Question

Using the trend line y = 2x + 15, for the data shown, complete the residual table.

Answer 1

Given:

The data table is given.

The equation of trend line is:

`y=2x+15`

To find:

Values for residual table.

Solution:

Formula for residual:

`Residual=\text{Observed value}-\text{Predicted value}`

The equation of trend line is:

`y=2x+15` ...(i)

Substituting
`x=5` in (i), we get

`y=2(5)+15`

`y=10+15`

`y=25`

The value of y from the table at
`x=5` is 25. So,

`Residual=25-25`

`Residual=0`

Similarly,

Substituting
`x=6` in (i), we get

`y=2(6)+15`

`y=12+15`

`y=27`

The value of y from the table at
`x=6` is 28. So,

`Residual=28-27`

`Residual=1`

Substituting
`x=7` in (i), we get

`y=2(7)+15`

`y=14+15`

`y=29`

The value of y from the table at
`x=7` is 29. So,

`Residual=29-29`

`Residual=0`

Substituting
`x=8` in (i), we get

`y=2(8)+15`

`y=16+15`

`y=31`

The value of y from the table at
`x=8` is 30. So,

`Residual=30-31`

`Residual=-1`

Substituting
`x=9` in (i), we get

`y=2(9)+15`

`y=18+15`

`y=33`

The value of y from the table at
`x=9` is 32. So,

`Residual=32-33`

`Residual=-1`

Therefore, the complete residual table is:

x : 5 6 7 8 9

Residuals : 0 1 0 -1 -1