To find the residual for the data point (4, 14.59) using the equation \( y = -0.694x + 17.22 \), we first need to calculate the predicted value of \( y \) when \( x = 4 \).
- Substitute \( x = 4 \) into the equation:
\[ y = -0.694(4) + 17.22 \]
- Calculate \( -0.694 \times 4 \):
\[ -0.694 \times 4 = -2.776 \]
- Now, add this to 17.22:
\[ y = -2.776 + 17.22 = 14.444 \]
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The predicted value of \( y \) when \( x = 4 \) is 14.444.
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Now, calculate the residual:
The residual is given by the formula:
\[ \text{Residual} = \text{Actual Value} - \text{Predicted Value} \]
Substituting the actual value (14.59) and the predicted value (14.444):
\[ \text{Residual} = 14.59 - 14.444 = 0.146 \]
- Round to the nearest thousandths:
\[ \text{Residual} \approx 0.146 \]
So, the residual of the data point (4, 14.59) is 0.146.