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Under the null hypothesis, F has an F distribution with J and N – K degrees of freedom, denoted as F-. If we use the definition of the R from (2.42), we can also write this F-statistic as (R - R)/J (1 - R)/(N – K) (2.59) where R; and R; are the usual goodness-of-fit measures for the unrestricted and the restricted models, respectively. This shows that the test can be interpreted as testing whether the increase in R² moving from the restricted model to the more general model is significant. It is clear that in this case only very large values for the test statistic imply rejection of the null hypothesis. Despite the two-sided alternative hypothesis, the critical values F-k for this test are one-sided and defined by the following equality: N-Ki

Under the null hypothesis, F has an F distribution with J and N – K degrees of freedom, denoted as F-. If we use the definition of the R from (2.42), we can also write this F-statistic as (R - R)/J (1 - R)/(N – K) (2.59) where R; and R; are the usual goodness-of-fit measures for the unrestricted and the restricted models, respectively. This shows that the test can be interpreted as testing whether the increase in R² moving from the restricted model to the more general model is significant. It is clear that in this case only very large values for the test statistic imply rejection of the null hypothesis. Despite the two-sided alternative hypothesis, the critical values F-k for this test are one-sided and defined by the following equality: N-Ki

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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What is J expalining in a F test

k = constant + coefficient

N = Sample size

Under the null hypothesis, F has an F distribution with J and N – K degrees of freedom, denoted as F-K. If we use the definition of the R? from (2.42), we can also write this F-statistic as (R – R)/J F = (1 – R)/(N – K) (2.59) where R and R are the usual goodness-of-fit measures for the unrestricted and the restricted models, respectively. This shows that the test can be interpreted as testing whether the increase in R² moving from the restricted model to the more general model is significant. It is clear that in this case only very large values for the test statistic imply rejection of the null hypothesis. Despite the two-sided alternative hypothesis, the critical values for this test are one-sided and defined by the following equality: N-Ka
Transcribed Image Text:Under the null hypothesis, F has an F distribution with J and N – K degrees of freedom, denoted as F-K. If we use the definition of the R? from (2.42), we can also write this F-statistic as (R – R)/J F = (1 – R)/(N – K) (2.59) where R and R are the usual goodness-of-fit measures for the unrestricted and the restricted models, respectively. This shows that the test can be interpreted as testing whether the increase in R² moving from the restricted model to the more general model is significant. It is clear that in this case only very large values for the test statistic imply rejection of the null hypothesis. Despite the two-sided alternative hypothesis, the critical values for this test are one-sided and defined by the following equality: N-Ka
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