Question

the scatter plot and line of best fit below show the length of 8 peoples femur (the long leg bone in the thigh) and their height in centimeters. what is the meaning of the x - value on the line when y = 170? answer the height of an actual person with a femur length of 45.9 centimeters is 170 centimeters. an expected height of 170 centimeters when the femur has a length of 45.9 centimeters. the height of an actual person with a femur length of 170 centimeters is 45.9 centimeters. an expected height of 45.9 centimeters when the femur has a length of 170 centimeters.

Explanation:

The line of best fit in a scatter plot represents the trend or expected relationship between two variables. Here, the \( y \)-axis is height (in cm) and the \( x \)-axis is femur length (in cm). When \( y = 170 \) (height), the \( x \)-value on the line of best fit gives the expected femur length for a person with a height of 170 cm, or more accurately, the expected femur length that corresponds to an expected height of 170 cm. Let's analyze the options:

• Option 1: The line of best fit is not about actual values but expected (since it's a model), so this is incorrect.
• Option 2: This correctly states that when the femur length is 45.9 cm (the \( x \)-value), the expected height ( \( y \)-value) is 170 cm.
• Option 3: The axes are mixed up (femur length is \( x \), height is \( y \)), so this is incorrect.
• Option 4: The axes are mixed up, and the interpretation of the variables is wrong.

Answer:

An expected height of 170 centimeters when the femur has a length of 45.9 centimeters.