MediumStatistics & Data ScienceHigh School (9–10)High School (11–12)UndergraduateGeneralStatistics Basics › Correlation and RegressionNumericalConceptual
Four made-up seedlings are measured. After 1, 2, 3 and 4 weeks their heights are 4, 6, 8 and 11 cm…
Contributed by StemPy LabTry it on paper first. A hint, the key idea and the worked solution are here when you need them.
Four made-up seedlings are measured. After , , and weeks their heights are , , and cm. Asha draws the line , and Ben draws . Find the sum of squared residuals of each line. Which line fits better? Then find the SSE of the least-squares line, which is .
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. Asha. Residuals , , and cm. SSE .
Step 2. Ben. Residuals , , and cm. SSE .
Step 3. Least squares. The predictions are , , and cm, so the residuals are , , and cm. SSE .
Answer: Asha , Ben , least squares . Asha's line fits better than Ben's, and the least-squares line beats both.
Check. The residuals of the least-squares line add up to , as they must.
Discussion (0)
Log in to join the discussion.
Loading…