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 RNA extracted from a wheat plant (Electronic Journal of Biotechnology, April 15, 2004). The proportion (x1) of RNA extracted from a cold-exposed wheat plant was varied, and the transcript copy number (y, in thousands) was measured for each of two cloned genes: Mn Superoxide Dismutose (MnSOD) and Phospholipose D (PLD). The data are listed in the accompanying table. Letting x₁ = RNA proportion and x₂ = {1 if MnSOD, 0 if PLD), consider the second-order model for number of copies (y):

E(y) = β₀ + β₁x₁ + β₂x₁² + β₃x₂ + β₄x₁x₂ + β₅x₁²x₂

(a) MINITAB was used to fit the model to the data. Locate the least squares prediction equation for y on the printout shown below.

(b) Is the overall model statistically useful for predicting transcript copy number (y)? Test using α = .01.

(c) Based on the MINITAB results, is there evidence to indicate that transcript copy number (y) is curvilinearly related to proportion of RNA (x₁)? Explain.