Question

ramona used the regression equation $y =.444x - 21.29$, where $x$ represents height and $y$ represents shoe size, to predict the approximate height of a man who wears a size 8.5 shoe.

1. $y =.444(8.5) - 21.29$
2. $y = 3.774 - 21.29$
3. $y = -17.52$

ramona determined that her answer was incorrect because a man who is $-17.52$ inches tall does not make any sense. what was ramona’s mistake?
\bigcirc she substituted the 8.5 for the wrong variable.
\bigcirc she should have added.444 and 8.5.
\bigcirc the value for $y$ should be positive.
\bigcirc the solution of $-17.52$ should be the shoe size.

Explanation:

The regression equation is \( y = 0.444x - 21.29 \), where \( x \) is height and \( y \) is shoe size. Ramona was supposed to predict height (x) for a given shoe size (y = 8.5). But she substituted 8.5 for \( x \) (height) instead of \( y \) (shoe size). So she used the wrong variable for substitution. The other options are incorrect: adding 0.444 and 8.5 is not how regression substitution works, the sign of \( y \) isn't the issue here (she mixed up variables), and -17.52 is not a shoe size (she was solving for height incorrectly).

Answer:

A. She substituted the 8.5 for the wrong variable.