A data set of 32 stream sections includes the following variables: X1 is the depth of flow; X2 is the roughness of the channel bottom; X3 is the slope of the stream bed; X4 is the mean soil particle diameter;

and Y is the erosion rate of the channel bed. The data yield the following correlation matrix:

X1 X2 X3 X4 Y X1 1.00 –0.26 –0.66 –0.08 0.76 X2 1.00 –0.31 0.87 –0.27 X3 1.00 0.06 0.61 X4 1.00 –0.43 Y 1.00 Discuss:

(a) the potential accuracy of a relationship between Y and all of the X variables;

(b) the predictor variable that would yield the most accurate bivariate model;

(c) the rationality of the correlation coefficients;

(d) the potential effect of intercorrelation on the rationality of the regression coefficients.