To find the missing residual values, we need to understand what residuals are. The residual for a data point is the difference between the given (observed) value and the predicted value calculated using a line of best fit.
The formula for a residual is:
[tex]\[ \text{Residual} = \text{Given value} - \text{Predicted value} \][/tex]
Let's find the residuals for each given [tex]\(x\)[/tex]:
1. For [tex]\(x = 1\)[/tex]:
[tex]\[
\text{Given} = 6, \quad \text{Predicted} = 7
\][/tex]
[tex]\[
\text{Residual} = 6 - 7 = -1
\][/tex]
2. For [tex]\(x = 2\)[/tex]:
[tex]\[
\text{Given} = 12, \quad \text{Predicted} = 11
\][/tex]
[tex]\[
\text{Residual} = 12 - 11 = 1
\][/tex]
3. For [tex]\(x = 3\)[/tex]:
[tex]\[
\text{Given} = 13, \quad \text{Predicted} = 15
\][/tex]
[tex]\[
\text{Residual} = 13 - 15 = -2
\][/tex]
4. For [tex]\(x = 4\)[/tex]:
[tex]\[
\text{Given} = 20, \quad \text{Predicted} = 19
\][/tex]
[tex]\[
\text{Residual} = 20 - 19 = 1
\][/tex]
Thus, the missing residual values are:
- For [tex]\(x = 3\)[/tex], [tex]\(g = -2\)[/tex]
- For [tex]\(x = 4\)[/tex], [tex]\(h = 1\)[/tex]
Therefore, the correct answer is:
[tex]\[ g = -2 \quad \text{and} \quad h = 1 \][/tex]
Hence, the correct option is:
[tex]\[ g = -2 \text{ and } h = 1 \][/tex]
