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.

Question

1. y = .444 (8.5) minus 21.29. 2. y = 3.774 minus 21.29. 3. y = negative 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?
She substituted the 8.5 for the wrong variable.
She should have added .444 and 8.5.
The value for y should be positive.
The solution of –17.52 should be the shoe size.

Answer 1

Ramona’s mistake is that she substituted the 8.5 for the wrong variable.

In the equation \( y = 0.444x - 21.29 \), \( x \) represents height and \( y \) represents shoe size. Since she was trying to predict height based on the shoe size of 8.5, she should have substituted 8.5 for \( y \) instead of for \( x \) to calculate the corresponding height.

The correct procedure would be to rearrange the equation to solve for \( x \) given \( y = 8.5 \):

1. Substitute \( y = 8.5 \): \[ 8.5 = 0.444x - 21.29 \]

2. Add 21.29 to both sides: \[ 8.5 + 21.29 = 0.444x \] \[ 29.79 = 0.444x \]

3. Divide both sides by 0.444 to solve for \( x \): \[ x = \frac{29.79}{0.444} \approx 67.1 \]

Thus, the height of a man who wears a size 8.5 shoe would be approximately 67.1 inches.