Changing the Units of Measurement Obviously Will Have an Effect $Y ^ { * } = a Y \text { and } X ^ { * } = b X \text {. }$

question 51

Essay

Changing the units of measurement obviously will have an effect on the slope of your regression function. For example, let $Y ^ { * } = a Y \text { and } X ^ { * } = b X \text {. }$
Then it is easy
but tedious to show that $\widehat { \beta } _ { 1 } ^ { * } = \frac { \sum _ { i = 1 } ^ { n } x _ { i } ^ { * } y _ { i } ^ { * } } { \sum _ { i = 1 } ^ { n } x _ { i } ^ { * 2 } } = \frac { a } { b } \widehat { \beta } _ { 1 }$ Given this result, how do you think
the standard errors and the regression $R ^ { 2 }$ will change?

---

Definitions:

Posttraumatic Stress Disorder

A mental health condition triggered by experiencing or witnessing a terrifying event, characterized by flashbacks, nightmares, and severe anxiety.

Acute Stress Disorder

A disorder in which fear and related symptoms are experienced soon after a traumatic event and last less than a month.

Dissociative Amnesia

A dissociative disorder marked by an inability to recall important personal events and information.

Traumatic Episode

A distressing experience that causes intense emotional and physical reactions, which can lead to long-term psychological effects.