Answer
$SSE=0.18$
(better fit than (a))
Work Step by Step
Residuals and Sum-of-Squares Error (SSE)
If we model a collection of data $(x_{1}, y_{1})$ , . , $(x_{n}, y_{n})$ with a linear equation $\hat{y}=mx+b$,
then the residuals are the $n$ quantities (Observed Value-Predicted Value):
$(y_{1}-\hat{y}_{1}), (y_{2}-\hat{y}_{2}), \ldots, (y_{n}-\hat{y}_{n})$ .
The sum-of-squares error (SSE) is the sum of the squares of the residuals:
SSE $=(y_{1}-\hat{y}_{1})^{2}+(y_{2}-\hat{y}_{2})^{2}+\cdots+(y_{n}-\hat{y}_{n})^{2}.$
The model with smaller SSE gives the better fit.
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(b)
Build a table,(the table below was generated in Excel)
\begin{array}{|cc|c|c|c|cc|}
\hline & x & y & y'=0.5x+0.9 & (y-y') & (y-y')^ 2 \\
\hline & 0 & 1 & 0.9 & 0.1 & 0.01 \\
& 1 & 1 & 1.4 & -0.4 & 0.16 \\
& 2 & 2 & 1.9 & 0.1 & 0.01 \\
& & & & & \\
\hline & & & & {\bf SSE}= & {\bf 0.18} \\ \hline
\end{array}
This model provides a better fit than (a), where SSE=0.27
