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 α = .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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RNA Proportion Number of Copies (y, thousands) (xi) MnSOD PLD 401 336 337 0.00 0.00 0.00 0.33 0.33 0.33 0.50 0.50 0.50 0.67 0.67 0.67 0.80 0.80 080 1.00 1.00 1.00 637 602 985 650 747 904 1,007 1,047 1.151 1,098 1,061 1,261 1,272 1.256 80 83 75 132 148 115 147 142 146 146 150 184 173 201 181 193 187 199