To determine which model best represents the data in the table, we need to compare the sum of squared errors (SSE) for each model. The SSE measures how well each model's predicted values match the actual data points.
Based on the provided information, let's examine the estimated lines of code per hour for different numbers of programmers [tex]\(x\)[/tex] and match them to the respective models. The [tex]\(y\)[/tex]-values are:
[tex]\[ \begin{array}{|c|c|}
\hline
x & y \\
\hline
2 & \text{(not defined)} \\
\hline
4 & 50 \\
\hline
6 & 110 \\
\hline
8 & 160 \\
\hline
10 & 210 \\
\hline
12 & 320 \\
\hline
\end{array} \][/tex]
The models provided are:
1. [tex]\( y = 47(1.191)^x \)[/tex]
2. [tex]\( y = 34(1.204)^x \)[/tex]
3. [tex]\( y = 26.9x - 1.3 \)[/tex]
4. [tex]\( y = 27x - 4 \)[/tex]
We have the sum of squared errors for each model:
1. 11026.27
2. 677.25
3. 11916.45
4. 11060.00
The model with the smallest sum of squared errors is the model that best fits the data. Here's the SSE for each model:
1. For [tex]\( y = 47(1.191)^x \)[/tex]: SSE = 11026.27
2. For [tex]\( y = 34(1.204)^x \)[/tex]: SSE = 677.25
3. For [tex]\( y = 26.9x - 1.3 \)[/tex]: SSE = 11916.45
4. For [tex]\( y = 27x - 4 \)[/tex]: SSE = 11060.00
Comparing these errors, we see that the smallest SSE is 677.25 for the model [tex]\( y = 34(1.204)^x \)[/tex].
Thus, the model that best represents the data is:
[tex]\[ y = 34(1.204)^x \][/tex]
