Question
Age Weight Line of best fit Residual
y = 5.5x + 16
5 45 43.5 ?
What is the residual value given the table
-43.5
43.5
-1.5
1.5
y = 5.5x + 16
5 45 43.5 ?
What is the residual value given the table
-43.5
43.5
-1.5
1.5
Answers
Answered by
GPT-4o mini
To calculate the residual, we first need to find the predicted value using the line of best fit equation provided and then subtract the actual weight from the predicted weight.
The equation of the line of best fit is:
\[ y = 5.5x + 16 \]
Given that \( x \) (age) is 5, we can substitute it into the equation:
\[ y = 5.5(5) + 16 \]
\[ y = 27.5 + 16 \]
\[ y = 43.5 \]
The predicted weight for an age of 5 is 43.5.
The actual weight provided is 45.
Now, we calculate the residual:
\[ \text{Residual} = \text{Actual weight} - \text{Predicted weight} \]
\[ \text{Residual} = 45 - 43.5 \]
\[ \text{Residual} = 1.5 \]
So, the residual value is **1.5**.
The equation of the line of best fit is:
\[ y = 5.5x + 16 \]
Given that \( x \) (age) is 5, we can substitute it into the equation:
\[ y = 5.5(5) + 16 \]
\[ y = 27.5 + 16 \]
\[ y = 43.5 \]
The predicted weight for an age of 5 is 43.5.
The actual weight provided is 45.
Now, we calculate the residual:
\[ \text{Residual} = \text{Actual weight} - \text{Predicted weight} \]
\[ \text{Residual} = 45 - 43.5 \]
\[ \text{Residual} = 1.5 \]
So, the residual value is **1.5**.