Marissa wants to understand the possible effects of the weather on amusement park attendance, so she studies a linear association between the attendance at the amusement park and the temperature. Marissa makes the residual plot at right.

1. Is a linear model appropriate? Why or why not?

   Answer (a):

   The residual plot shows a clear U-shape. A curved regression model would have been better.

2. Marissa’s data follows. She has rounded attendance to the nearest hundred people. Make a scatterplot of the data. What kind of model might better represent Marissa’s data? Why?

   Temperature ($˚$F)	$71$	$73$	$78$	$83$	$91$	$92$	$73$	$88$	$95$	$94$	checksum $838$
   Attendance (thousands)	$8.6$	$13$	$21.6$	$25.9$	$23.8$	$25.9$	$17.3$	$25.9$	$17.3$	$21.6$	checksum $200.9$

3. Fit a quadratic model to the data. What attendance does your model predict for a $95°$F day? Use appropriate precision.

   Answer (c):

   $a = −0.083t^2 + 14.2t − 579$, where a is the attendance (in $1000$s of people) and t is the high temperature ($°$F) that day. $20{,}900$ people, rounded to the nearest $100$ people.