Show First That the Regression $R ^ { 2 }$ Is the Square of the Sample Correlation Coefficient

question 6

Essay

Show first that the regression $R ^ { 2 }$ 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 $R ^ { 2 }$ equals one.

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Definitions:

Centenarians

Are people who have reached 100 years of age or more.

Ontario

A province of Canada, located in the eastern part of the country, known for its diverse landscapes, the national capital Ottawa, and the populous city of Toronto.

Elisabeth Kübler-Ross

A Swiss-American psychiatrist known for her theory on the five stages of grief, originally described in her book "On Death and Dying".

Stages of Dying

A concept, often associated with Elisabeth Kübler-Ross, outlining the typical progression of emotional stages experienced by terminally ill patients, including denial, anger, bargaining, depression, and acceptance.