Data on the polysilicon thickness of semiconductor wafers processed using rapid thermal chemical vapor deposition was analyzed in the Journal of the American Statistical Association (March 1998). The polysilicon thickness measurements (in angstroms) as well as the thickness of oxide applied to the wafer (in angstroms) and the deposition time (in seconds) for 22 wafers processed at a particular location are listed in the accompanying table.

a. Write a complete second-order model for polysilicon thickness (y) as a function of oxide thickness (x₁) and deposition time (x₂).

b. Fit the model to the data. Give the least-squares prediction equation.

c. Conduct a test to determine if the quadratic terms in the model are necessary. Test using α = .05.
d. Conduct a test to determine if oxide thickness (x₁) and deposition time (x₂) interact. Test using α = .05.
e. Based on the results, parts c and d, what model modifications do you recommend? Explain.

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WAFER2 Oxide Thickness Time (X1, angstroms) (X2, seconds) Polysilicon Thickness (y, angstroms) 1059 18 494 1049 35 853 1039 52 1090 1026 52 1058 1001 18 517 986 35 882 1447 35 732 458 35 1143 1263 23 608 1283 23 590 1301 47 940 1287 47 920 1300 47 917 1307 23 581 632 23 738 621 23 732 623 23 750 620 47 1205 613 47 1194 615 47 1221 478 35 1209 1498 35 708