1. The results of a planned experiment involving a chemical reaction were analyzed by Box and Youle in 1955. The input (independent) variables are temperature 20 2 = concentration C3 = time. The yield (dependent) variables are y1 = percentage of unchanged starting material y2 = percentage converted to the desired product y3 = percentage of unwanted by-product. The researchers were also interested in the quadratic forms of each of the input variables as well as the interaction terms for each of the input variables. (a) A canonical correlation was run to investigate the relationship between the input variables and the yield variables. Report the canonical correlations. How many of them should be retained for further analysis? Justify your decision. The CANCORR Procedure Canonical Correlation Analysis Eigenvalues of Inv(E).H - CanRsq/(1-CanRsq) Test of HO: The canonical correlations in the current row and all that follow are zero Adjusted Approximate Squared Canonical Canonical Standard Canonical Likelihood Approximate Correlation Correlation Error |Correlation Eigenvalue Difference Proportion Cumulative Ratio F Value Num DF Den DF Pr > F 1 0.989931 0.984570 0.004723 0.979963 48.9084 39.0626 0.8286 0.8286 0.00145222 6.54 27 21.086 :.0001 2 0.952785 0.934923 0.021732 0.907799 9.8458 9.5737 0. 1668 0.9954 0.07247788 2.71 16 16 0.0269 w 0.462510 0. 192555 0. 185282 0.213916 0.2721 0.0046 1.0000 0.78608406 0.35 0.9100 Multivariate Statistics and F Approximations S=3 M=2.5 N=2.5 Statistic Value F Value Num DF Den DF Pr > F Wilks' Lambda 0.00145222 6.54 27 21.086 <.0001 pillai trace hotelling-lawley roy greatest root note: f statistic for is an upper bound. write the equations of significant canonical variables on method that you think more appropriate unstandardized or standardized comment their relative importance original to variables. sas output below. cancorr procedure correlation analysis yield coefficients input raw yield1 yield2 yield3 observations y1 y2 means and standard deviations y3 variable mean deviation v3 y input2 input3 input1 x1 x2 x x3 x1x2 x1x3 x2x3 x1sq x2sq x3sq correlations among between interpret version redundancy analysis. variance explained by own opposite cumulative number proportion r-square in _ u1="-1.5360" sy2 sys syl v1="5.0126" s sx12 sx1 con ac c23 co c3 sx2x3 sxi sx2 sx1x3the second pair are u2="-4.470491" syz sy3 x12 v2="-38.3053" sx1x2 c123 sx123>