Question

Calculate the residual for each of the coordinate pairs (x, y) given the line of best fit: y = 1.12 + 3.4.

a. (5, 8.8)
b. (2.5, 5.95)
c. (0, 3.72)
d. (1.5, 5.05)
e. (-3, 0)
f. (-5, -4.86)

Answer 1

To calculate the residual for each coordinate pair given the line of best fit, substitute the x-value into the equation and subtract the predicted y-value from the actual y-value. For example, for (5, 8.8), the residual is -9.32.

Step-by-step explanation:

To calculate the residual for each of the coordinate pairs (x, y) given the line of best fit, we need to substitute the x-value into the equation of the line and subtract the predicted y-value from the actual y-value.

1. For (5, 8.8):
   Substituting x=5 into the equation: y = 1.12 + 3.4(5) = 1.12 + 17 = 18.12
   Residual = Actual y - Predicted y = 8.8 - 18.12 = -9.32
2. For (2.5, 5.95):
   Substituting x=2.5 into the equation: y = 1.12 + 3.4(2.5) = 1.12 + 8.5 = 9.62
   Residual = Actual y - Predicted y = 5.95 - 9.62 = -3.67
3. For (0, 3.72):
   Substituting x=0 into the equation: y = 1.12 + 3.4(0) = 1.12 + 0 = 1.12
   Residual = Actual y - Predicted y = 3.72 - 1.12 = 2.6
4. For (1.5, 5.05):
   Substituting x=1.5 into the equation: y = 1.12 + 3.4(1.5) = 1.12 + 5.1 = 6.22
   Residual = Actual y - Predicted y = 5.05 - 6.22 = -1.17
5. For (-3, 0):
   Substituting x=-3 into the equation: y = 1.12 + 3.4(-3) = 1.12 + (-10.2) = -9.08
   Residual = Actual y - Predicted y = 0 - (-9.08) = 9.08
6. For (-5, -4.86):
   Substituting x=-5 into the equation: y = 1.12 + 3.4(-5) = 1.12 + (-17) = -15.88
   Residual = Actual y - Predicted y = -4.86 - (-15.88) = 11.02