Question

The eggs of a species of bird have an average diameter of 23 mm and an SD of 0.45 mm. The weights of the chicks that hatch from these eggs have an average of 6 grams and an SD of 0.5 grams. The correlation between the two variables is 0.75 and the scatter diagram is roughly football shaped. Find the regression estimate of the weight of a chick that hatches from an egg 24 mm in diameter. Find the regression estimate of the weight of a chick that hatches from an egg 22.5 mm in diameter.

Answer 1

The z-score of an egg measuring 25 mm in diameter is as follows:
\[z _{1}=\frac{24-23}{0.45}=2.2222\]
The z-score for the chick weight estimate corresponding to an egg diameter of 24 mm is found by multiplying z1 by the correlation giving
\[z _{2}=2.2222\times 0.75=1.6666\]
The z-score for the weight estimate is is used to find the estimated weight w as follows:
\[1.6666=\frac{w-6}{0.5}\]
Solving for w gives
\[w=6+(0.5\times 1.6666)=you\ can\ calculate\]