Let's find the missing residual values step-by-step.
1. We have the given values and predicted values as follows:
- For [tex]\(x = 1\)[/tex]: Given = 6, Predicted = 7
- For [tex]\(x = 2\)[/tex]: Given = 12, Predicted = 11
- For [tex]\(x = 3\)[/tex]: Given = 13, Predicted = 15
- For [tex]\(x = 4\)[/tex]: Given = 20, Predicted = 19
2. The residual value is calculated as the difference between the given value and the predicted value:
- Residual = Given - Predicted
3. Let's calculate the residuals for each [tex]\(x\)[/tex]:
For [tex]\(x = 1\)[/tex]:
[tex]\[
\text{Residual} = 6 - 7 = -1
\][/tex]
For [tex]\(x = 2\)[/tex]:
[tex]\[
\text{Residual} = 12 - 11 = 1
\][/tex]
For [tex]\(x = 3\)[/tex]:
[tex]\[
g = 13 - 15 = -2
\][/tex]
For [tex]\(x = 4\)[/tex]:
[tex]\[
h = 20 - 19 = 1
\][/tex]
4. Thus, the values of [tex]\(g\)[/tex] and [tex]\(h\)[/tex] are:
[tex]\[
g = -2 \quad \text{and} \quad h = 1
\][/tex]
So, the correct answer is:
[tex]\(g = -2\)[/tex] and [tex]\(h = 1\)[/tex].
Thus, the correct choice is:
[tex]\[ \boxed{g = -2 \quad \text{and} \quad h = 1} \][/tex]
