Source: Haim Levy and Marshall Sarnat, Portfolio and Investment Selection: Theory and Practice, Prentice-Hall International, Englewood Cliffs, N.J., 1984, pp. 730 and 738. These data were obtained by the authors from Weisenberg Investment Service, Investment Companies, 1981 edition.

Source: Haim Levy and Marshall Sarnat, Portfolio and Investment Selection: Theory and Practice, Prentice-Hall International, Englewood Cliffs, N.J., 1984, pp. 730 and 738. These data were obtained by the authors from Weisenberg Investment Service, Investment Companies, 1981 edition.

(Continued)

4Henri Theil points out that if the intercept is in fact absent, the slope coefficient may be estimated with far greater precision than with the intercept term left in. See his Introduction to Econometrics, Prentice Hall, Englewood Cliffs, N.J., 1978, p. 76. See also the numerical example given next.

CHAPTER SIX: EXTENSIONS OF THE TWO-VARIABLE LINEAR REGRESSION MODEL 169

AN ILLUSTRATIVE EXAMPLE (Continued)

If we decide to use model (6.1.11), we obtain the following regression results

which shows that fS, is significantly greater than zero. The interpretation is that a 1 percent increase in the market rate of return leads on the average to about 1.09 percent increase in the rate of return on Afuture Fund.

How can we be sure that model (6.1.11), not (6.1.10), is appropriate, especially in view of the fact that there is no strong a priori belief in the hypothesis that a, is in fact zero? This can be checked by running the regression (6.1.10). Using the data given in Table 6.1, we obtained the following results:

Note: The r2 values of (6.1.12) and (6.1.13) are not directly comparable. From these results one cannot reject the hypothesis that the true intercept is equal to zero, thereby justifying the use of (6.1.1), that is, regression through the origin.

In passing, note that there is not a great deal of difference in the results of (6.1.12) and (6.1.13), although the estimated standard error of ยก3 is slightly lower for the regression-through-the-origin model, thus supporting Theil's argument given in footnote 4 that if ai is in fact zero, the slope coefficient may be measured with greater precision: using the data given in Table 6.1 and the regression results, the reader can easily verify that the 95% confidence interval for the slope coefficient of the regression-through-the-origin model is (0.6566, 1.5232) whereas for the model (6.1.13) it is (0.5195, 1.6186); that is, the former confidence interval is narrower that the latter.

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