R Notebook

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# Generate age data
age <- c(25, 30, 35, 40, 45, 50, 55, 60, 65, 70)

# Generate corresponding height data
height <- c(160, 165, 170, 175, 180, 185, 190, 195, 200, 205)

# Calculate xy
age_height <- age * height

# Calculate the sum of xy
sum_age_height <- sum(age_height)

# Calculate n (number of data points)
n <- length(age)

# Calculate n * sum_xy
n_times_sum_age_height <- n * sum_age_height

# Calculate sum of age
sum_age <- sum(age)

# Calculate sum of height
sum_height <- sum(height)

# Calculate sum of age * sum of height
sum_age_times_sum_height <- sum_age * sum_height

# Calculate the numerator
num <- n * sum_age_height - sum_age * sum_height

# Calculate sq of age
age_sq <- age^2

# Calculate sum of sq of age
sum_age_sq <- sum(age_sq)

# Calculate n * sum of sq of age
n_times_sum_age_sq <- n * sum_age_sq

# Calculate sq of sum age
sq_sum_age <- sum_age^2

# Calculate sq of height
height_sq <- height^2

# Calculate sum of sq of height
sum_height_sq <- sum(height_sq)

# Calculate n * sum of sq of height
n_times_sum_height_sq <- n * sum_height_sq

# Calculate sq of sum height
sq_sum_height <- sum_height^2

# Calculate the denominator
deno <- ((n * sum_age_sq) - sq_sum_age) * ((n * sum_height_sq) - sq_sum_height)

# Calculate the square root of the denominator
sq_root_deno <- deno^0.5

# Calculate the correlation coefficient (R)
r <- num / sq_root_deno

# Output the correlation coefficient
r

## [1] 1