Hyla chrysoscelis is a type of tree frog with a distinct mating call. Field biol
ID: 3362681 • Letter: H
Question
Hyla chrysoscelis is a type of tree frog with a distinct mating call. Field biologists wanted to know if the temperature of its natural habitat affects the frog’s mating call, so they sampled 28 frogs and measured the ground temperature where they sat and their mating call frequency. The correlation between ground temperature and mating call frequency was r = 0.76. The ground temperatures had a mean of 27.1C and a standard deviation of 3.20C. The frequency of the mating calls had a mean of 45.1 notes/sec and a standard deviation of 3.9 notes/sec.
Assuming all relevant assumptions were met, find the OLS linear regression equation for predicting mating call frequency based on ground temperature.
What do your slope and intercept mean in the context of the problem?
If a frog was sitting on 30C ground and had call frequency of 52 notes/sec, what is this frog’s residual?
Is ground temperature a significant linear predictor of mating call frequency? Include all steps for full credit. Note that your assumptions have been met. Given: SEb1 = 0.67
Explanation / Answer
a) here slope b1 =r*Sy/Sx =0.76*3.9/3.20=0.9263
and intercept bo=Ybar0b1*Xbar =45.1-0.926*27.1=19.9986
therefore linear regression equation:Y =19.9986+0.9263*X
b) slope represent that for each degree temerature increase ; there is increase in mating frequency call by 0.9263.
intercept represent for 0 degree temerature ; mating frequency call is 19.9986
c)for 30 degree frequency of the mating calls =19.9986+0.9263*30 =47.7861
therefore residual =actual-predicted =52-47.7861=4.2139
e) here test statistic t =b1/SEb1 =0.9263/0.67=1.3825
for above test statsitic and (n-2=26) degree of freedom ; p value =0.1786
as p value is relatively high we do not have evidence that ground temperature is a significant linear predictor of mating call frequency
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