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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

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.1: Measures Of Center
Problem 9PPS
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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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