Consider the following data \begin{tabular}{lr} $\mathrm{x}$ & \multicolumn{1}{c}{$\mathrm{y}$} \\ \hline \multicolumn{1}{1}{} & \\ O & $-7.4406$ \\ 1 & $9.5042$ \\ 2 & $9.1978$ \\ 3 & $25.5994$ \\ 4...

Extracted text: Consider the following data \begin{tabular}{lr} $\mathrm{x}$ & \multicolumn{1}{c}{$\mathrm{y}$} \\ \hline \multicolumn{1}{1}{} & \\ O & $-7.4406$ \\ 1 & $9.5042$ \\ 2 & $9.1978$ \\ 3 & $25.5994$ \\ 4 & $33.6258$ \\ 5 & $11.2584$ \\ 6 & $6.8671$ \\ 7 & $25.1113$ \\ 8 & $31.0453$ \\ 9 & $40.3589$ \\ 10 & $48.7861$ \end{tabular} Construct a least square fit of the data using polynomial basis functions (like $x^{i}, i=0,1,2, \cdots$ ) and trigonometric basis functions (like $\sin (i x), \cos (i x), i=1,2, \cdots)$. CS. JG. 17