Exam 1

1. Metainformation

   Tag	Value
   file	Inferential_Statistics_vufgb-ftestforcomparingnestedmodels-004-en_vufgb-ftestforcomparingnestedmodels-004-en
   name	vufgb-ftestforcomparingnestedmodels-004-en
   section	Inferential Statistics/Regression/Multiple linear regression/F-test for comparing (nested) models, Inferential Statistics/Parametric Techniques/ANOVA
   type	schoice
   solution	FALSE, FALSE, TRUE, FALSE
   Type	Performing analysis, Calculation, Interpreting output
   Program
   Language	English
   Level	Statistical Thinking

   Question

   Given are the ANOVA tables of two regression models: one model with two predictors, and one model with two predictors and their interaction.

   Use the Model Comparison Test to determine whether there is a significant interaction.

   

   
   
   1. FALSE: $F(df_{1}=3, \; df_{2}=21)= 3.16 > 3.07$, so significant interaction
   2. FALSE: $F(df_{1}=1, \; df_{2}=3)= 0.57 <10.13$, so no significant interaction
   3. TRUE: $F(df_{1}=1, \; df_{2}=21)= 1.82 < 4.32$, so no significant interaction
   4. FALSE: $F(df_{1}=1, \; df_{2}=1)= 0.54 < 161.4$, so no significant interaction
   
   

   Solution

   $F= \frac{[(SSE_{r}-SSE_{c})/df_{1}]}{[SSE_{c}/df_{2}]} =\frac{[(565-520)/1]}{[520/21]} = \frac{45}{24.76}=1.82$. With $df_{1} = 1$ (difference in df’s between complete and reduced model) and $df_{2} = 21$ (df of SSE in complete model). Look in the F-table at $df_{1} = 1$ and $df_{2}=21$ what the critical F-value is, this is 4.32. Founded F < critical F, so adding the interaction-term in model 2 does not lead to significant less error, so there is no significant interaction.

   
   
   1. Incorrect
   2. Incorrect
   3. Correct
   4. Incorrect