Question

the scatter plot and line of best fit below show the length of 10 peoples femur (the long leg bone in the thigh) and their height in centimeters. what does the slope of the line represent?
answer
the expected femur length when the height is 1 centimeter.
the change in expected femur length for every one additional centimeter of height.
the change in expected height for every one additional centimeter of femur length.
the expected height when the femur has a length of 1 centimeter.

Explanation:

1. Recall the definition of slope in a linear regression (line of best fit) context: Slope = $\frac{\text{Change in } y\text{-variable}}{\text{Change in } x\text{-variable}}$.
2. Identify the variables: The x - axis is femur length (independent variable), and the y - axis is height (dependent variable).
3. Analyze each option:

• Option 1: Slope is not about femur length when height is 1 (that would be related to the inverse or misinterpreting variables).
• Option 2: Slope is not about change in femur length per height unit (since femur is x, height is y).
• Option 3: Since y is height and x is femur length, slope = $\frac{\Delta \text{height}}{\Delta \text{femur length}}$, so it's the change in expected height for each additional centimeter of femur length.
• Option 4: The y - intercept (not slope) would be related to expected height when femur length is 0 (or 1 in misinterpretation), but slope is about rate of change.

Answer:

The change in expected height for every one additional centimeter of femur length.