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
( mathrm{cm}^{2} )
cm per kg
( mathrm{kg}^{2} )
c) do you think the slope is positive or negative? explain.
the slope is probably because

Explanation:

• Part a: In a regression, the predictor variable (independent variable) is what we use to predict the response variable (dependent variable). Here, length (in cm) is used to predict weight (in kg).
• Part b: The slope formula in regression is \(b_1=\frac{\sum(x_i - \bar{x})(y_i-\bar{y})}{\sum(x_i - \bar{x})^2}\). The units of \(y\) (weight in kg) divided by the units of \(x\) (length in cm) gives kg per cm.
• Part c: In general, as the length of a newborn boy increases, we would expect their weight to also increase. A positive slope indicates a positive linear relationship between the two variables (as \(x\) (length) increases, \(y\) (weight) increases).

Answer:

a) Predictor variable: Length (units: cm); Response variable: Weight (units: kg)
b) kg per cm
c) positive; as the length of a newborn boy increases, we expect their weight to increase (a positive linear relationship)