________________ is used to test the hypothesis that the values of the regression parameters B1, B2, ... Bq are all zero.

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BlackTom AI · Accepted Answer

The question asks about a statistical test used to evaluate the hypothesis that all regression coefficients B1, B2, ..., Bq in a model are equal to zero. In the context of linear regression, this is a joint hypothesis test about multiple parameters. Typically, the standard approach to test whether all these coefficients are zero is to use an F test, which compares the fit of the full regression model against a reduced model that excludes the predictors corresponding to those coefficients. The F statistic assesses whether the additional predictors provide a significant improvement in explaining the variability in the dependent variable, relative to the amount of noise in the data. On the other hand, t-tests are used to test individual coefficients one at a time (e.g., testing Bk = 0 for a single predictor). While t-tests can be related to F tests under certain conditions (a multiple regression with one predictor yields an equivalent t and F test), the specific hypothesis that all of B1 through Bq are zero is a multivariate, joint hypothesis that is conventionally tested with an F statistic rather than a single t test. If the available options were different or more numerous, one would expect to see an option explicitly naming an F test as addressing the joint hypothesis, alongside other tests like t-tests for individual coefficients or tests of subsets of coefficients. Since the prompt’s provided answer option is “An F test,” this aligns with the standard interpretation for testing whether all regression parameters are zero. If other options were present, they would need to be evaluated for whether they test the joint null hypothesis (all B’s equal to zero) versus only individual coefficients or different hypotheses. In summary, for a joint test of the null that every Bk equals zero, the F-test is the standard chosen method in the framework of linear regression analysis.

________________ is used to test the hypothesis that the values of the regression parameters B1, B2, ... Bq are all zero.

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