Answer
$SSE=0.5$
(better fit)
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.
----
(a)
Build a table,(the table below was generated in Excel)
\begin{array}{|cc|c|c|c|cc|}
\hline & x & y & y'=1.5x-1 & (y-y') & (y-y')^2 \\
\hline & 1 & 1 & 0.5 & 0.5 & 0.25 \\
& 2 & 2 & 2 & 0 & 0 \\
& 3 & 4 & 3.5 & 0.5 & 0.25 \\
\hline & & & & {\bf SSE}= & {\bf 0.5} \\\hline
\end{array}
When we solve (b) we will be able to tell which model fits better.
