Show First That the Regression R² Is the Square of the Sample

question 35

Essay

Show first that the regression R² is the square of the sample correlation coefficient. Next, show that the slope of a simple regression of Y on X is only identical to the inverse of the regression slope of X on Y if the regression R² equals one.

---

Definitions:

Physical Appearance

The outward look or aspect of a person, including body shape, skin color, hair style, and other physical traits.

Perspective-taking Skills

The cognitive capacity to view situations from the viewpoints of others, facilitating empathy and social understanding.

More Than One Perspective

The recognition that there can be multiple viewpoints or interpretations of a given situation, reflecting the complexity of human thought and understanding.

Robert Selman

A psychologist known for his work in the development of social understanding in children and his stages of perspective-taking.