12.12 A town has 10 different supermarkets. For each market, data are available on the following three variables: X1¼food sales, X2¼nonfood sales, and X3¼size of store in thousands of square feet.

Calculate the partial tau coefficient for X1 and X2, when the effects of X3 are eliminated.

Size of Store (1000 ft2)
Food Sales ($10,000)
Nonfood Sales ($10,000)
1 35 305 35 2 22 130 98 3 27 189 83 4 16 175 76 5 28 101 93 6 46 269 77 7 56 421 44 8 12 195 57 9 40 282 31 10 32 203 92