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:

Foot Drop

A gait abnormality where the forefoot drops due to weakness, irritation or damage to the peroneal nerve, or paralysis of the muscles in the anterior portion of the lower leg.

High-Top Tennis Shoes

Athletic shoes that extend significantly above the ankle, offering extra support, commonly used in sports and as casual wear.

Podiatry Consult

A professional evaluation by a podiatrist, a specialist in diagnosing and treating conditions of the foot, ankle, and lower leg.

Compromised Family Coping

A situation where a family's usual strategies for managing stress and problems are overwhelmed or ineffective.