For the data given in the following table, regress average compensation Y on average productivity X, treating employment size as the unit of observation. Interpret your results, and see if your results agree with those given in Eq. (11.5.3).

a. From the preceding regression obtain the residuals û_i.

b. Following the Park test, regress ln uÌ‚²_i on ln X_i and verify the regression Eq. (11.5.4).

c. Following the Glejser approach, regress |uÌ‚_i| on Xi and then regress |uÌ‚_i| on ˆšX_i and comment on your results.

d. Find the rank correlation between |û_i| and X_i and comment on the nature of heteroscedasticity, if any, present in the data.

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Employment Size (average number of employees) Industry 1-4 5-9 10-19 20-49 50-99 100-249 250–499 500-999 1,000–2,499 Food and kindred 5,342 3,822 products Tobacco products 2,994 1,721 3,295 2,057 3,565 3,336 3,907 3,320 4,189 2,980 4,486 2,848 4,676 3,072 4,968 2,969 Textile mill products Apparel and related products Paper and allied products Printing and publishing Chemicals and 3,600 3,657 3,674 3,437 3,340 3,334 3,225 3,163 3,168 3,787 3,494 3,533 3,215 3,030 2,834 2,750 2,967 3,453 3,498 3,847 3,913 4,135 4,445 4,885 5,132 5,342 5,326 3,611 4,695 4,206 5,083 5,301 5,269 5,182 5,395 5,552 allied products Petroleum and 3,875 4,930 5,248 4,660 5,005 5,114 5,630 5,870 5,876 6,347 coal products Rubber and 4,616 5,181 5,317 5,337 5,421 5,710 6,316 6,455 3,984 4,905 plastic products Leather and 3,538 4,014 4,287 4,221 4,539 4,721 5,481 3,149 leather products Average compensation Standard deviation 3,016 3,196 3,317 3,414 3,254 3,177 3,346 4,067 4,388 929.9 1,080.6 1,241.2 1,307.7 3,787 4,013 4,538 3,396 4,104 4,146 4,241 4,843 1,110.7 742.2 851.4 727.8 805.06 Average productivity 9,418 9,355 8,584 7,962 8,275 8,389 9,795 10,281 11,750