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