The following table gives data on the sales/cash ratio in U.S. manufacturing industries classified by the asset size of the establishment for the period 1971–I to 1973–IV. (The data are on a quarterly basis.) The sales/cash ratio may be regarded as a measure of income velocity in the corporate sector, that is, the number of times a dollar turns over.

a. For each asset size compute the mean and standard deviation of the sales/cash ratio.

b. Plot the mean value against the standard deviation as computed in (a), using asset size as the unit of observation.

c. By means of a suitable regression model decide whether standard deviation of the ratio increases with the mean value. If not, how would you rationalize the result?

d. If there is a statistically significant relationship between the two, how would youtransform the data so that there is no heteroscedasticity?