Question

danila breeds peregrine falcons. she recorded the breadth (in mm) of each egg and the mass (in g) of the falcon chick that hatched from it. after plotting her results, danila noticed that the relationship between the two variables was fairly linear, so she used the data to calculate the following least squares regression equation for predicting the mass of the chick from the breadth of the egg: $hat{y}=-47 + 2x$. what is the residual of a 29 g falcon chick who hatches from an egg with a breadth of 40 mm?

Explanation:

Step1: Calculate predicted value

The regression equation is $\hat{y}=-47 + 2x$. Substitute $x = 40$ into the equation.
$\hat{y}=-47+2\times40=-47 + 80=33$.

Step2: Calculate residual

The formula for residual is $e=y-\hat{y}$. Given $y = 29$ and $\hat{y}=33$.
$e=29 - 33=-4$.

Answer:

$-4$