Question
The scatter plot and line of best fit below show the length of 12 people's femur (the long leg bone in the thigh) and their height in centimeters. Calculate the residual for the data point that corresponds to someone with a femur length of 45 cm and a height of 157.8 cm.
0
x
y
0
(60,197)
(63,204)
(45,162)
Height (centimeters)
Femur Length (centimeters)
Answer
Attempt
0
x
y
0
(60,197)
(63,204)
(45,162)
Height (centimeters)
Femur Length (centimeters)
Answer
Attempt
Answers
GPT-4o mini
To calculate the residual for a given data point, you first need to find the predicted height based on the line of best fit, and then subtract that predicted height from the actual height of the data point.
1. **Identify the data point**: The data point corresponds to a femur length of 45 cm and a height of 157.8 cm.
2. **Find the predicted height from the line of best fit**:
Since I cannot see the scatter plot or the line of best fit, I won't be able to give you the exact value. However, I'll guide you through the process:
- If you could determine the equation of the line of best fit (it often takes the form \( y = mx + b \)), substitute the femur length (45 cm) into this equation to get the predicted height.
- Calculate it as follows: \( \text{predicted height} = m(45) + b \).
3. **Calculate the residual**:
The residual is calculated using the formula:
\[
\text{Residual} = \text{Actual height} - \text{Predicted height}
\]
For example, if the predicted height for a femur length of 45 cm is 162 cm, then:
\[
\text{Residual} = 157.8 \text{ cm} - 162 \text{ cm} = -4.2 \text{ cm}
\]
Once you find the predicted height, replace it in the equation above to find the exact residual value. If you provide the equation of the line or the predicted value, I can help you further with the calculation.
1. **Identify the data point**: The data point corresponds to a femur length of 45 cm and a height of 157.8 cm.
2. **Find the predicted height from the line of best fit**:
Since I cannot see the scatter plot or the line of best fit, I won't be able to give you the exact value. However, I'll guide you through the process:
- If you could determine the equation of the line of best fit (it often takes the form \( y = mx + b \)), substitute the femur length (45 cm) into this equation to get the predicted height.
- Calculate it as follows: \( \text{predicted height} = m(45) + b \).
3. **Calculate the residual**:
The residual is calculated using the formula:
\[
\text{Residual} = \text{Actual height} - \text{Predicted height}
\]
For example, if the predicted height for a femur length of 45 cm is 162 cm, then:
\[
\text{Residual} = 157.8 \text{ cm} - 162 \text{ cm} = -4.2 \text{ cm}
\]
Once you find the predicted height, replace it in the equation above to find the exact residual value. If you provide the equation of the line or the predicted value, I can help you further with the calculation.