Question

Based on the following data and its regression equation y=2.22sin(1.13x−2.93) 4.26 , what is the residual for the point x=7 ?

Answer 1

The residual for the point x=7 in the regression equation is approximately 0.137.

Step-by-step explanation:

The residual for the point x=7 can be determined by substituting x=7 into the regression equation y=2.22sin(1.13x−2.93)+4.26. So the residual is:

residual = y - predicted value

Let's calculate the predicted value using the regression equation:

y = 2.22sin(1.13(7)−2.93)+4.26

y = 2.22sin(4.91−2.93)+4.26

y = 2.22sin(1.98)+4.26

y ≈ 0.137+4.26

y ≈ 4.397

Now we can calculate the residual:

residual = 4.397 - 4.26

residual ≈ 0.137