A z-score, also known as the standard score, is a numerical value that measures the distance of a value from a mean using standard deviations. This value can be either positive or negative, with positive showing the value lies above the mean, and negative showing it lies below the mean.

To calculate the z-score of tree 8’s height in the dataset trees, we first need to find the mean and standard deviation of the heights in the dataset:

# Value, Mean, and Standard Deviation
df$Height[8]

[1] 75

mean(df$Height)

[1] 76

sd(df$Height)

[1] 6.371813

\({75-76\over 6.371813} = -0.1569412\)

To calculate the z-score of tree 26’s volume in the dataset trees, we first need to find the mean and standard deviation of the volumes in the dataset:

# Value, Mean, and Standard Deviation
df$Volume[26]

[1] 55.4

mean(df$Volume)

[1] 30.17097

sd(df$Volume)

[1] 16.43785

\({55.4-30.17097\over 16.43785} = 1.534813\)

## `geom_smooth()` using formula 'y ~ x'

## `geom_smooth()` using formula 'y ~ x'

fig <- plot_ly(data = df, x = c(1:31), y = df$Height,
    marker = list(size = 10, color = "darksalmon",
        line = list(color = "darkred", width = 2)),
    type = "scatter", mode = "markers") %>%
    layout(title = "Height of Cherry Trees")

ggplot(df, aes(c(1:31), Girth)) + geom_point() +
    geom_smooth(method = lm, size = 1, color = "deeppink") +
    labs(x = "Trees", title = "Girth of Cherry Trees")

## `geom_smooth()` using formula 'y ~ x'

ggplot(df, aes(Volume, Height)) + geom_point() +
    geom_smooth(method = lm, size = 1, color = "maroon") +
    labs(title = "Height against Volume of Cherry Trees")

## `geom_smooth()` using formula 'y ~ x'