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3.3 Global hypothesis test (F & r 2 )

3.3 Global hypothesis test (F & r 2 ) As in the individual test, we posit an hypothesis to be rejected  all coefficients taken together F distribution: critical F vs. F-stat What is the relationship with the r 2 ? Extreme examples: F* = +∞  sure rejection (r 2 = 1)

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3.3 Global hypothesis test (F & r 2 )

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  1. 3.3 Global hypothesis test (F & r2) As in the individual test, we posit an hypothesis to be rejected  all coefficients taken together F distribution: critical F vs. F-stat What is the relationship with the r2? Extreme examples: F* = +∞  sure rejection (r2 = 1) F* = 0  NO rejection: The X’s do not explain the model (r2 = 0) The test gives an idea of the joint significance of all X’s ¿Do the X’s jointly explain the variability of Y? We usually reject (even when we don’t reject individual tests)

  2. 3.4 Omission of relevant variables & inclusion of irrelevant Omission of relevant var.  biased estimations What does it mean? On average we don’t get the true value of the parameter (population) Inclusion of irrelevant var.  inefficient estimations What does it mean? The variability from sample to sample (embedded in the sigmas/deviations) will be higher Which one is worse? Both should be corrected, if possible, but having biased estimations is worse

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