8. 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: 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(ui)=2xi2 The estimated equation was xy=(0.009)0.121+(4.570)3.803(1/x)R2=0.03 In terms of the original variables, we have y=3.803+0.121x The estimation gave the following results: (a) An investigator looks at the drop in R2 and concludes that the first equation is better. Is this conclusion valid? (b) What would the equation to be estimated be if var(ui)=2xi instead of 2xi2 ? How would you determine which of these alternative hypotheses is the better one? (c) Comment on the computation of R2 from the transformed equation and the R2 from the equation in terms of the original variables. 8. 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: 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(ui)=2xi2 The estimated equation was xy=(0.009)0.121+(4.570)3.803(1/x)R2=0.03 In terms of the original variables, we have y=3.803+0.121x The estimation gave the following results: (a) An investigator looks at the drop in R2 and concludes that the first equation is better. Is this conclusion valid? (b) What would the equation to be estimated be if var(ui)=2xi instead of 2xi2 ? How would you determine which of these alternative hypotheses is the better one? (c) Comment on the computation of R2 from the transformed equation and the R2 from the equation in terms of the original variables