The common cricket can be used as a crude thermometer. The colder the temperature, the slower the rate of chirping. The table below shows the average chirp rate of a cricket at various temperatures.
$\begin{array} { c c }
\hline \begin{array} { c }
\text { Chirp Rate } \
\text { (chirps/second) }
\end{array} & \begin{array} { c }
\text { Temperature } \
\left( { } ^ { \circ } \mathrm { F } \right)
\end{array} \
\hline 2.8 & 70.5 \
1.7 & 54.7 \
3.3 & 71.6 \
2.7 & 69 \
2.3 & 54.1 \
3.4 & 73.1 \
\hline
\end{array}$
The least-squares regression line for predicting the temperature from the chirp rate is y = 32.298 + 12.297x.If two chirp rates differ by 1.5 chirps per second, by how much would the temperature differ?
A) 48 ºF
B) 17 ºF
C) 18 ºF
D) 21 ºF

Question

The common cricket can be used as a crude thermometer. The colder the temperature, the slower the rate of chirping. The table below shows the average chirp rate of a cricket at various temperatures. 
$\begin{array} { c c } 
\hline \begin{array} { c } 
\text { Chirp Rate } \
\text { (chirps/second) }
\end{array} & \begin{array} { c } 
\text { Temperature } \
\left( { } ^ { \circ } \mathrm { F } \right)
\end{array} \
\hline 2.8 & 70.5 \
1.7 & 54.7 \
3.3 & 71.6 \
2.7 & 69 \
2.3 & 54.1 \
3.4 & 73.1 \
\hline
\end{array}$
 The least-squares regression line for predicting the temperature from the chirp rate is y = 32.298 + 12.297x.If two chirp rates differ by 1.5 chirps per second, by how much would the temperature differ?
A) 48 ºF
B) 17 ºF
C) 18 ºF
D) 21 ºF

Quizplus · Accepted Answer

We know that the least squares regression line is y= 32.298+12.297x, where y is the temperature and x is the chirp rate. 
If two chirp rates differ by 1.5 chirps per second, we can set up an equation as follows:
y2 - y1 = (12.297)(1.5)
where y1 and y2 are the temperatures corresponding to the two chirp rates. 
Substituting the values given in the table, we get:
y2 - y1 = (12.297)(1.5) 
=> 71.6 - 73.1 = (12.297)(-1.5)
=> -(y2 - y1) = 18.44
=> y2 - y1 = -18.44
Since we are asked for the absolute value, the answer is therefore 18 ºF. Thus, the correct answer is C.

The Common Cricket Can Be Used as a Crude Thermometer