qf(0.95, df1 = df1, df2 = df2), 5, 0.02),
df1 = df1, df2 = df2), 0)
polygon(cord.x, cord.y, col = "skyblue")
curve(df(x, df1 = df1, df2 = df2),
from = 0,
to = 5,
lwd = 2.5,
xlab = "",
ylab = "",
add = TRUE)
df1 <- 15
df2 <- 15
# Two tails on the right
curve(df(x, df1 = df1, df2 = df2),
from = 0,
to = 5,
lwd = 2.5,
xlab = "",
ylab = "",
ylim = c(-0.05, 0.9))
abline(h = 0)
# Add the shaded area.
cord.x <- c(qf(0.95, df1 = df1, df2 = df2),
seq(qf(0.95, df1 = df1, df2 = df2), 5, 0.02),
qf(0.95, df1 = df1, df2 = df2))
cord.y <- c(0,
df(seq(qf(0.95, df1 = df1, df2 = df2), 5, 0.02),
df1 = df1, df2 = df2), 0)
polygon(cord.x, cord.y, col = "skyblue")
curve(df(x, df1 = df1, df2 = df2),
from = 0,
to = 5,
lwd = 2.5,
xlab = "",
ylab = "",
add = TRUE,
ylim = c(-0.05, 0.9))
qf(0.95, df1 = df1, df2 = df2)
text(x = -0.025, y = qf(0.95, df1 = df1, df2 = df2), pos = 4,
labels = "Reject equality of variances")
text(x = 0, y = qf(0.95, df1 = df1, df2 = df2), pos = 4,
labels = "Reject equality of variances")
text(y = -0.025, x = qf(0.95, df1 = df1, df2 = df2), pos = 4,
labels = "Reject equality of variances")
text(y = -0.03, x = qf(0.95, df1 = df1, df2 = df2), pos = 4,
labels = "Reject equality of variances")
text(y = -0.04, x = qf(0.95, df1 = df1, df2 = df2), pos = 4,
labels = "Reject equality of variances")
# Two tails on the right
curve(df(x, df1 = df1, df2 = df2),
from = 0,
to = 5,
lwd = 2.5,
xlab = "",
ylab = "",
ylim = c(-0.05, 0.9))
abline(h = 0)
# Add the shaded area.
cord.x <- c(qf(0.95, df1 = df1, df2 = df2),
seq(qf(0.95, df1 = df1, df2 = df2), 5, 0.02),
qf(0.95, df1 = df1, df2 = df2))
cord.y <- c(0,
df(seq(qf(0.95, df1 = df1, df2 = df2), 5, 0.02),
df1 = df1, df2 = df2), 0)
polygon(cord.x, cord.y, col = "skyblue")
curve(df(x, df1 = df1, df2 = df2),
from = 0,
to = 5,
lwd = 2.5,
xlab = "",
ylab = "",
add = TRUE,
ylim = c(-0.05, 0.9))
text(y = -0.04, x = qf(0.95, df1 = df1, df2 = df2), pos = 4,
labels = "Reject equality of variances")
text(y = -0.04, x = qf(0.95, df1 = df1, df2 = df2), pos = 4,
labels = "Reject equality of variances", col = "red")
qf(0.95, df1 = df1, df2 = df2)
lines(x = c(2.5, 2.8), y = c(0.03, 0.20))
library(latex2exp)
plot(x, Y, pch = ".", # xaxt = "n", yaxt = "n",
xlab = "X", ylab = "Y",
xlim = c(0,10), ylim = c(0,17),
bty = "l", cex.lab = 1.5, cex = 1.75,
main = "Population line and X-Y values")
text(2, 14, TeX(\\mu_{Y|X} = \\beta_0 + \\beta_1 \\times{X}), cex = 1.7, col = "blue")
text(2, 14, labels =TeX(\\mu_{Y|X} = \\beta_0 + \\beta_1 \\times{X}), cex = 1.7, col = "blue")
plot(TeX(\\mu_{Y|X} = \\beta_0 + \\beta_1 \\times{X}))
text(2, 14, labels =TeX("\\mu_{Y|X} = \\beta_0 + \\beta_1 \\times{X}""), cex = 1.7, col = "blue")
plot(TeX("\\mu_{Y|X} = \\beta_0 + \\beta_1 \\times{X}"))
text(2, 14, labels =TeX("\mu_{Y|X} = \beta_0 + \beta_1 \times{X}"), cex = 1.7, col = "blue")
text(2, 14, labels =TeX("\\mu_{Y|X} = \beta_0 + \beta_1 \times{X}"), cex = 1.7, col = "blue")
text(2, 14, labels =TeX("\\mu_{Y|X} = \\beta_0 + \\beta_1 \\times{X}"), cex = 1.7, col = "blue")
plot(TeX("\\mu_{Y|X} = \\beta_0 + \\beta_1 \\times{X}"), cex = 1.7, col = "blue"))
plot(TeX("\\mu_{Y|X} = \\beta_0 + \\beta_1 \\times{X}"))
plot(TeX("$\\mu_{Y|X} = \\beta_0 + \\beta_1 \\times{X}$"))
text(2, 14, labels =TeX("$\\mu_{Y|X} = \\beta_0 + \\beta_1 \\times{X}$"), cex = 1.7, col = "blue")
########make a figure and label it slr#####
library(latex2exp)
library(shape)
set.seed(400)
x <- 1:1000/100
Y <- 5 + 0.9 * x +rnorm(1000)
plot(x, Y, pch = ".", # xaxt = "n", yaxt = "n",
xlab = "X", ylab = "Y",
xlim = c(0,10), ylim = c(0,17),
bty = "l", cex.lab = 1.5, cex = 1.75,
main = "Population line and X-Y values")
lines(x = c(6, 6), y = c(8, 10.4), col = "red", lty = 1, lwd = 2)
points(6, 8, pch = 20)
lines(0:10, 5 + 0.9 * 0:10, lwd = 2, col = "blue")
text(7, 9, labels = expression(Y[i] - Y == epsilon[i]),cex = 1.5, col = "red")
arrows(x0 = 0.5, y0 = 5.45, x1 = 4, y1 = 5.45, code = 0, lwd = 2, lty = 2)
arrows(x0 = 4, x1 = 4, y0 = 5.45, y1 = 8.6, code = 0, lwd = 2, lty = 2)
text(2.5, 4.5, labels = expression(paste(Delta,"X")), cex = 1.5)
text(4.3, 7, labels = expression(paste(Delta,"Y")), cex = 1.5)
text(4.2, 4,expression(beta[1] == over(Delta*Y,Delta*X)), cex = 1.5)
text(2, 14, labels =TeX("$\\mu_{Y|X} = \\beta_0 + \\beta_1 \\times{X}$"), cex = 1.7, col = "blue")
text(2, 12.5, expression(Y == 5 + 0.9*X), cex = 1.6, col = "blue")
Arrows(3.5, 1.0, 3.1, 2.8, lwd = 1.5, col = "blue")
text(2, 14, labels =TeX("$\\mu_{Y|X} = \\beta_0 + \\beta_1 \\times X$"), cex = 1.7, col = "blue")
########make a figure and label it slr#####
library(latex2exp)
library(shape)
set.seed(400)
x <- 1:1000/100
Y <- 5 + 0.9 * x +rnorm(1000)
plot(x, Y, pch = ".", # xaxt = "n", yaxt = "n",
xlab = "X", ylab = "Y",
xlim = c(0,10), ylim = c(0,17),
bty = "l", cex.lab = 1.5, cex = 1.75,
main = "Population line and X-Y values")
lines(x = c(6, 6), y = c(8, 10.4), col = "red", lty = 1, lwd = 2)
points(6, 8, pch = 20)
lines(0:10, 5 + 0.9 * 0:10, lwd = 2, col = "blue")
text(7, 9, labels = expression(Y[i] - Y == epsilon[i]),cex = 1.5, col = "red")
arrows(x0 = 0.5, y0 = 5.45, x1 = 4, y1 = 5.45, code = 0, lwd = 2, lty = 2)
arrows(x0 = 4, x1 = 4, y0 = 5.45, y1 = 8.6, code = 0, lwd = 2, lty = 2)
text(2.5, 4.5, labels = expression(paste(Delta,"X")), cex = 1.5)
text(4.3, 7, labels = expression(paste(Delta,"Y")), cex = 1.5)
text(4.2, 4,expression(beta[1] == over(Delta*Y,Delta*X)), cex = 1.5)
text(2, 14, labels =TeX("$\\mu_{Y|X} = \\beta_0 + \\beta_1 \\ X$"), cex = 1.7, col = "blue")
text(2, 12.5, expression(Y == 5 + 0.9*X), cex = 1.6, col = "blue")
Arrows(3.5, 1.0, 3.1, 2.8, lwd = 1.5, col = "blue")
Arrows(2, 12, 3, 7.75, lwd = 1.5, col = "blue")
Arrows(2, 111.7, 3, 7.85, lwd = 1.5, col = "blue")
Arrows(2, 11.7, 3, 7.85, lwd = 1.5, col = "blue")
set.seed(400)
x <- 1:1000/100
Y <- 5 + 0.9 * x +rnorm(1000)
plot(x, Y, pch = ".", # xaxt = "n", yaxt = "n",
xlab = "X", ylab = "Y",
xlim = c(0,10), ylim = c(0,17),
bty = "l", cex.lab = 1.5, cex = 1.75,
main = "Population line and X-Y values")
lines(x = c(6, 6), y = c(8, 10.4), col = "red", lty = 1, lwd = 2)
points(6, 8, pch = 20)
lines(0:10, 5 + 0.9 * 0:10, lwd = 2, col = "blue")
text(7, 9, labels = expression(Y[i] - Y == epsilon[i]),cex = 1.5, col = "red")
arrows(x0 = 0.5, y0 = 5.45, x1 = 4, y1 = 5.45, code = 0, lwd = 2, lty = 2)
arrows(x0 = 4, x1 = 4, y0 = 5.45, y1 = 8.6, code = 0, lwd = 2, lty = 2)
text(2.5, 4.5, labels = expression(paste(Delta,"X")), cex = 1.5)
text(4.3, 7, labels = expression(paste(Delta,"Y")), cex = 1.5)
text(4.2, 4,expression(beta[1] == over(Delta*Y,Delta*X)), cex = 1.5)
text(2, 14, labels =TeX("$\\mu_{Y|X} = \\beta_0 + \\beta_1 X$"), cex = 1.7, col = "blue")
text(2, 12.5, expression(Y == 5 + 0.9*X), cex = 1.6, col = "blue")
Arrows(2, 11.7, 3, 7.85, lwd = 1.5, col = "blue")
Arrows(2, 11.7, 3, 7.95, lwd = 1.5, col = "blue")
Arrows(2, 11.7, 3, 8, lwd = 1.5, col = "blue")
########make a figure and label it slr#####
library(latex2exp)
library(shape)
set.seed(400)
x <- 1:1000/100
Y <- 5 + 0.9 * x +rnorm(1000)
plot(x, Y, pch = ".", # xaxt = "n", yaxt = "n",
xlab = "X", ylab = "Y",
xlim = c(0,10), ylim = c(0,17),
bty = "l", cex.lab = 1.5, cex = 1.75,
main = "Population line and X-Y values")
lines(x = c(6, 6), y = c(8, 10.4), col = "red", lty = 1, lwd = 2)
points(6, 8, pch = 20)
lines(0:10, 5 + 0.9 * 0:10, lwd = 2, col = "blue")
text(7, 9, labels = expression(Y[i] - Y == epsilon[i]),cex = 1.5, col = "red")
arrows(x0 = 0.5, y0 = 5.45, x1 = 4, y1 = 5.45, code = 0, lwd = 2, lty = 2)
arrows(x0 = 4, x1 = 4, y0 = 5.45, y1 = 8.6, code = 0, lwd = 2, lty = 2)
text(2.5, 4.5, labels = expression(paste(Delta,"X")), cex = 1.5)
text(4.3, 7, labels = expression(paste(Delta,"Y")), cex = 1.5)
text(4.2, 4,expression(beta[1] == over(Delta*Y,Delta*X)), cex = 1.5)
text(2, 14, labels =TeX("$\\mu_{Y|X} = \\beta_0 + \\beta_1 X$"), cex = 1.7, col = "blue")
text(2, 12.5, expression(Y == 5 + 0.9*X), cex = 1.6, col = "blue")
Arrows(2, 11.7, 3, 8, lwd = 1.5, col = "blue")
Arrows(2.2, 11.7, 3, 8.1, lwd = 1.5, col = "blue")
########make a figure and label it slr#####
library(latex2exp)
library(shape)
set.seed(400)
x <- 1:1000/100
Y <- 5 + 0.9 * x +rnorm(1000)
plot(x, Y, pch = ".", # xaxt = "n", yaxt = "n",
xlab = "X", ylab = "Y",
xlim = c(0,10), ylim = c(0,17),
bty = "l", cex.lab = 1.5, cex = 1.75,
main = "Population line and X-Y values")
lines(x = c(6, 6), y = c(8, 10.4), col = "red", lty = 1, lwd = 2)
points(6, 8, pch = 20)
lines(0:10, 5 + 0.9 * 0:10, lwd = 2, col = "blue")
text(7, 9, labels = expression(Y[i] - Y == epsilon[i]),cex = 1.5, col = "red")
arrows(x0 = 0.5, y0 = 5.45, x1 = 4, y1 = 5.45, code = 0, lwd = 2, lty = 2)
arrows(x0 = 4, x1 = 4, y0 = 5.45, y1 = 8.6, code = 0, lwd = 2, lty = 2)
text(2.5, 4.5, labels = expression(paste(Delta,"X")), cex = 1.5)
text(4.3, 7, labels = expression(paste(Delta,"Y")), cex = 1.5)
text(4.2, 4,expression(beta[1] == over(Delta*Y,Delta*X)), cex = 1.5)
text(2, 14, labels =TeX("$\\mu_{Y|X} = \\beta_0 + \\beta_1 X$"), cex = 1.7, col = "blue")
text(2, 12.5, expression(Y == 5 + 0.9*X), cex = 1.6, col = "blue")
Arrows(2.2, 11.7, 3, 8.1, lwd = 1.5, col = "blue")
text(2, 12.5, TeX("$\\mu_{Y|X} = 5 + 9 X$"), cex = 1.6, col = "blue")
text(7, 9, labels = TeX("$\\mu_{Y|X} - Y-i = \\epsilon_i$"),cex = 1.5, col = "red")
########make a figure and label it slr#####
library(latex2exp)
<<<<<<< HEAD
library(shape)
set.seed(400)
x <- 1:1000/100
Y <- 5 + 0.9 * x +rnorm(1000)
plot(x, Y, pch = ".", # xaxt = "n", yaxt = "n",
xlab = "X", ylab = "Y",
xlim = c(0,10), ylim = c(0,17),
bty = "l", cex.lab = 1.5, cex = 1.75,
main = "Population line and X-Y values")
lines(x = c(6, 6), y = c(8, 10.4), col = "red", lty = 1, lwd = 2)
points(6, 8, pch = 20)
lines(0:10, 5 + 0.9 * 0:10, lwd = 2, col = "blue")
text(7, 9, labels = TeX("$\\mu_{Y|X} - Y-i = \\epsilon_i$"),cex = 1.5, col = "red")
arrows(x0 = 0.5, y0 = 5.45, x1 = 4, y1 = 5.45, code = 0, lwd = 2, lty = 2)
arrows(x0 = 4, x1 = 4, y0 = 5.45, y1 = 8.6, code = 0, lwd = 2, lty = 2)
text(2.5, 4.5, labels = expression(paste(Delta,"X")), cex = 1.5)
text(4.3, 7, labels = expression(paste(Delta,"Y")), cex = 1.5)
text(4.2, 4,expression(beta[1] == over(Delta*Y,Delta*X)), cex = 1.5)
text(2, 14, labels =TeX("$\\mu_{Y|X} = \\beta_0 + \\beta_1 X$"), cex = 1.7, col = "blue")
text(2, 12.5, TeX("$\\mu_{Y|X} = 5 + 9 X$"), cex = 1.6, col = "blue")
Arrows(2.2, 11.7, 3, 8.1, lwd = 1.5, col = "blue")
text(7.5, 9, labels = TeX("$\\epsilon_i = \\mu_{Y|X} - Y_i$"),cex = 1.5, col = "red")
########make a figure and label it slr#####
library(latex2exp)
library(shape)
set.seed(400)
x <- 1:1000/100
Y <- 5 + 0.9 * x +rnorm(1000)
plot(x, Y, pch = ".", # xaxt = "n", yaxt = "n",
xlab = "X", ylab = "Y",
xlim = c(0,10), ylim = c(0,17),
bty = "l", cex.lab = 1.5, cex = 1,
main = "Population line and X-Y values")
lines(x = c(6, 6), y = c(8, 10.4), col = "red", lty = 1, lwd = 2)
points(6, 8, pch = 20)
lines(0:10, 5 + 0.9 * 0:10, lwd = 2, col = "blue")
text(7.5, 9, labels = TeX("$\\epsilon_i = \\mu_{Y|X} - Y_i$"),cex = 1.5, col = "red")
arrows(x0 = 0.5, y0 = 5.45, x1 = 4, y1 = 5.45, code = 0, lwd = 2, lty = 2)
arrows(x0 = 4, x1 = 4, y0 = 5.45, y1 = 8.6, code = 0, lwd = 2, lty = 2)
text(2.5, 4.5, labels = expression(paste(Delta,"X")), cex = 1.5)
text(4.3, 7, labels = expression(paste(Delta,"Y")), cex = 1.5)
text(4.2, 4,expression(beta[1] == over(Delta*Y,Delta*X)), cex = 1.5)
text(2, 14, labels =TeX("$\\mu_{Y|X} = \\beta_0 + \\beta_1 X$"), cex = 1.7, col = "blue")
text(2, 12.5, TeX("$\\mu_{Y|X} = 5 + 9 X$"), cex = 1.6, col = "blue")
Arrows(2.2, 11.7, 3, 8.1, lwd = 1.5, col = "blue")
########make a figure and label it slr#####
library(latex2exp)
library(shape)
set.seed(400)
x <- 1:10000/100
Y <- 5 + 0.9 * x +rnorm(10000)
plot(x, Y, pch = ".", # xaxt = "n", yaxt = "n",
xlab = "X", ylab = "Y",
xlim = c(0,10), ylim = c(0,17),
bty = "l", cex.lab = 1.5, cex = 1,
main = "Population line and X-Y values")
lines(x = c(6, 6), y = c(8, 10.4), col = "red", lty = 1, lwd = 2)
points(6, 8, pch = 20)
lines(0:10, 5 + 0.9 * 0:10, lwd = 2, col = "blue")
text(7.5, 9, labels = TeX("$\\epsilon_i = \\mu_{Y|X} - Y_i$"),cex = 1.5, col = "red")
arrows(x0 = 0.5, y0 = 5.45, x1 = 4, y1 = 5.45, code = 0, lwd = 2, lty = 2)
arrows(x0 = 4, x1 = 4, y0 = 5.45, y1 = 8.6, code = 0, lwd = 2, lty = 2)
text(2.5, 4.5, labels = expression(paste(Delta,"X")), cex = 1.5)
text(4.3, 7, labels = expression(paste(Delta,"Y")), cex = 1.5)
text(4.2, 4,expression(beta[1] == over(Delta*Y,Delta*X)), cex = 1.5)
text(2, 14, labels =TeX("$\\mu_{Y|X} = \\beta_0 + \\beta_1 X$"), cex = 1.7, col = "blue")
text(2, 12.5, TeX("$\\mu_{Y|X} = 5 + 9 X$"), cex = 1.6, col = "blue")
Arrows(2.2, 11.7, 3, 8.1, lwd = 1.5, col = "blue")
########make a figure and label it slr#####
library(latex2exp)
library(shape)
set.seed(400)
x <- 1:10000/1000
Y <- 5 + 0.9 * x +rnorm(10000)
plot(x, Y, pch = ".", # xaxt = "n", yaxt = "n",
xlab = "X", ylab = "Y",
xlim = c(0,10), ylim = c(0,17),
bty = "l", cex.lab = 1.5, cex = 1,
main = "Population line and X-Y values")
lines(x = c(6, 6), y = c(8, 10.4), col = "red", lty = 1, lwd = 2)
points(6, 8, pch = 20)
lines(0:10, 5 + 0.9 * 0:10, lwd = 2, col = "blue")
text(7.5, 9, labels = TeX("$\\epsilon_i = \\mu_{Y|X} - Y_i$"),cex = 1.5, col = "red")
arrows(x0 = 0.5, y0 = 5.45, x1 = 4, y1 = 5.45, code = 0, lwd = 2, lty = 2)
arrows(x0 = 4, x1 = 4, y0 = 5.45, y1 = 8.6, code = 0, lwd = 2, lty = 2)
text(2.5, 4.5, labels = expression(paste(Delta,"X")), cex = 1.5)
text(4.3, 7, labels = expression(paste(Delta,"Y")), cex = 1.5)
text(4.2, 4,expression(beta[1] == over(Delta*Y,Delta*X)), cex = 1.5)
text(2, 14, labels =TeX("$\\mu_{Y|X} = \\beta_0 + \\beta_1 X$"), cex = 1.7, col = "blue")
text(2, 12.5, TeX("$\\mu_{Y|X} = 5 + 9 X$"), cex = 1.6, col = "blue")
Arrows(2.2, 11.7, 3, 8.1, lwd = 1.5, col = "blue")
########make a figure and label it slr#####
library(latex2exp)
library(shape)
set.seed(400)
x <- 1:10000/1000
Y <- 5 + 0.9 * x +rnorm(10000, sd = 2)
plot(x, Y, pch = ".", # xaxt = "n", yaxt = "n",
xlab = "X", ylab = "Y",
xlim = c(0,10), ylim = c(0,17),
bty = "l", cex.lab = 1.5, cex = 1,
main = "Population line and X-Y values")
lines(x = c(6, 6), y = c(8, 10.4), col = "red", lty = 1, lwd = 2)
points(6, 8, pch = 20)
lines(0:10, 5 + 0.9 * 0:10, lwd = 2, col = "blue")
text(7.5, 9, labels = TeX("$\\epsilon_i = \\mu_{Y|X} - Y_i$"),cex = 1.5, col = "red")
arrows(x0 = 0.5, y0 = 5.45, x1 = 4, y1 = 5.45, code = 0, lwd = 2, lty = 2)
arrows(x0 = 4, x1 = 4, y0 = 5.45, y1 = 8.6, code = 0, lwd = 2, lty = 2)
text(2.5, 4.5, labels = expression(paste(Delta,"X")), cex = 1.5)
text(4.3, 7, labels = expression(paste(Delta,"Y")), cex = 1.5)
text(4.2, 4,expression(beta[1] == over(Delta*Y,Delta*X)), cex = 1.5)
text(2, 14, labels =TeX("$\\mu_{Y|X} = \\beta_0 + \\beta_1 X$"), cex = 1.7, col = "blue")
text(2, 12.5, TeX("$\\mu_{Y|X} = 5 + 9 X$"), cex = 1.6, col = "blue")
Arrows(2.2, 11.7, 3, 8.1, lwd = 1.5, col = "blue")
Y <- 5 + 0.9 * x +rnorm(10000, sd = 0.9)
########make a figure and label it slr#####
library(latex2exp)
library(shape)
set.seed(400)
x <- 1:10000/1000
Y <- 5 + 0.9 * x +rnorm(10000, sd = 0.9)
plot(x, Y, pch = ".", # xaxt = "n", yaxt = "n",
xlab = "X", ylab = "Y",
xlim = c(0,10), ylim = c(0,17),
bty = "l", cex.lab = 1.5, cex = 1,
main = "Population line and X-Y values")
lines(x = c(6, 6), y = c(8, 10.4), col = "red", lty = 1, lwd = 2)
points(6, 8, pch = 20)
lines(0:10, 5 + 0.9 * 0:10, lwd = 2, col = "blue")
text(7.5, 9, labels = TeX("$\\epsilon_i = \\mu_{Y|X} - Y_i$"),cex = 1.5, col = "red")
arrows(x0 = 0.5, y0 = 5.45, x1 = 4, y1 = 5.45, code = 0, lwd = 2, lty = 2)
arrows(x0 = 4, x1 = 4, y0 = 5.45, y1 = 8.6, code = 0, lwd = 2, lty = 2)
text(2.5, 4.5, labels = expression(paste(Delta,"X")), cex = 1.5)
text(4.3, 7, labels = expression(paste(Delta,"Y")), cex = 1.5)
text(4.2, 4,expression(beta[1] == over(Delta*Y,Delta*X)), cex = 1.5)
text(2, 14, labels =TeX("$\\mu_{Y|X} = \\beta_0 + \\beta_1 X$"), cex = 1.7, col = "blue")
text(2, 12.5, TeX("$\\mu_{Y|X} = 5 + 9 X$"), cex = 1.6, col = "blue")
Arrows(2.2, 11.7, 3, 8.1, lwd = 1.5, col = "blue")
Y <- 5 + 0.9 * x +rnorm(5000, sd = 1.4)
########make a figure and label it slr#####
library(latex2exp)
library(shape)
set.seed(400)
x <- 1:5000/1000
Y <- 5 + 0.9 * x +rnorm(5000, sd = 1.4)
plot(x, Y, pch = ".", # xaxt = "n", yaxt = "n",
xlab = "X", ylab = "Y",
xlim = c(0,10), ylim = c(0,17),
bty = "l", cex.lab = 1.5, cex = 1,
main = "Population line and X-Y values")
lines(x = c(6, 6), y = c(8, 10.4), col = "red", lty = 1, lwd = 2)
points(6, 8, pch = 20)
lines(0:10, 5 + 0.9 * 0:10, lwd = 2, col = "blue")
text(7.5, 9, labels = TeX("$\\epsilon_i = \\mu_{Y|X} - Y_i$"),cex = 1.5, col = "red")
arrows(x0 = 0.5, y0 = 5.45, x1 = 4, y1 = 5.45, code = 0, lwd = 2, lty = 2)
arrows(x0 = 4, x1 = 4, y0 = 5.45, y1 = 8.6, code = 0, lwd = 2, lty = 2)
text(2.5, 4.5, labels = expression(paste(Delta,"X")), cex = 1.5)
text(4.3, 7, labels = expression(paste(Delta,"Y")), cex = 1.5)
text(4.2, 4,expression(beta[1] == over(Delta*Y,Delta*X)), cex = 1.5)
text(2, 14, labels =TeX("$\\mu_{Y|X} = \\beta_0 + \\beta_1 X$"), cex = 1.7, col = "blue")
text(2, 12.5, TeX("$\\mu_{Y|X} = 5 + 9 X$"), cex = 1.6, col = "blue")
Arrows(2.2, 11.7, 3, 8.1, lwd = 1.5, col = "blue")
########make a figure and label it slr#####
library(latex2exp)
library(shape)
set.seed(400)
x <- 1:5000/500
Y <- 5 + 0.9 * x +rnorm(5000, sd = 1.4)
plot(x, Y, pch = ".", # xaxt = "n", yaxt = "n",
xlab = "X", ylab = "Y",
xlim = c(0,10), ylim = c(0,17),
bty = "l", cex.lab = 1.5, cex = 1,
main = "Population line and X-Y values")
lines(x = c(6, 6), y = c(8, 10.4), col = "red", lty = 1, lwd = 2)
points(6, 8, pch = 20)
lines(0:10, 5 + 0.9 * 0:10, lwd = 2, col = "blue")
text(7.5, 9, labels = TeX("$\\epsilon_i = \\mu_{Y|X} - Y_i$"),cex = 1.5, col = "red")
arrows(x0 = 0.5, y0 = 5.45, x1 = 4, y1 = 5.45, code = 0, lwd = 2, lty = 2)
arrows(x0 = 4, x1 = 4, y0 = 5.45, y1 = 8.6, code = 0, lwd = 2, lty = 2)
text(2.5, 4.5, labels = expression(paste(Delta,"X")), cex = 1.5)
text(4.3, 7, labels = expression(paste(Delta,"Y")), cex = 1.5)
text(4.2, 4,expression(beta[1] == over(Delta*Y,Delta*X)), cex = 1.5)
text(2, 14, labels =TeX("$\\mu_{Y|X} = \\beta_0 + \\beta_1 X$"), cex = 1.7, col = "blue")
text(2, 12.5, TeX("$\\mu_{Y|X} = 5 + 9 X$"), cex = 1.6, col = "blue")
Arrows(2.2, 11.7, 3, 8.1, lwd = 1.5, col = "blue")
########make a figure and label it slr#####
library(latex2exp)
library(shape)
set.seed(400)
x <- 1:5000/500
Y <- 5 + 0.9 * x +rnorm(5000, sd = 1)
plot(x, Y, pch = ".", # xaxt = "n", yaxt = "n",
xlab = "X", ylab = "Y",
xlim = c(0,10), ylim = c(0,17),
bty = "l", cex.lab = 1.5, cex = 1,
main = "Population line and X-Y values")
lines(x = c(6, 6), y = c(8, 10.4), col = "red", lty = 1, lwd = 2)
points(6, 8, pch = 20)
lines(0:10, 5 + 0.9 * 0:10, lwd = 2, col = "blue")
text(7.5, 9, labels = TeX("$\\epsilon_i = \\mu_{Y|X} - Y_i$"),cex = 1.5, col = "red")
arrows(x0 = 0.5, y0 = 5.45, x1 = 4, y1 = 5.45, code = 0, lwd = 2, lty = 2)
arrows(x0 = 4, x1 = 4, y0 = 5.45, y1 = 8.6, code = 0, lwd = 2, lty = 2)
text(2.5, 4.5, labels = expression(paste(Delta,"X")), cex = 1.5)
text(4.3, 7, labels = expression(paste(Delta,"Y")), cex = 1.5)
text(4.2, 4,expression(beta[1] == over(Delta*Y,Delta*X)), cex = 1.5)
text(2, 14, labels =TeX("$\\mu_{Y|X} = \\beta_0 + \\beta_1 X$"), cex = 1.7, col = "blue")
text(2, 12.5, TeX("$\\mu_{Y|X} = 5 + 9 X$"), cex = 1.6, col = "blue")
Arrows(2.2, 11.7, 3, 8.1, lwd = 1.5, col = "blue")
rice <- read.csv("./Datasets/rainYield.csv")
rice
rice <- read.csv("./Datasets/rainYield.csv")
rice
plot(rice$rain.mm, rice$yield.kg.ha, xlab = "Annual rainfall", ylab = "Rice crop yield (kg/ha)", cex.lab = 1.5, cex = 1.25)
rice <- read.csv("Datasets/rainYield.csv")
plot(rice$rain.mm, rice$yield.kg.ha, xlab = "Annual rainfall", ylab = "Rice crop yield (kg/ha)", cex.lab = 1.5, cex = 1.25)
plot(rice$rain.mm, rice$yield.kg.ha, xlab = "Annual rainfall", ylab = "Rice crop yield (kg/ha)", cex.lab = 1.5, cex = 1.25)
lines(lm(yield.kg.ha ~ rain.mm, rice))
abline(lm(yield.kg.ha ~ rain.mm, rice))
set.seed(400)
x <- 0:10
Y <- x +rnorm(10)
plot(x, Y,  pch = 20, xaxt = "n", yaxt = "n", xlab = "X", ylab = "Y", xlim = c(0,10), ylim = c(0,10), bty = "l")
lines(0:10, 0:10, lwd = 2)
slopes <- seq(0, 1, .20)
b0 <- sort(seq(0,5, 1), decreasing = T)
for(i in 1:6){
y <-  b0[i] + x*slopes[i]
lines(0:10, y, lty = 3, lwd = 1.5)
}
?lm
=======
text(y = 0.19, x = 2.80, pos = 4,
labels = TeX("$\\frac{\\alpha}{2}"), col = "blue")
bean.yield <- data.frame(
yield = c("yield 1", "yield 2", "yield 3", "yield 4"),
drought = c(590, 720, 720, 190 ),
irrigated = c(2990, 2950, 2660, 2120))
bean.yield
t.test(x=bean.yield$drought, y = bean.yield$irrigated)
var(bean.yield$drought)
var(bean.yield$irrigated)
# calculate the sample variances for each treatment "by hand"
var1 <- sum((bean.yield$drought - Ybar1)^2) / (r1 - 1)
t.test(x=bean.yield$drought, y = bean.yield$irrigated, var.equal = TRUE)
qf(p = 0.95, df1 = 3, df2 = 3)
# calculation of F-critical value using alpha = 0.10 /2 since the F-test is two-tailed
p <- 0.10/2
Fcrit.upper <- qf(p, r1-1, r2-1, lower.tail = FALSE)
x <- seq(0.000001,16, 0.25)
pd <- df(x, df1 = 3, df2 = 3, ncp = 0)
plot(x, pd,
type = "l",
xlab = "F-Value", ylab = "Probability Distribution",
main = "the F-Distribution Curve",
lwd = 1.5)
abline(v = Fcrit.upper,
col = "chartreuse3",
lty = 3)
(2*var(bean.yield$drought) + 2*var(bean.yield$irrigated)/4
(2*var(bean.yield$drought) + 2*var(bean.yield$irrigated))/4
# the pooled variance can be calculated from taking the average of the to sample variances, since they have the same sample size
pooled.var <- ( var1 + var2 ) / 2
(3*var(bean.yield$drought) + 3*var(bean.yield$irrigated))/6
2*(r-1)
# since r1 = r2 = 4, we can just use r = 4 for continued calculations
r <- length(bean.yield$yield)
2*(r-1)
#a quicker method to calculate the t-statistic
bean.test <- t.test(bean.yield$irrigated, bean.yield$drought,
alternative = "two.sided", paired = FALSE,
var.equal = TRUE)
bean.test
#a quicker method to calculate the t-statistic
bean.test <- t.test(bean.yield$irrigated, bean.yield$drought,
alternative = "two.sided", paired = FALSE,
var.equal = FALSE)
bean.test
#a quicker method to calculate the t-statistic
bean.test <- t.test(bean.yield$irrigated, bean.yield$drought,
alternative = "greater", paired = FALSE,
var.equal = TRUE)
bean.test
qt(0.025, df = 6)
qt(p = 0.975, df = r1 - 1)
qt(p = 0.975, df = r - 1)
var(bean.yield$drought)
var(bean.yield$irrigated)
sqrt(var(bean.yield$drought)/4 + var(bean.yield$irrigated))
2125/420.4065
qt(0.975, 3)
(bean.test.unequal <- t.test(bean.yield$irrigated, bean.yield$drought,
alternative = "two.sided", paired = FALSE,
var.equal = FALSE))
bean.yield$irrigated
bean.yield$drought
2125 -3.182446 * 420.41
pt(5.055, df = 3)
1-pt(5.055, df = 3)
d1 <- rnorm(5, mean = 200, sd = 18)
d1
d1 <- round(rnorm(5, mean = 200, sd = 18),1)
d1
d1 <- round(rnorm(5, mean = 200, sd = 18), 0)
d1
mean(d1)
var(d1)
sd(d1)
df1 = length(d1) - 1
df1
mu0 <- 210
var.hat.ybar <- var(d1)/df1
var.hat.ybar
sd.hat.ybar <- sqrt(var.hat.ybar)
sd.hat.ybar
confint(lm(d1 ~1))
(204.962 - 177.838)/2
tcrit <- qt(0.975, df = df1)
tcrit
tcrit * sd.hat.ybar
summary(lm(d1 ~1))
var.hat.ybar <- var(d1)/length(d1)
sd.hat.ybar <- sqrt(var.hat.ybar)
tcrit * sd.hat.ybar
d1
mean(d1)
sd(d1)
sd.hat.ybar
(191.4 - 210)/sd.hat.ybar
qt(0.025, df = df1)
tcrit
df1
qt(0.025, df1)
walking.spiders <- data.frame(
'spider' = c(1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15),
'control' = c(2.5, 5.5, 1.1, 2.7, 2.8, 1.6, 3.2, 4.5, 5.0, 6.9, 2.2, 3.9, 3.8, 3.5, 5.7),
'mantis' = c(0.4, 1.9, 1.2, 2.6, 4.3, 0.3, 1.0, 1.5, 3.3, 2.6, 0.7, 1.4, 2.1, 3.4, 2.3),
'dif' = c(2.1, 3.6, -0.1, 0.1, -1.5, 1.3, 2.2, 3.0, 1.7, 4.3, 1.5, 2.5, 1.7, 0.1, 3.4))
dif = c(2.1, 3.6, -0.1, 0.1, -1.5, 1.3, 2.2, 3.0, 1.7, 4.3, 1.5, 2.5, 1.7, 0.1, 3.4)
mean(dif)
var(dif)
qt(p = 0.975, df = 14)
spd <- data.frame(
spider = c(1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15),
control = c(2.5, 5.5, 1.1, 2.7, 2.8, 1.6, 3.2, 4.5, 5.0, 6.9, 2.2, 3.9, 3.8, 3.5, 5.7),
mantis = c(0.4, 1.9, 1.2, 2.6, 4.3, 0.3, 1.0, 1.5, 3.3, 2.6, 0.7, 1.4, 2.1, 3.4, 2.3))
t.test(x = spd$control,
y = spd$mantis,
alternative = "two.sided",
mu = 0,
paired = TRUE,
conf.level = 0.95)
rats <- data.frame(
'males' = c(700, 825, 425, 500, 575, 725, 800, 475, 575, 725, 500, 700, 575, 775),
'females' = c(450, 725, 675, 725, 750, 850, 690, 725, 475, 700, 725, 475, 825, 725))
(sample.avg <- sapply(rat.life, mean))
(sample.avg <- sapply(rat, mean))
(sample.avg <- sapply(rats, mean))
str(sample.avg)
sample.avg["males"]
sample.avg["males"]
sample.avg[1]
sample.avg["females"]
sample.avg[2]
t.test(x = rats$male,
y = rats$females,
alternative = "two.sided",
mu = 0,
paired = FALSE,
conf.level = 0.95)
spd <- data.frame(
spider = c(1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15),
control = c(2.5, 5.5, 1.1, 2.7, 2.8, 1.6, 3.2, 4.5, 5.0, 6.9, 2.2, 3.9, 3.8, 3.5, 5.7),
mantis = c(0.4, 1.9, 1.2, 2.6, 4.3, 0.3, 1.0, 1.5, 3.3, 2.6, 0.7, 1.4, 2.1, 3.4, 2.3))
(control.avg <- mean(spd$control))
(mantis.avg <- mean(spd$mantis))
(control.var <- var(spd$control))
(mantis.var <- var(spd$mantis))
(spd$dif <- spd$control - spd$mantis)
(d.bar <- mean(spd$dif))
(dif.var <- var(spd$dif))
(r <- length(spd$dif))
d.bar.var <- dif.var / r
(d.bar.var <- dif.var / r)
(tcalc <- d.bar / sqrt(d.bar.var))
(tcrit <- qt(p =0.975, df = r-1))
(CIlo <- d.bar - tcrit * sqrt(d.bar.var))
(CIhi <- d.bar + tcrit * sqrt(d.bar.var))
t.test(x = spd$control,
y = spd$mantis,
alternative = "two.sided",
mu = 0,
paired = TRUE,
conf.level = 0.95)
rats <- data.frame(
'males' = c(700, 825, 425, 500, 575, 725, 800, 475, 575, 725, 500, 700, 575, 775),
'females' = c(450, 725, 675, 725, 750, 850, 690, 725, 475, 700, 725, 475, 825, 725))
(sample.avg <- sapply(rats, mean))
(sample.var <- sapply(rats, var))
sample.avg["males"]
sample.avg[1]
sample.avg["females"]
sample.avg[2]
r1 <- length(rats$males)
r2 <- length(rats$females)
(fem.var <- var(rats$females))
(male.var <- var(rats$males))
(pooled.var <- ((r1 - 1) * male.var + (r2 - 1) * female.var) / (r1 + r2 - 2))
(pooled.var <- ((r1 - 1) * male.var + (r2 - 1) * fem.var) / (r1 + r2 - 2))
(rat.d.bar.var <- pooled.var / r1 + pooled.var / r2)
rat.d.bar <- sample.avg[1] - sample.avg[2]
(rat.tcalc <- rat.d.bar / sqrt(rat.d.bar.var))
t.test(x = rats$male,
y = rats$females,
alternative = "two.sided",
mu = 0,
paired = FALSE,
conf.level = 0.95)
pt(q = abs(rat.tcalc), df = rat.df, lower.tail = FALSE)
(rat.df <- r1 + r2 - 2)
pt(q = abs(rat.tcalc), df = rat.df, lower.tail = FALSE)
2 * pt(q = abs(rat.tcalc), df = rat.df, lower.tail = FALSE)
r1
transg.aa.m1 <- lm(wgain ~ variety, data = aaAnovaExmpl1.dat)
summary(transg.aa.m1)
anova(transg.aa.m1)
>>>>>>> EAL11Oct18
>>>>>>> master