Question

a least squares regression line was calculated to relate the length (cm) of newborn boys to their weight in kg. $r^{2}=68.1%$. complete parts a through c below.
a) what are the variables and what are the units in this regression?
the predictor variable is length in units of cm and the response variable is weight in units of kg.
b) what are the units for the slope?
kg per cm
$cm^{2}$
cm per kg
$kg^{2}$

Explanation:

The slope of a regression line \(y = a+bx\) is calculated as \(b=\frac{\sum(x_i - \bar{x})(y_i - \bar{y})}{\sum(x_i - \bar{x})^2}\). In the context of a regression relating length (\(x\), units \(cm\)) and weight (\(y\), units \(kg\)), the units of the slope \(b\) are determined by the units of \(y\) (response variable) divided by the units of \(x\) (predictor variable).

Answer:

kg per cm