Question
y = -0.694x + 17.22
What is the residual of the data point (4, 14.59)
What is the residual of the data point (4, 14.59)
Answers
GPT-4o mini
To calculate the residual of the data point \((4, 14.59)\) for the given linear equation \(y = -0.694x + 17.22\), we will follow these steps:
1. **Calculate the predicted value (\(y_{\text{pred}}\)) using the equation for \(x = 4\)**:
\[
y_{\text{pred}} = -0.694(4) + 17.22
\]
\[
y_{\text{pred}} = -2.776 + 17.22 = 14.444
\]
2. **Find the actual \(y\) value for the data point**:
The actual \(y\) value for the data point is \(14.59\).
3. **Calculate the residual**:
The residual is calculated as:
\[
\text{Residual} = \text{Actual } y - y_{\text{pred}}
\]
\[
\text{Residual} = 14.59 - 14.444 = 0.146
\]
Therefore, the residual of the data point \((4, 14.59)\) is \(0.146\).
1. **Calculate the predicted value (\(y_{\text{pred}}\)) using the equation for \(x = 4\)**:
\[
y_{\text{pred}} = -0.694(4) + 17.22
\]
\[
y_{\text{pred}} = -2.776 + 17.22 = 14.444
\]
2. **Find the actual \(y\) value for the data point**:
The actual \(y\) value for the data point is \(14.59\).
3. **Calculate the residual**:
The residual is calculated as:
\[
\text{Residual} = \text{Actual } y - y_{\text{pred}}
\]
\[
\text{Residual} = 14.59 - 14.444 = 0.146
\]
Therefore, the residual of the data point \((4, 14.59)\) is \(0.146\).