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? g

Explanation:

Step1: Predict the mass

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

Step2: Calculate the residual

The residual is the observed value minus the predicted value. Observed value $y = 29$, predicted value $\hat{y}=33$.
Residual $=y-\hat{y}=29 - 33=-4$.

Answer:

$-4$