Juvenile Height

In the table below we show average juvenile height as a function of age [4].

1. Compute the difference from the y value of the data point to y value on the line
   e_i = y_i - y(x_i) = y_i - (ax_i + b), i = 1,...n.
2. Square the error, then add all the errors together.

For the juvenile height, we have

e₁ = y₁ - (6.46x₁ + 72.3) = 75 - (6.46(1) + 72.3) = -3.76

e₂ = y₂ - (6.46x₂ + 72.3) = 92 - (6.46(3) + 72.3) = 0.32

e₃ = 108 - (6.46(5) + 72.3) = 3.40

e₄ = 121 - (6.46(7) + 72.3) = 3.48

e₅ = 130 - (6.46(9) + 72.3) = -0.44

e₆ = 142 - (6.46(11) + 72.3) = -1.36

e₇ = 155 - (6.46(13) + 72.3) = -1.28

The sum of square errors is

e₁² + e₂² +... + e₇² = (-3.76)² + (0.32)² + ... + (-1.28)² = 41.5