Given:
The data table is given.
The equation of trend line is:
![y=2x+15](https://tex.z-dn.net/?f=y%3D2x%2B15)
To find:
Values for residual table.
Solution:
Formula for residual:
![Residual=\text{Observed value}-\text{Predicted value}](https://tex.z-dn.net/?f=Residual%3D%5Ctext%7BObserved%20value%7D-%5Ctext%7BPredicted%20value%7D)
The equation of trend line is:
...(i)
Substituting
in (i), we get
![y=2(5)+15](https://tex.z-dn.net/?f=y%3D2%285%29%2B15)
![y=10+15](https://tex.z-dn.net/?f=y%3D10%2B15)
![y=25](https://tex.z-dn.net/?f=y%3D25)
The value of y from the table at
is 25. So,
![Residual=25-25](https://tex.z-dn.net/?f=Residual%3D25-25)
![Residual=0](https://tex.z-dn.net/?f=Residual%3D0)
Similarly,
Substituting
in (i), we get
![y=2(6)+15](https://tex.z-dn.net/?f=y%3D2%286%29%2B15)
![y=12+15](https://tex.z-dn.net/?f=y%3D12%2B15)
![y=27](https://tex.z-dn.net/?f=y%3D27)
The value of y from the table at
is 28. So,
![Residual=28-27](https://tex.z-dn.net/?f=Residual%3D28-27)
![Residual=1](https://tex.z-dn.net/?f=Residual%3D1)
Substituting
in (i), we get
![y=2(7)+15](https://tex.z-dn.net/?f=y%3D2%287%29%2B15)
![y=14+15](https://tex.z-dn.net/?f=y%3D14%2B15)
![y=29](https://tex.z-dn.net/?f=y%3D29)
The value of y from the table at
is 29. So,
![Residual=29-29](https://tex.z-dn.net/?f=Residual%3D29-29)
![Residual=0](https://tex.z-dn.net/?f=Residual%3D0)
Substituting
in (i), we get
![y=2(8)+15](https://tex.z-dn.net/?f=y%3D2%288%29%2B15)
![y=16+15](https://tex.z-dn.net/?f=y%3D16%2B15)
![y=31](https://tex.z-dn.net/?f=y%3D31)
The value of y from the table at
is 30. So,
![Residual=30-31](https://tex.z-dn.net/?f=Residual%3D30-31)
![Residual=-1](https://tex.z-dn.net/?f=Residual%3D-1)
Substituting
in (i), we get
![y=2(9)+15](https://tex.z-dn.net/?f=y%3D2%289%29%2B15)
![y=18+15](https://tex.z-dn.net/?f=y%3D18%2B15)
![y=33](https://tex.z-dn.net/?f=y%3D33)
The value of y from the table at
is 32. So,
![Residual=32-33](https://tex.z-dn.net/?f=Residual%3D32-33)
![Residual=-1](https://tex.z-dn.net/?f=Residual%3D-1)
Therefore, the complete residual table is:
x : 5 6 7 8 9
Residuals : 0 1 0 -1 -1