Question

the scatter plot and line of best fit below show the length of 5 peoples femur (the long leg bone in the thigh) and their height in centimeters. what is the meaning of the y - value on the line when ( x = 45 )?
answer
as expected height of 157.3 centimeters when the
femur has a length of 45 centimeters.

as expected height of 45 centimeters when the
femur has a length of 157.3 centimeters.

the height of an actual person with a femur length
of 157.3 centimeters is 45 centimeters.

the height of an actual person with a femur length
of 45 centimeters is 157.3 centimeters.

Explanation:

Step1: Understand the line of best fit concept

The line of best fit in a scatter - plot is used to predict values. Here, \(x\) represents height (in centimeters) and \(y\) represents femur length (in centimeters). We are asked to find the \(y\) - value (femur length) when \(x = 45\) (height is 45 centimeters).

Step2: Interpret the axes labels

The \(x\) - axis is labeled "Height (centimeters)" and the \(y\) - axis is labeled "Femur Length (centimeters)". When we talk about the \(y\) - value on the line for a given \(x\) - value, we are making a prediction. In the context of regression (line of best fit), the \(y\) - value for a given \(x\) is the expected value. So, when \(x = 45\) (height = 45 centimeters), the \(y\) - value on the line is the expected femur length.

Answer:

An expected femur length of 45 centimeters when the height is 157.3 centimeters.