Statistics Forestry Horticulture 572 Course website TA Email Website of TA Office Office hour Phone 1 Discussion 4 http www stat wisc edu courses st572 larget Xu He Mario hexu stat wisc edu www stat wisc edu hexu 1275F MSC Th 11 00 12 00 4 00 6 00 608 334 9792 Problem 1 The following data is collected to study the relationship between frequency of chirps made by a ground cricket and the corresponding ground temperature The frequency is measured as the number 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 1 temperature 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 the model b Fit another linear model 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 standardize the explanatory variable What are the slope and intercept of the model d Use these three models to predict chirp frequency under similar conditions when the temperature is 88 F 2 Problem 2 In the early 1990s scientists became concerned about rapid declines in populations of amphibians worldwide After some analysis researchers consider global atmospheric causes such as thinning of the ozone layer and the resulting increased exposure to damaging ultraviolet UV B light to be the answer Rana cascadae is a kind of amphibians who lay eggs in open shallow water which is highly exposed to sunlight Therefore the effect of UV B could be explained by the damage over eggs Researchers place Rana eggs under UV B treatments having three levels a a UV B blocking filter b a UV B transmitting filter and c no filter Percentage of eggs failing to hatch perF is calculated at two sites Three Creeks Small Lake No filter 38 7 44 0 30 0 38 7 36 7 69 6 39 3 34 0 UV B transmitting 28 7 32 7 36 0 40 7 70 0 54 0 48 7 51 3 UV B blocking 25 3 18 7 21 3 16 7 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 transformation on perF and refit the linear model Why should we do this transformation How do you interpret this model c Predict the percentage of eggs failing to hatch in Small Lake and under UV B blocking from both models 3 Problem 3 The board of directors of a professional association conducted a random sample survey of 30 members to assess the effects of several possible amounts of dues increase Two values are recorded 1 dollar The 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 at that amount of dues renew dollar renew dollar 0 30 1 40 1 30 1 40 0 30 0 41 0 31 1 42 0 32 1 43 0 33 1 44 1 34 0 45 0 35 1 45 0 35 1 45 1 35 0 46 1 36 1 47 0 37 1 48 0 38 0 49 1 39 1 50 0 40 1 50 a Fit a generalized linear model with the data using binomial it s actually binary here family and 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 website 2
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