1. In a study of 27 industrial establishments of varying size, y = the number of supervisors and x = the number of supervised workers. y varies from 30 to 210 and x from 247 to 1650. The results obtained were as follows: variable coefficient SE X 0.115 0.011 9.30 constant 14.448 9.562 1.51 N = 27 R-=0.776 After the estimation of the equation and plotting the residuals against x, it was found that the variance of the residuals increased with x. Plotting the residuals against 1/x showed that there was no such relationship. Hence the assumption made was var(1 ) = 1'12The estimated equation was 1 0.021 + 3.803 R2=0.03 (0.009) (4.570) The estimated gave the following results: variable coefficient SE X 0.121 0.009 13.44 constant 3.803 4.570 0.832 N = 27 R-=0.7587 (a) The investigator looks at the drop in R- and concludes that the first equation is better. Is this conclusion valid? (b) What would the equation to be estimated be if var(1,) = 1 1,? How would you determine which of these alternative hypotheses is the better one