4.1.1 The F-test
An F-test was conducted to cross check the model accuracy and goodness
of fit, since the R2-statistic only gives the
variation of dependent variable with the independent variable(Forest et
al., 2001). The adjusted R2 tests the results based on
independent variables only. The F-test statistic is indicative of
response and predictor relation. A low F value means a weak relation and
a zero F value would mean there is no relationship at all(Loureiro &
González, 2008).
The higher the F-value more than 1 gives enough reason to reject the
null hypothesis (H0) that all regression coefficients
are zero (β0, β1, β2,
β3…… βn =0). An F-test statistic is calculated
by(Forest et al., 2001; Loureiro & González, 2008)-
F=\(\frac{(TSS-RSS)/p}{RSS/(n-p-1)}\) (9)
Where TSS is total sum of squares, TSS= Σ (𝑦𝑖 −
(\(\overset{\overline{}}{y}\) )2 and RSS is the
Residual Sum of Squares RSS= Σ (𝑦𝑖 -
(\(\hat{y}\)))2 , and yi is response
value, \(\hat{y}\) is predicted
value and\(\overset{\overline{}}{y}\) is
sample mean(Happé & Frith, 2006).
The OLS regression results are given in TABLE 3 at 97.5% confidence
level-
TABLE 3. OLS Regression Residuals