Start with 15.1 row:
For 15.1, the observed is shown on the table. It's 65.
The predicted can be found by using the formula in the problem.
y=3.7x + 13.38
y= 3.7(15.1) + 13.38
y= 69.25. That's the predicted.
The residual for each observation is the difference between predicted values of y (dependent variable) and observed values of y.
So predicted was 69.25. Observed is 65.
69.25-65 = 4.25. That's your residual.
17.9 row:
Now let's do 17.9. Look at observed on the table. It's 75.
The predicted can be found by using the formula in the problem.
y=3.7x + 13.38
y=3.7(17.9) + 13.38
y = 79.61. That's the predicted.
Residual is predicted - observed.
79.61 - 75 = 4.61. That's your residual.