Chapter 11.2, Problem 1Q

Crickets make their chirping sound by sliding one wing cover very rapidly back and forth over the other. Biologists have long been aware that there is a linear relationship between temperature and the frequency with which a cricket chirps, although the slope and $y$-intercept of the relationship vary from species to species. The following table lists fifteen frequency-temperature observations recorded for the striped ground cricket, Nemobius fasciatus fasciatus $\left(145\right)$. Plot these data and find the equation of the least squares line, $y=a+bx$. Suppose a cricket of this species is observed to chirp eighteen times per second. What would be the estimated temperature?

For the data in the table, the sums needed are:

$\begin{array}{l}{\displaystyle \underset{i=1}{\overset{15}{\sum }}{x}_i=}249.8{\displaystyle \underset{i=1}{\overset{15}{\sum }}{x}_i^2=}4,200.56\\ {\displaystyle \underset{i=1}{\overset{15}{\sum }}{y}_i=1,200.6}{\displaystyle \underset{i=1}{\overset{15}{\sum }}{x}_i{y}_i=20,127.47}\end{array}$

Observation Number	Chirps per Second, $x$	Temperature, $y\left(°F\right)$
1	20.0	88.6
2	16.0	71.6
3	19.8	93.3
4	18.4	84.3
5	17.1	80.6
6	15.5	75.2
7	14.7	69.7
8	17.1	82.0
9	15.4	69.4
10	16.2	83.3
11	15.0	79.6
12	17.2	82.6
13	16.0	80.6
14	17.0	83.5
15	14.4	76.3