102 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 , April 15, 2004). The proportion

(x1) 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 next table and saved in the WHEATRNA file.

a. Write a first-order model for number of copies ( y ) as a function of proportion (x1) 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 (x1)
of RNA extracted for the MnSOD gene type.

e. Repeat part d for the PLD gene type.

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Data for Exercise 102 RNA Proportion Number of Copies (y, thousands) (x1) MnSOD PLD 0.00 401 80 0.00 336 83 0.00 337 75 0.33 711 132 0.33 637 148 0.33 602 115 0.50 985 147 0.50 650 142 0.50 747 146 0.67 904 146 0.67 1,007 150 0.67 1,047 184 0.80 1,151 173 0.80 1,098 201 0.80 1,061 181 1.00 1,261 193 1.00 1,272 187 1.00 1,256 199 Based on Back K. H., and Skinner, D. Z. "Quantitative real-time PCR method to detect changes in specific transcript and total RNA amounts." Electronic Journal of Biotechnology, Vol. 7, No. 1, April 15, 2004 (adapted from Figure 2).