Critical values of R² when true R² 0. Equation (8.4.11) gave the relationship between F and R² under the hypothesis that all partial slope coefficients are simultaneously equal to zero (i.e., R² = 0). Just as we can find the critical F value at the α level of significance from the F table, we can find the critical R² value from the following relation:

R² = (k – 1) F / (k – 1) F + (n – k)

where k is the number of parameters in the regression model including the intercept and where F is the critical F value at the α level of significance. If the observed R² exceeds the critical R² obtained from the preceding formula, we can reject the hypothesis that the true R² is zero.

Establish the preceding formula and find out the critical R² value (at α = 5 percent) for the regression (8.1.4).