A biologist compared the effect of temperature for each of two media on the growth of human amniotic cells in a tissue culture. The data shown in the following table were obtained.
a. Assuming that a parabolic model is appropriate for describing the relationship between Y and X for each medium, provide a single regression model that incorporates two separate parabolic models, one corresponding to each medium.
b. Use the SAS output provided here to determine and plot the separate fitted parabolas for each medium. (Z = 0 for medium A, and Z = 1 for medium B.)
c. Test for "parallelism" of the two parabolas.
d. Test for coincidence of the two parabolas.
e. Is it possible to test whether a quadratic term should be included in the model for each medium using only the provided SAS output? Explain.

Regression of Y on X, X2, Z, ZX, and ZX2
Where Z = 1 if Medium B, 0 Otherwise
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Medium A Medium B No. of Cells Temperature Cells Temperature Cells Temperature Cells Temperature -6 100 100 2 ANALYSIS OF VARIANCE Sum of Mean DF Squares Square FValue Pr>F Source Model Error Corrected Total 5 26.06864 5.21373 58397,0001 34 0.30356 0.00893 39 26.37220 Root MSE Dependent Mean Coeff Var 0.09449 1.99275 R-Square 0.9885 275 Adj R-Sq 4.74163 0.9868 PARAMETER ESTIMATES Standard Parameter Estimate Pr> It Variablo DF Error t Value Type I SS 2.04 0.0493 0.72 0.4763 4.12 0.0002 0.34303495 042 06779 0.12 0.9074 -012 0.9074 158.842103 25.668613 0.290702 0,109202 0.0000005 0.000122 0.494600 0.005370 0.00745505 0.000217 0.00005282 Intercept 0.24256234 X2 -0.143700 0.001235 0.01054303 zx 1 0.00000875 Zx2