Let's start by understanding what residual values are. Residual values are the differences between the given values and the predicted values. They help us assess the accuracy of predictions.
The formula for the residual is:
[tex]\[ \text{Residual} = \text{Given} - \text{Predicted} \][/tex]
We already have the given and predicted values in the chart:
1. [tex]$(6, 7)$[/tex]
2. [tex]$(12, 11)$[/tex]
3. [tex]$(13, 15)$[/tex]
4. [tex]$(20, 19)$[/tex]
Given the formula, we can calculate the residuals for each pair:
1. For [tex]$x=1$[/tex]:
[tex]\[ \text{Residual} = 6 - 7 = -1 \][/tex]
2. For [tex]$x=2$[/tex]:
[tex]\[ \text{Residual} = 12 - 11 = 1 \][/tex]
3. For [tex]$x=3$[/tex]:
[tex]\[ \text{Residual} = 13 - 15 = -2 \][/tex]
4. For [tex]$x=4$[/tex]:
[tex]\[ \text{Residual} = 20 - 19 = 1 \][/tex]
Thus, the residuals we calculated are:
- [tex]$x=1$[/tex]: Residual is [tex]$-1$[/tex]
- [tex]$x=2$[/tex]: Residual is [tex]$1$[/tex]
- [tex]$x=3$[/tex]: Residual is [tex]$-2$[/tex]
- [tex]$x=4$[/tex]: Residual is [tex]$1$[/tex]
Accordingly, the missing residual values are:
[tex]\[
g = -2 \quad \text{and} \quad h = 1
\][/tex]
So, the correct answer is:
[tex]\[ g=-2 \text{ and } h=1 \][/tex]
