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:
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Calculate the predicted value (\(y_{\text{pred}}\)) using the equation for \(x = 4\):
\[ y_{\text{pred}} = -0.694(4) + 17.22 \]
\[ y_{\text{pred}} = -2.776 + 17.22 = 14.444 \]
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Find the actual \(y\) value for the data point:
The actual \(y\) value for the data point is \(14.59\).
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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 \(0.146\).