Question

If the line of best fit is y = 1.416x - 0.76, what is the residual value for the coordinate (4, 6)?

1) 1.736
2) -1.736
3) 1.096
4) -1.096

Answer 1

The residual value for the coordinate (4, 6) given the line of best fit y = 1.416x - 0.76 is calculated by subtracting the predicted y-value found using the equation from the observed y-value, resulting in a residual of 1.096.

Step-by-step explanation:

The student has asked for the residual value for the coordinate (4, 6) given the line of best fit y = 1.416x - 0.76. To find the residual, we need to first calculate the predicted y-value (ŷ) using the line of best fit for the given x-coordinate, which is 4 in this case.

Substituting x = 4 into the equation, we get:
ŷ = 1.416(4) - 0.76
ŷ = 5.664 - 0.76
ŷ = 4.904

The residual is the observed y-value minus the predicted y-value. So for the coordinate (4, 6), the residual is:
Residual = 6 - 4.904
Residual = 1.096

Therefore, the correct residual value is option 3) 1.096.