9. In a study of the effects of predatory intertidal crab species on snail pop- ulations, researchers investigated the r

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9 In A Study Of The Effects Of Predatory Intertidal Crab Species On Snail Pop Ulations Researchers Investigated The R 1 (482.42 KiB) Viewed 88 times

9. In a study of the effects of predatory intertidal crab species on snail pop- ulations, researchers investigated the relationship between closing forces and propodus heights of the claws for three species of crabs. The total sample size was 38. The table below shows output from the least squares fit to the separate-lines model for the regression of log force (y) on log height (xi). The regression model for log force was E(y) = Bo + B121 + Bat2 + B313 + B4X122 +- B52113, s 1, if species 2; where y = log(force), xı = log(height), 22 = and x3 = otherwise. 10, otherwise. { 7 10, Variable Constant 11 C2 Estimate 0.5191 0.4083 -4.2992 -2.2992 2.5653 1.6601 SE t-stat 1.0000 0.5191 .4868 0.8387 1.5283 -2.8131 1.7606 -1.4123 0.7354 3.4885 0.7889 2.1043 p-value 0.6073 0.4079 0.0083 0.1675 0.0014 0.0433 13 X1 X 12 21 X X3 (a) State the assumptions that are necessary for this multiple regression. Using the following plots, comment on whether the assumptions appear to be met. If you cannot assess an assumption using these plots, name an alternative assessment method. (b) Conduct a test of the hypothesis that the slope in the regression of log force on log height is the same for species 2 as it is for species 1. Use a = 0.05. (c) Find a 95% confidence interval for the amount by which the slope for species 3 exceeds the slope for species 1. Fit Diagnostics for y 1.0 - 2 ୫ 0 2 Go D 000 0.5 1 1 o 0. 2. oº Residual RStudent 00 RStudent 0 0.0 0 0 0 00 0 99.00 00 o O O 0 -1 O -1 -0.5 - o 2 -2 1.0 0.1 0.4 1.0 1.5 2.0 2.5 3.0 3.5 Predicted Value 1.5 2.0 2.5 3.0 3.5 Predicted Value 0.2 0.3 Leverage 1.0 3.5 0.15 3.0 0.5 2.5 0.10 Residual 0.0 2.0 Cook's D 0 -0.5 1.5 - 0.05 PowermaxxoooOo 1.0 -1.0 0.0 0.00 -2 -1 0 1 2 0 40 1.0 1.5 2.0 2.5 3.0 3.5 Predicted Value 10 20 30 Observation Quantile 30 Fit-Mean Residual 25 1.0 20 2 017 0.5 - Percent (మరింతలు ooo. 15 0.0 10 -0.5 5 -1.0 0 -1.35 : 1.35 -0.45 0.45 Residual -0.0 0.4 0.8 0.0 0.4 0.8 Proportion Less