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In a made-up fish farm, the lengths of some young fish have mean 20 cm and standard deviation 4 cm…
Contributed by StemPy LabTry it on paper first. A hint, the key idea and the worked solution are here when you need them.
In a made-up fish farm, the lengths of some young fish have mean cm and standard deviation cm. Their masses have mean g and standard deviation g. The correlation is . Find the slope and the intercept of the least-squares line that predicts mass from length. Then predict the mass of a fish cm long.
Need a reminder? The key ideaShow
The least-squares line has
The slope is the change in for each extra unit of . Predict inside the range of the data.
The worked solution
Have you tried it?
Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.
Step 1. Slope. g per cm.
Step 2. Intercept. g.
Step 3. Prediction. g.
Answer: ; a cm fish is predicted to weigh g.
Check. A fish cm longer than average is predicted g heavier than average. That is standard deviations in length, but only standard deviation in mass, because shrinks the step.
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