True or False?
(a) The main purpose of multiple regression is to increase the predictability of the response or Y variable from the predictor or X variables; (b) multiple regression is only applicable when the relationship between the Y variable and each of the X variables is linear or can be linearized; (c) as with simple linear regression (SLR), multiple linear regression (MLR) is also referred to as ordinary least squares (OLS) regression because it is also based on minimization of the sum of the squares of the residuals; (d) one advantage of multiple regression is that increasing the number of predictor variables unfailingly leads to a better quality model; (e) for exploratory graphical review of the data, the scatterplot matrix is to multiple regression as the scatterplot is to simple regression; (f) the assumptions of SLR and MLR are essentially the same, except that MLR also assumes the absence of multicollinearity; (g) if the VIF for some of the X variables in a MLR model is larger than 10, it indicates that the regression results may be unreliable due to problems with multicollinearity; (h) multicollinearity inflates the standard errors of the coefficients, thereby artificially reducing theirt values and making them seem insignificant; (i) either the VIF or the Tolerance can be used to detect the presence of multicollinearity in an MLR, and each should have a value close to 1 if multicollinearity is absent; (j) centering the X variables is an effective remedy for structural multicollinearity in interaction models; (k) the adjusted R-squared is a useful statistic for assessing the cost–benefit of including additional X variables in an MLR model; (l) the difference between the sequential (i.e., Type I) sums of squares (SS) and the partial or adjusted (i.e., Type III) SS in an MLR is that the sequence of entering the X variables in the model affects Type I SS but not Type III SS, when interaction among the X variables is present; (m) including interaction terms in a MLR always results in an increase (i.e., improvement) in the adjusted R2 and the overall model quality.
