Story: Cricket (the Insect) (borrowed from : http://exploringdata.cqu.edu.au/stories.htm#chirps)
"Factoid: Crickets make their chirping sounds by rapidly sliding one wing over the other. The faster they move their wings, the higher the chirping sound that is produced. Scientists have noticed that crickets move their wings faster in warm temperatures than in cold temperatures. Therefore, by listening to the pitch of the chirp of crickets, it is possible to tell the temperature of the air. The table below gives the recorded pitch (in vibrations per second) of a cricket chirping recorded at 15 different temperatures. [the table was supplied as a gif file]."
1. What is a factoid?
2. Does anyone have access to any real cricket and temperature data? This 'factoid' sounds suspiciously to me like the 'life of light bulbs is normally distributed' story, ie endlessly repeated, but with no basis in reality. The phrase 'Scientists have noticed....' is a dead giveaway, I reckon.
Jerry Thornhill, (), Southwest Virginia Community College wrote:
According to the American Heritage Electronic Dictionary, Version 3.6, a factoid is: Unverified or inaccurate information that is presented in the press as factual, often as part of a publicity effort, and that is then accepted as true because of constant repetition
In this case, factoid (with the above definition) is probably inappropriate. In a 1948 book called The Song of Insects, George W. Pierce, a Havard physics professor, presented real data relating the number of chirps per second for striped ground crickets to the temperature in degrees F. The data is real cricket and temperature data. Apparently the number of chirps represents some kind of average since it is given to the nearest tenth. I have no idea whether the original book is still in print.
Variable Names:
- Chirps: the number of chirps per second
- Temperature: the temperature in degrees Farenheit
We want to use the crickets to predict the temperature
Thus x = chirps/sec = independent (predictor) variable
Y = Temperature ( F) = dependent (response variable)
Look at the scatter diagram
Examining the scatter diagram, one can say that in general temperature of the air increases whenever the chirps/sec is high. But the points pretty much scattered. Thus the linear relationship may not be as strong.
Regression Analysis
The regression equation is
temp(F) = 25.2 + 3.29 chirps/sec
Predictor Coef StDev T P
Constant 25.23 10.06 2.51 0.026
chirps/s 3.2911 0.6012 5.47 0.000
S = 3.829 R-Sq = 69.7% R-Sq(adj) = 67.4%
The regression model is y = A + Bx + e
The estimated model is y = a + bx where a = 25.23, b = 3.29
The p-value corresponding to a shows that thr factor a plays significant role when alpha = .05 but at alphs = .01, a is not significant. Whereas p-value corresponding to b is very small thus we always tend to reject the null hypothesis that B = 0. And hence conclude that b plays a significant role in the regression model.
The value of R-sq tells that 70% of the variation the data can be explained by the estimated model while 30% of the variation is attributed to error term (or due to the factors we are not controlling). This may not be considered as an adequate model because of small value of R-sq
Using the model for prediction purpose
If the chirps/sec increases to 25, what would be the temperature?
Temp(F) = 25.2 + 3.29*25
The predicted temp is 107 F
If chirps/sec drop to zero (i.e. crickets are quiet) what would be the temp
Temp(F) = 25.2 + 3.29*0 = 25.2
That is if crickets are not chirping, the temp may be below 25.2 F