R2 = bExly / 2y2
 = 0.5416(4.875) / 3.2483
 = 0.81

which is lower than for the quadratic equation.
 The significance of b can be tested using


 tb = b
 {(zy2 [(Exly)2 / Zx12]}1/2 / [(n-2)Ex12] /2

 = 0.5416 / {(3.2483-[(4.875)2 / 9]) / 4(9)}1/2
 = 4.1686

and with n k 1 = 4 degrees of freedom, b is
significantly different from zero.
 The F value for the linear equation is:

 Fc = tb2
 = 17.38

With k and n k 1, or 1 and 4,degrees of freedom this is
significant at the 5% level.
 Another test of the linear versus the quadratic
equation is the "F" test, based on an analysis of
variance. The method is used for evaluating the
significance of additional terms. Total variation ( y2)
is divided into three parts: (1) the variation explained
by the equation without the additional term, that is, the
linear equation; (2) the increase in the explained
variation resulting from adding the additional (quadratic)
term; and (3) the error or residual. The part explained
by the equation without the additional term is

 E(biExiy)

where i varies from 1 to k 1, and the increase in
explained variation from the additional term is

 E(bjZxjy) E(bixiy)

where j varies from 1 to k and i varies from 1 to k 1 as
before. The term k is the additional term. Because
different terms are included in the two equations, the