The critical value for a two-tailed test of h0: β1 = 0 at α = .05 in a simple regression with 22 observations is 4.35.
A critical value can be calculated for different types of hypothesis tests. The critical value of a particular test can be interpreted from the distribution of the test statistic and the significance level.
Test of significance of linear regression between x and y.
Null hypothesis: There is no significant linear relationship between x and y.
Alternative hypothesis: There is a significant linear relationship between x and y.
Test statistic:
F0 = Mean square due to regression/ mean squared error ~ F(1, n-2)
Critical value: [tex]F_{\alpha}(1, n-2) = F_{0.05}(1,20) = 4.35[/tex]
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