Chapter 9, Problem 4CS

To determine

To calculate: The model of the form $V\left(t\right)=P\sin \left(\frac{\pi t}{6}\right)+Q\cos \left(\frac{\pi t}{6}\right)+Bt+C{x}_1+D{x}_2+E$ using the regression on the original data where $x_1=\{\begin{array}{l}1\text{ if }t=11,23,35,\mathrm{...}\\ 0\text{ if not }\end{array}\text{ and }{x}_2=\{\begin{array}{l}1\text{ if }t=6,7,18,\mathrm{19...}\\ 0\text{ if not }\end{array}$. Also, sketch the graph of the model with the original data.

Month	Empty Seat Miles (billions)		Month	Empty Seat Miles (billions)		Month	Empty Seat Miles (billions)		Month	Empty Seat Miles (billions)
$1$	$25$			$21$		$23$			$41$	$20$		$61$	$23$
$2$	$21$			$22$		$22$			$42$	$16$		$62$	$20$
$3$	$18$			$23$		$21$			$43$	$15$		$63$	$17$
$4$	$21$			$24$		$21$			$44$	$18$		$64$	$17$
$5$	$21$			$25$		$26$			$45$	$21$		$65$	$18$
$6$	$18$			$26$		$23$			$46$	$21$		$66$	$13$
$7$	$19$			$27$		$20$			$47$	$19$		$67$	$14$
$8$	$19$		$28$	$19$		$48$	$20$		$68$	$15$
$9$	$25$		$29$	$21$		$49$	$22$		$69$	$21$
$10$	$24$		$30$	$16$		$50$	$19$		$70$	$19$
$11$	$24$		$31$	$16$		$51$	$17$		$71$	$19$
$12$	$21$		$32$	$19$		$52$	$17$		$72$	$21$
$13$	$26$		$33$	$22$		$53$	$17$		$73$	$23$
$14$	$22$		$34$	$21$		$54$	$14$		$74$	$21$
$15$	$22$		$35$	$22$		$55$	$14$		$75$	$17$
$16$	$22$		$36$	$23$		$56$	$18$		$76$	$18$
$17$	$19$		$37$	$24$		$57$	$21$		$77$	$18$
$18$	$16$		$38$	$22$		$58$	$20$		$78$	$15$
$19$	$15$		$39$	$18$		$59$	$19$		$79$	$15$
$20$	$17$		$40$	$20$		$60$	$20$		$80$	$16$