3. Consider the following partial output from a regression of the average brain and body weights for 62 species of mammals (variables are transformed on the log-scale). 1m (formula = brain body) Estimate Std. Error (Intercept) 2.13479 Body 0.75169 0.09604 0.02846 Residual standard error: 0.6943 on 60 degrees of freedom Multiple R-squared: 0.9208, Adjusted R-squared: 0.9195 F-statistic: 697.4 on 1 and 60 DF, p-value: < 2.2e-16 (a) Test the null hypothesis of no association between body and brain weights at the 0.01 level of significance. (b) Use the following approximate distribution to obtain a test of size a for the null hy- pothesis Ho: p: = 0 against H: p 0 based on R, the sample correlation coefficient. 1+ R R + p 1 In (1 2) = N (1 m (12), 13) 2 In 2 (c) What is the sample correlation coefficient for these data? (d) Apply the procedure in (b) to the mammals data using the significance level a = 0.01. (e) Based on the above results, state your conclusion about the relationship between body and brain weight of mammals.