Respuesta :
Answer:
N=27 participants
Step-by-step explanation:
Analysis of variance (ANOVA) "is used to analyze the differences among group means in a sample".
The sum of squares "is the sum of the square of variation, where variation is defined as the spread between each individual value and the grand mean"
When we conduct a multiple regression we want to know about the relationship between several independent or predictor variables and a dependent or criterion variable.
If we assume that we have [tex]k[/tex] independent variables and we have [tex]j=1,\dots,j[/tex] individuals, we can define the following formulas of variation:
[tex]SS_{total}=\sum_{j=1}^n (y_j-\bar y)^2[/tex]
[tex]SS_{regression}=SS_{model}=\sum_{j=1}^n (\hat y_{j}-\bar y)^2 [/tex]
[tex]SS_{error}=\sum_{j=1}^n (y_{j}-\hat y_j)^2 [/tex]
And we have this property
[tex]SST=SS_{regression}+SS_{error}[/tex]
The degrees of freedom for the model on this case is given by [tex]df_{model}=df_{regression}=k=2[/tex] where k =2 represent the number of variables.
The degrees of freedom for the error on this case is given by [tex]df_{error}=N-k-1=24[/tex]. Sinc we know k we can find N.
[tex]N=24+k+1=24+2+1=27[/tex]
And the total degrees of freedom would be [tex]df=N-1=27 -1 =26[/tex]
On this case the correct answer would be N=27 participants
