Question

A researcher evaluates the significance of a multiple-regression equation and obtains an F-ratio with df = 2,24. How many participants were in the sample?

Answer 1

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 $k$ independent variables and we have  $j=1,\dots,j$ individuals, we can define the following formulas of variation:  

$SS_{total}=\sum_{j=1}^n (y_j-\bar y)^2$  

$SS_{regression}=SS_{model}=\sum_{j=1}^n (\hat y_{j}-\bar y)^2$  

$SS_{error}=\sum_{j=1}^n (y_{j}-\hat y_j)^2$  

And we have this property  

$SST=SS_{regression}+SS_{error}$  

The degrees of freedom for the model on this case is given by $df_{model}=df_{regression}=k=2$ where k =2 represent the number of variables.

The degrees of freedom for the error on this case is given by $df_{error}=N-k-1=24$. Sinc we know k we can find N.

$N=24+k+1=24+2+1=27$

And the total degrees of freedom would be $df=N-1=27 -1 =26$

On this case the correct answer would be N=27 participants