In regression analysis, which of the following statements must be false? Why?

(a) ryx1

= 0.01, ryx2

= −0.75, R = 0.2

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

(c) For the model E(y) = α + β1x1, y is significantly related to x1 at the 0.05 level, but when x2 is added to the model, y is not significantly related to x1 at the 0.05 level.

(d) The estimated coefficient of x1 is positive in the bivariate model but negative in the multiple regression model.

(e) When the model is refitted after y is multiplied by 10, R2, ryx1 , ryx1·x2, and the F statistics and t 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 t tests have P < 0.05.

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

(h) r2 yx1

= r2 yx2

= 0.6 and R2 = 1.2.

(i) The correlation between y and ˆy equals −0.10.

(j) For every F test, there is an equivalent test using the t distribution.

(k) When |b1| > |b2| in a multiple regression prediction equation, we can conclude that x1 has a stronger effect than x2 on y.

(l) The estimated standardized regression coefficient for an explanatory variable in a multiple regression model can be interpreted as the value the ordinary slope would equal for the linear prediction equation if that explanatory variable and y were scaled so that they both had the same standard deviation value.

(m) If ˆy = 31.3 + 0.15x1 − 0.05x2 − 0.002x1x2, then the estimated effect x1 on y decreases as x2 increases.

(n) Suppose ˆy = 31.3 + 0.15x1 − 0.05x2 − 0.002x1x2, with x1 and x2 taking values between 0 and 100. Then, since the coefficient of x1x2 is so small compared to the coefficients of x1 and of x2, we can conclude that the amount of interaction is negligible.

For Exercises 11.49–11.52, select the correct answer(s) and indicate why the other responses are inappropriate. (More than one response may be correct.)