A biology student noticed that crickets seemed to chirp faster in the summer than in the spring or fall.  Her grandmother had always told her that she could determine the temperature by listening to the crickets.  Over the next season she counted the chirps per minute of a cricket and recorded the temperature (F).  Her data is provided in the table below.

Chirps Temp
55    50
67    54
75    55
83    58
91    58
99    60
119    67
134    69
140    70
149    74
164    77
178    79

Copy and paste the data into Excel or Fathom or transfer the data to your graphing calculator for analysis.

Questions to consider.

a. Find a mathematical model that the student can use to estimate the temperature by listening to the crickets.

b. Interpret the slope and y-intercept in terms of the phenomenon.

c. What are the residuals from the prediction line to the actual data?

c. Explain how this model could by used to estimate the temperature quickly by counting chirps for only 15 seconds.

d. Interpret the value of r and r^2 for this data.

e. If you wanted to describe mathematically the relationship between temperature and cricket chirps, which variable is more appropriate to consider as the dependent variable?  Is this the same variable that you treated as the dependent variable in part a?  If not, find a new model.  Interpret the slope and y-intercept.