A bioengineer wants to model the amount (y) of carbohydrate solubilized during steam processing of peat as a function of temeprature (x ₁ ) , exposure time (x ₂ ) , and pH value (x ₃ ) . Data collected for each of 15 peat sampels were used to fit the model

E(y) = β ₀ +β ₁ x ₁ + β ₂ x ₂ + β ₃ x ₃

A summary of the regression results follows:

ŷ = –3,000 + 3.2 _x1 –.4 _x2 – 1.1 _x3 R ² = .93

S _β̂1 = 2.4 S _β̂2 = .6 S _β̂3 = .8

r ₁₂ = .92 r ₁₃ = .87 r ₂₃ = .81

Based on these results, the bioengineer concludes that none of the three independent variables, x ₁ , x ₂ , and x ₃ , is a useful predictor of carbohydrate amount y . Do you agree with this statement? Explain.