Statistics/Forestry/Horticulture 572 Discussion 4Course website http://www.stat.wisc.edu/courses/st572-larget/TA Xu He(Mario)Email [email protected] of TA www.stat.wisc.edu/∼hexuOffice 1275F, MSCOffice hour Th 11:00-12:00, 4:00-6:00Phone (608)334-97921 Problem 1The following data is collected to study the relationship between frequency of chirps made by aground cricket and the corresponding ground temperature. The frequency is measured as the num-ber of wing vibrations per second.chirps (/second) 20.0 16.0 19.8 18.4 17.1 15.5 14.7 17.1 15.4 16.2 15.0 17.2 16.0 17.0 14.1temperature (F) 88.6 71.6 93.3 84.3 80.6 75.2 69.7 82.0 69.4 83.3 78.6 82.6 80.6 83.5 76.3(a) Fit a linear model to predict chirps from temperature. What are the slope and intercept of themodel?(b) Fit another linear mod el, using a linear transformation to centralize the explanatory variable.What are the slope and intercept of the model?(c) Fit another linear model, using a linear transformation to centralize and s tandardize the ex-planatory variable. What are the slope and intercept of the model?(d) Use these three models to predict chirp frequency under similar conditions when the tempera-ture is 88 F.2 Problem 2In the early 1990s, scientists became concerned about rapid declines in populations of amphibiansworldwide. After some analysis, researchers consider global atmosph eric causes, such as thinningof the ozone layer and the resulting increased exp osure to damaging ultraviolet (UV-B) light to bethe answer.Rana cascadae is a kind of amphibians who lay eggs in open shallow water which is highlyexposed to sunlight. Therefore the effect of UV-B could be explained by the d amage over eggs.Researchers place Rana eggs under UV-B treatments having three levels: (a) a UV-B blockingfilter; (b) a UV-B transmitting filter; and (c) no filter. Percentage of eggs failing to hatch (perF)is calculated at two sites:No filter UV-B transmitting UV-B blockingThree Creeks 38.7 44.0 30.0 38.7 28.7 32.7 36.0 40.7 25.3 18.7 21.3 16.7Small Lake 36.7 69.6 39.3 34.0 70.0 54.0 48.7 51.3 24.7 25.3 39.3 32.7(a) Fit a linear model to predict perF from site and treatment, without interaction.1(b) Do a log trans formation on perF and r efi t the linear model. Why should we do this transf or-mation? How do you interpret this model?(c) Predict the percentage of eggs failing to hatch in Small Lake and under UV-B blocking fromboth models.3 Problem 3The board of directors of a professional asso ciation conducted a random sample survey of 30members to assess the effects of several possible amounts of dues increase. Two values are recorded:(1) dollar: T he collar increase in annual dues posted in the survey interview.(2) renew: Whether or not the interviewee indicated that the membership will not be renewed atthat amount of dues.renew 0 1 0 0 0 0 1 0 0 1 1 0 0 1 0dollar 30 30 30 31 32 33 34 35 35 35 36 37 38 39 40renew 1 1 0 1 1 1 0 1 1 0 1 1 0 1 1dollar 40 40 41 42 43 44 45 45 45 46 47 48 49 50 50(a) Fit a generalized linear mod el with the data, u s ing binomial (it’s actually b inary here) familyand logit link function.(b) Predict the possibility of not renewing when the dollar increase is 30, 40 and 50 respectively.Note: the data are available as three txt files on the course
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