ABSTRACT
Observe that this is also equivalent to rejecting H0 whenever r 2=c, where the
constant c depends on the level of significance a of the test. Example 8.3.1. Consider the data given in Example 5.3.1. Let ?2 be the square of
the population multiple correlation coefficient between X6 and (X1,…, X5). The
square of the sample multiple correlation coefficient r2 based on 27 observations for each year’s data is given by
We wish to test the hypothesis at a=0.01 that the wheat yield is independent of the variables plant height at harvesting (X1), number of effective tillers (X2), length of ear (X3), number of fertile spikelets per 10 ears (X4), and number of grains per 10
ears (X5). We compare the value of (21/5)(r 2/(1-r2)) with a F5,21,0.01=9.53 for each
year’s data. Obviously for each year’s data (21/5)(r2/(1-r2))>9.53, which implies that the result is highly significant. Thus the wheat yield is highly dependent on (X1, …, X5).
