RNA analysis of wheat genes. Engineers from the Department of Crop and Soil Sciences at Washington State University used regression to estimate the number of copies of a gene transcript in an aliquot of ribonucleic acid (RNA) extracted from a wheat plant (Electronic Journal of Biotechnology, Apr. 15, 2004). The proportion 1x12 of RNA extracted from a wheat plant exposed to the cold was varied, and the transcript copy number (y, in thousands) was measured for each of two cloned genes:

Mn superoxide dismutase (MnSOD) and phospholipase D (PLD). The data are listed in the table on p. 792.

a. Write a first-order model for number of copies (y) as a function of proportion 1x12 of RNA extracted and gene type (MnSOD or PLD). Assume that proportion of RNA and gene type interact to affect y.

b. Fit the model you wrote in part a to the data. Give the least squares prediction equation for y.

c. Conduct a test to determine whether, in fact, proportion of RNA and gene type interact. Test using a = .01.

d. Use the results from part b to estimate the rate of increase of number of copies (y) with proportion 1x12 of RNA extracted for the MnSOD gene type.

e. Repeat part d for the PLD gene type.

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Data for Exercise 12.197 Sale Price No. of Apartments, Age of Structure, No. of On-Site Condition of Code No. y ($) X1 X2 (years) Lot Size xs (sq. ft.) Parking Spaces, X4 Gross Building Area X5 (sq. ft.) Apartment Building 0229 90,300 4 82 4,635 0 4,266 F 0094 384,000 20 13 17,798 0 14,391 G 0043 157,500 5 66 5,913 0 6,615 G 0079 676,200 26 64 7,750 6 34,144 0134 165,000 5 55 5,150 0 6,120 0179 300,000 10 65 12,506 0 14,552 0087 108,750 4 82 7,160 0 3,040 0120 276,538 11 23 5,120 0 7,881 0246 420,000 20 18 11,745 20 12,600 0025 950,000 62 71 21,000 3 39,448 G 0015 560,000 26 74 11,221 0 30,000 0131 268,000 13 56 7,818 13 8,088 F 0172 290,000 9 76 4,900 0 11,315 E 0095 173,200 6 21 5,424 6 4,461 G 0121 323,650 11 24 11,834 8 9,000 G 0077 162,500 5 19 5,246 5 3,828 G 0060 353,500 20 62 11,223 2 13,680 F 0174 134,400 4 70 5,834 0 4,680 E 0084 187,000 8 19 9,075 7,392 G 0031 155,700 4 57 5,280 0 6,030 E 0019 93,600 4 82 6,864 0 3,840 F 0074 110,000 4 50 4,510 0 3,092 G 0057 573,200 14 10 11,192 0 23,704 E 0104 79,300 4 82 7,425 0 3,876 F 0024 272,000 5 82 7,500 0 9,542 E