The skin response in rats to different concentrations of a newly developed vaccine was measured in an experiment, resulting in the data, models, and computer output that follow.

a. Plot the straight-line, quadratic, and cubic equations on the scatter diagram for this data set.
b. Test sequentially for significant straight-line fit, for significant addition of X2, and for significant addition of X3 to the model.
c. Which of the three models do you recommend, and why?
Linear regression of Y on X

Quadratic regression of Y on X

Cubic regression of Y on X

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Concentration 0.5 0.5 0 .0 5 15 2.0 2.0 25 25 3.0 3.0 Skin response 13.90 13.81 14.08 13.99 13.75 13.60 13.32 13.39 1345 13.53 13.59 13.64 ANALYSIS OF VARIANCE Sum of Mean Source Model Error Corrected Total DF Squares Square F Value Pr>F 0.28440 0.28440 8.22 0.0168 10 0.34609 0.03461 11 0.63049 PARAMETER ESTIMATES Paramoter Standard Error | tValue | Pr 0.12246 114.21 0001 Variable DF Estimate Intercept 13.98633 1 0.18029 0.06289 287 0.0168 ANALYSIS OF VARIANCE Sum of Mean Source Model Error Corrected Total DF Squares Square F Value Pr> F 2 0.35382 0.17681 9 0.27688 0.03076 11 0.63049 5.75 0.0246 PARAMETER ESTIMATES Parameter Standard Variable DF Estimate Error t ValuePr> It 64.32 .0001 -0.60654 0.29030 2.09 0.0663 1.50 0.1679 Intercept 14.27050 0.22186 X2 0.12179 0.08119 ANALYSIS OF VARIANCE Sum of Mean DF Squares Square F Value Pr> F Source Model Error Corrected Total 30.52218 0.17406 8 0.10831 0.01354 11 0.63049 12,86 0.0020 PARAMETER ESTIMATES Parameter Standard Variable D Intercept Error Value Pr >It 45.04 <.0001 1.67997 067601 249 0.0378 -1:39294 0.43264 3.22 0.0122 3.53 0.0077 13.36167 0.29065 X2 X3 028852 0.08177