  ### Home > INT2 > Chapter 12 > Lesson 12.1.1 > Problem12-13

12-13. 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?

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.

$a = −0.083t^2 + 14.2t − 579$, 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.