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Use the image to answer the question.

Four points are plotted on the first quadrant of a coordinate plane. The x-axis ranges from 0 to 10 in increments of 1 and the y-axis ranges from 0 to 17 in increments of 1. A line is drawn that almost passes through all the points.

Find the residual of the data point (4,14.59)
. Round the answer to the nearest thousandths.

(1 point)
The residual of the data point (4,14.59)
is
.

1 answer

To find the residual of the data point \((4, 14.59)\), we need to follow these steps:

  1. Identify the observed value (y): The observed value from the data point is \(y = 14.59\).

  2. Determine the predicted value (\(\hat{y}\)): This value is obtained from the line that is drawn through the points. Since the image is not provided, let's assume you have the equation of the line that fits those points. Let’s denote the equation of the line by \(y = mx + b\), where \(m\) is the slope and \(b\) is the y-intercept. You would substitute \(x = 4\) into this equation to find \(\hat{y}\).

  3. Calculate the residual: The residual is calculated using the formula: \[ \text{Residual} = \text{Observed value} - \text{Predicted value} \] or \[ \text{Residual} = y - \hat{y} \]

  4. Round off: Finally, round the residual to the nearest thousandth, as required.

Since the equation of the line is not available, I can't provide the numerical values. If you can provide the equation or the predicted value when substituting \(x=4\), I can help you calculate the residual!