4.30 (EX) The intriguing cerebellum. 5/5: Predict the cerebellum weight in grams

Question

4.30 (EX) The intriguing cerebellum. 5/5: Predict the cerebellum weight in grams of a species weighing 100,000 g (100 kg or about 220lb) to be [1]. Make sure to transform the grams into log units first and then back into grams for the prediction (remember that y =10log(y)). Round your answer in grams to 2 decimal places.

Species Body Cerebellum Log (body) Log (cerebellum) Mouse 58 0.09 1.76 -1.05 Bat 30 0.09 1.48 -1.05 Flying Fox 130 0.30 2.11 -0.52 Pigeon 500 0.40 2.70 -0.40 Guinea Pig 485 0.90 2.69 -0.05 Squirrel 350 1.50 2.54 0.18 Chinchilla 500 1.70 2.70 0.23 Rabbit 1,800 1.90 3.26 0.28 Hare 3,000 2.30 3.48 0.36 Cat 3,500 5.30 3.54 0.72 Dog 3,500 6.00 3.54 0.78 Macaque 6,000 7.80 3.78 0.89 Sheep 25,000 21.50 4.40 1.33 Bovine 300,000 35.70 5.48 1.55 Human 60,000 142.00 4.78 2.15

Explanation / Answer

log (cerebellum) = -2.15740801 + 0.782776122 * log(body)

cerebellum = 10^( -2.15740801 + 0.782776122 * log(body) )

cerebellum = 0.00695972*(body) ^ (0.782776122 )

when body = 100000

cerebellum = 57.0784771

SUMMARY OUTPUT Regression Statistics Multiple R 0.948992768 R Square 0.900587274 Adjusted R Square 0.892940141 Standard Error 0.299117792 Observations 15 ANOVA df SS MS F Significance F Regression 1 10.53687111 10.53687111 117.7679663 6.91175E-08 Residual 13 1.163128894 0.089471453 Total 14 11.7 Coefficients Standard Error t Stat P-value Lower 95% Intercept -2.15740801 0.244493101 -8.82400363 7.52565E-07 -2.685603241 Log (body) 0.782776122 0.072131337 10.85209502 6.91175E-08 0.626945843

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