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