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A made-up solar garden lamp is tested on three days…
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 solar garden lamp is tested on three days. With , and hours of sunshine, it gives light for , and hours at night. A student draws the line , where is the sunshine in hours and the predicted hours of light. Find the three residuals and the sum of squared residuals.
Need a reminder? The key ideaShow
The residual of a point is , observed minus predicted. The sum of squared residuals (SSE) scores a line. The least-squares line has the smallest SSE, and its residuals add up to .
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. Predictions. , and hours.
Step 2. Residuals. hour, hours and hours.
Step 3. SSE. .
Answer: residuals of , and hours, and an SSE of .
Check. All residuals are or positive, so the student's line sits a little low. The least-squares line would be higher, with residuals that add up to .
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