For each of the following sets of statements, state whether the conclusion is corrector incorrect based on the facts given, and explain the rationales of your answer in nomore than four sentences. (No marks will be given for only indicating the conclusionas correct or incorrect without any explanation.)a. Facts (given): When an interval variable Y is regressed on three intervalvariables X1, X2, and X3, simultaneously (i.e., within the same multipleregression equation), the multiple correlation coefficient and the regressioncoefficients of X1 and X2 are all statistically significant and the regressioncoefficient of X3 is not statistically significant.Conclusion: When Y is regressed on X3 (in a bivariate regression analysis),the regression coefficient of X3 is not necessarily non-significant (statistically).b. Facts (given): When an interval variable YY is regressed on an intervalvariable XX1 (a bivariate regression), the standardized regression coefficient,beta1, is statistically significant; When YY is regressed on another intervalvariable XX2 (a bivariate regression), the standardized regression coefficient,beta2, is statistically significant.Conclusion: when YY is regressed on XX1 and XX2 simultaneously (i.e.,within the same multiple regression equation), generally the multiplecorrelation coefficient can be calculated using the values of beta1 and beta2only.c. Facts (given): the same facts for the same variables of part b.Conclusion: When YY is regressed on XX1 and XX2 simultaneously, i.e.,within the same multiple regression equation, the multiple correlationcoefficient of the regression equation will not be smaller than beta1.

For each of the following sets of statements, state whether the conclusion is correct or incorrect based on the facts given, and explain the rationales of your answer in no more than four sentences. (No marks will be given for only indicating the conclusion as correct or incorrect without any explanation.) a. Facts (given): When an interval variable Y is regressed on three interval variables X1, X2, and X3, simultaneously (i.e., within the same multiple regression equation), the multiple correlation coefficient and the regression coefficients of X1 and X2 are all statistically significant and the regression coefficient of X3 is not statistically significant. Conclusion: When Y is regressed on X3 (in a bivariate regression analysis). the regression coefficient of X3 is not necessarily non-significant (statistically).