Question: 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:

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.