Question
Find the best linear least squares fit of the following data using the indicated weights:(a)\begin{tabular}{c|cccc}$t_i$ & 1 & 2 & 3 & 4 \\\hline$y_i$ & .2 & .4 & .7 & 1.2 \\\hline$c_i$ & 1 & 2 & 3 & 4\end{tabular}(c)\begin{tabular}{c|ccccc}$t_i$ & -2 & -1 & 0 & 1 & 2 \\\hline$y_i$ & -5 & -3 & -2 & 0 & 3 \\\hline$c_i$ & 2 & 1 & .5 & 1 & 2\end{tabular}\begin{tabular}{c|cccccc}$x$ & 1 & 1 & 2 & 2 & 3 & 3 \\\hline$y$ & 1 & 2 & 1 & 2 & 2 & 4 \\\hline$z$ & 3 & 6 & 11 & -2 & 0 & 3\end{tabular}(b)\begin{tabular}{c|cccc}$t_i$ & 0 & 1 & 3 & 6 \\\hline$y_i$ & 2 & 3 & 7 & 12 \\\hline$c_i$ & 4 & 3 & 2 & 1\end{tabular}(d)\begin{tabular}{c|ccccc}$t_i$ & 1 & 2 & 3 & 4 & 5 \\\hline$y_i$ & 2 & 1.3 & 1.1 & .8 & .2 \\\hline$c_i$ & 5 & 4 & 3 & 2 & 1\end{tabular}
Step 1
Each data set includes values for \( t_i \), \( y_i \), and weights \( c_i \). The goal is to find a linear model \( y = a + bt \) that best fits the data according to the weighted least squares criterion. Show more…
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