Student's scores on the mathematics portion of the ACT examination, \(x\), and
on the final examination in the first-semester calculus ( 200 points
possible), \(y\), are given.
(a) Calculate the least squares regression line for these data.
(b) Plot the points and the least squares regression line on the same graph.
(c) Find point estimates for \(\alpha, \beta\), and \(\sigma^{2}\).
(d) Find 95 percent confidence intervals for \(\alpha\) and \(\beta\) under the
usual assumptions.
$$
\begin{array}{cc|cc}
\hline \mathrm{x} & \mathrm{y} & \mathrm{x} & \mathrm{y} \\
\hline 25 & 138 & 20 & 100 \\
20 & 84 & 25 & 143 \\
26 & 104 & 26 & 141 \\
26 & 112 & 28 & 161 \\
28 & 88 & 25 & 124 \\
28 & 132 & 31 & 118 \\
29 & 90 & 30 & 168 \\
32 & 183 & & \\
\hline
\end{array}
$$