11.48. In regression analysis, which ofthe following statements must be false? Why?

(a) ryXl = 0.01, ryX2 = -0.75,7? = 0.2

(b) The value ofthe residual sum ofsquares, SSE, can increase as we add additional variables to the model.

(c) For the model E(y) = a + jSixi, y is significantly related to xj at the 0.05 level, but when X2 is added to the model, y is not significantly related to x\ at the 0.05 level.

(d) The estimated coefficient ofxi is positive in the bivariate model but negative in the multiple regression model.

(e) When the model is refitted aftery is multiplied by 10, R 2

, ryXl, ryXvX2, and the Fstatistics and r statistics do not change.

(f) The F statistic for testing that all the regression coefficients equal 0 has P < 0.05, but none of the individual r tests have P < 0.05.

(g) If you compute the standardized regression coefficient for a bivariate model, you always get the correlation.

(h) r 2

X] = r 2

^ = 0.6 and R 2

= 1.2.

(i) The correlation between y andy equals -0.10.