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A made-up class records the height of a bean plant every few days for three weeks…
Contributed by StemPy LabTry it on paper first. A hint, the key idea and the worked solution are here when you need them.
A made-up class records the height of a bean plant every few days for three weeks. The least-squares line is , where is the time in days and the predicted height in centimetres. Say what the slope and the intercept mean. Predict the height on day , and the growth predicted over one week.
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. The slope. cm per day: the plant is predicted to grow about cm each day, on average.
Step 2. The intercept. cm is the predicted height at , the day the measuring started. Here it makes sense, because day is just inside the data.
Step 3. Day 10. cm.
Step 4. One week. cm.
Answer: cm on day , and cm of growth a week.
Watch out. After three weeks a bean plant may grow more slowly, or start to climb. Do not use the line for day .
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