13.5.1. Principle of Least Squares

Try these first

1. 1.

   What does the Principle of Least Squares aim to minimize?

   Hint

   Think about the differences between observed and adjusted values.

2. 2.

   Name one assumption of the Principle of Least Squares.

   Hint

   How do errors behave in this adjustment method?

3. 3.

   What does the Principle of Least Squares aim to minimize?

   • The sum of absolute values
   • The sum of squares of residuals
   • The sum of average values

   Hint

   Think about the formula for residuals and what we are trying to achieve.

4. 4.

   True or False: The observations in least squares adjustment can be assumed to have equal precision.

   • True
   • False

   Hint

   Consider how adjustments might differ based on reliability.

5. 5.

   Given the following observed values: [3, 5, 7, 8] and adjusted values: [2.5, 4.5, 6.5, 7.5], calculate the residuals and their sum of squares. Discuss how changing one of the observed values may affect the outcome.

   Hint

   Calculate residuals individually before summing them.

6. 6.

   Discuss the implications of violating the assumption of random error distribution in least squares adjustment. What strategies can be employed to address systematic errors in datasets?

   Hint

   Use examples from data collection processes to illustrate your answer.