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The chart represents a data set's given values, predicted values (using a line of best fit for the data), and residual values.

\begin{tabular}{|c|c|c|c|}
\hline[tex]$x$[/tex] & Given & Predicted & Residual \\
\hline 1 & 6 & 7 & -1 \\
\hline 2 & 12 & 11 & 1 \\
\hline 3 & 13 & 15 & [tex]$g$[/tex] \\
\hline 4 & 20 & 19 & [tex]$h$[/tex] \\
\hline
\end{tabular}

Which are the missing residual values?

A. [tex]$g=2$[/tex] and [tex]$h=-1$[/tex]
B. [tex]$g=28$[/tex] and [tex]$h=39$[/tex]
C. [tex]$g=-2$[/tex] and [tex]$h=1$[/tex]
D. [tex]$g=-28$[/tex] and [tex]$h=-39$[/tex]



Answer :

GinnyAnswer
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]

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