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Residuals

A residual is the difference between the actual value and the
Answer value.
Steps to finding a residual:
1. Substitute the point's
Answer
into the equation to find the
Answer
' value of y.
2. Subtract the
Answer
value of y from the point's
Answer
value of y.
Example: Suppose the regression line modeling ticket sales is y = -5.9x + 170.85, where x represents ticket price
and y represents attendance.
What is the predicted attendance when the ticket price is $5? Answer The actual attendance was 160 when the ticket price was $5.
Find the residual:
1 Answer
:: predicted
:: predicted
:: 160-141.3 = 18.7
:: predicted
÷ actual
:: x-value
:: 141.3

1 answer

Let's go through the process of finding the residual step by step based on the example given.

  1. Substitute the point's x-value (ticket price) into the equation to find the predicted value of y (attendance).

    The regression line modeling ticket sales is given by the equation: \[ y = -5.9x + 170.85 \] For a ticket price of $5 (where \(x = 5\)): \[ y = -5.9(5) + 170.85 \] \[ y = -29.5 + 170.85 \] \[ y = 141.35 \]

    So, the predicted attendance when the ticket price is $5 is 141.35.

  2. Subtract the predicted value of y from the actual value of y to find the residual.

    The actual attendance is given as 160.

    To find the residual: \[ \text{Residual} = \text{Actual attendance} - \text{Predicted attendance} \] \[ \text{Residual} = 160 - 141.35 \] \[ \text{Residual} = 18.65 \]

So, the residual is 18.65.

Summary:

  • Predicted attendance when ticket price is $5: 141.35
  • Actual attendance: 160
  • Residual: 18.65