Final answer:
The student's question involves various principles of mathematics, such as multivariate linear regression, the sum of squared errors, and the Pythagorean theorem. The statements given are related to statistics, physics, and geometry, and are generally found to be true or false based on mathematical laws and empirical evidence.
Step-by-step explanation:
The subject of the question refers to principles of multivariate linear regression, objective functions, and sum of squared errors (SSE), which are all essential concepts in the field of mathematics, particularly in the context of statistics and data analysis. The inquiries given can be deemed to imply a high school or possibly a college level of understanding, as they are concerned with mathematical theory and application.
- Concerning the original statement, the first objective function being the sum of squared errors in a multivariate linear regression problem mapping R^D to R is true.
- For an object moving with constant acceleration, the plot of displacement versus time will indeed be a curved line, and the plot of displacement versus time squared will be a straight line, making the statement true.
- The Pythagorean theorem is applicable to calculate the length of a resultant vector from two vectors at right angles to each other - also true.
- Finding the angle of a resultant addition vector knowing only the angles of two vectors is generally false since you also need the magnitude of the vectors.
- The addition of five vectors does not necessarily result in a vector of greater magnitude compared to any two - this statement is false as it depends on the direction and magnitude of the individual vectors.
- Wave-particle duality mainly exists in quantum mechanics and does not generally apply to macroscopic objects making this statement false.
- Lastly, the least-squares criterion is a method used for finding the best-fit line in regression by minimizing the SSE, which is true.