• A point estimate involves using sample data to determine a population or a single value.

• An example of this woule be to survey 150 people and find that the average is 7.2 hours. Therefore, 7.2 hours of sleep per night is the point value of sleep in the area.

• Parameter(\(\theta\)): unknown number of population

• Estimator(\(\hat{\theta}\)): a formula applied to a sample data set to estimate \(\theta\).

Population mean (\(\mu\)) is calculated by: \(\space\bar{X} = \frac{\Sigma^{}x_{i}}{n}\)

Population proportion (\(\rho\)) is calculated by: \(\hat{p} = \frac{X}{n}\)

Population variance (\(\sigma^2\)) is calculated by: \(\mathcal{S}^2 = \frac{1}{n-1}\Sigma(\mathcal{X}_{i}-\bar{\mathcal{X}})^2\)

Big dot to represent the point estimation for each species.

mean_set_pl <- mean(iris$Petal.Length[iris$Species == "setosa"])
mean_set_pw <- mean(iris$Petal.Width[iris$Species == "setosa"])
mean_ver_pl <- mean(iris$Petal.Length[iris$Species == "versicolor"])
mean_ver_pw <- mean(iris$Petal.Width[iris$Species == "versicolor"])
mean_vir_pl <- mean(iris$Petal.Length[iris$Species == "virginica"])
mean_vir_pw <- mean(iris$Petal.Width[iris$Species == "virginica"])

scatter_iris <- ggplot(iris, 
aes(x=Petal.Length, y=Petal.Width, color=Species)) +
  geom_point(alpha=1) +
  geom_point(aes(mean_vir_pl, mean_vir_pw), 
    alpha=.05, size= 7, color="blue") +
  geom_point(aes(mean_set_pl, mean_set_pw), 
    alpha=.05, size= 7, color="red") +
  geom_point(aes(mean_ver_pl, mean_ver_pw), 
    alpha=.05, size= 7, color="green") +
  labs(title = "Iris petal length vs width by species")

scatter_iris