Answer: At least one of the coefficients is statistically significantly different from zero

A joint hypothesis test is used to assess whether at least one of the independent variables explains a significant portion of the total variation exhibited by the dependent variable. To determine the statistical significance, the F-statistic calculated is compared with the always one-tailed critical F-value. The null hypothesis is rejected when the F-statistic > one-tailed critical value, indicating that at least one of the coefficients is statistically significantly different from zero. **Key Points:** 1. The joint hypothesis test (F-test) tests the null hypothesis that all coefficients are equal to zero: H₀: β₁ = β₂ = β₃ = 0 2. When the F-statistic exceeds the critical F-value, we reject the null hypothesis 3. Rejection of the null hypothesis means that at least one coefficient is statistically different from zero, but it doesn't tell us which ones or how many 4. Option B is incorrect because the F-test doesn't guarantee that ALL coefficients are significant - it only indicates that at least one is 5. Option C is incorrect because we reject the null hypothesis 6. Option D is incorrect because we cannot conclude that only one coefficient is significant from the F-test alone

Author: Nikitesh Somanthe