2. A random sample of n = 70 families will be surveyed to determine the association between certain "demographic" variables and certain "consumption variables. Define the Criterion set of variables by 31 = annual frequency of dining at a restaurant #2 = annual frequency of attending movies and the Predictor set by I = age of head of household ry = annual family income To = educational level of head of household Suppose 70 observations on the preceding variables give the sample correlation matrix 1.00 0.37 0.21 0.26 0.33 0.37 1.00 0.35 0.67 0.59 R = Rxx RXY = 0.21 0.35 1.00 0.34 0.34 Ryx Ryy 0.26 0.67 0.34 1.00 0.80 033 0.59 0.34 0.80 1.00 (a) Determine the sample canonical correlation coefficients, and find thep-value for a test of the null hypothesis Ho : Exy = 0. (b) If Ho : Exy = 0 is rejected at the or = .05 level, test the null hypothesis that the second and higher canonical correlations are all zero. (c) Using standardized variables, construct the canonical variables corresponding to the significant (@ = -05) canonical correlation(s). (d) Interpret the canonical variates corresponding to significant (x = 05) canonical cor- relation(s). (e) Do the demographic variables have something to say about the consumption vari- ables? Do the consumption variables provide information about the demographic variables