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kupik
3 months ago
11

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

ipants were in the sample?
Mathematics
1 answer:
Inessa [12.5K]3 months ago
6 0

Answer:

N=27 individuals

Step-by-step explanation:

Analysis of variance (ANOVA) is employed to assess the differences among group means in a sample.

The sum of squares refers to the cumulative square of variation, which is the dispersion between each individual value and the overall mean.

While conducting a multiple regression, we aim to understand the relationship between multiple independent or predictor variables and one dependent or outcome variable.

<passuming we="" have="" src="https://tex.z-dn.net/?f=k" id="TexFormula1" title="k" alt="k" align="absmiddle" class="latex-formula"> independent variables and j=1,\dots,j individuals, we are able to define the corresponding 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

We also have this property

SST=SS_{regression}+SS_{error}

The model's degrees of freedom in this instance is determined by df_{model}=df_{regression}=k=2 where k = 2 represents the number of variables.

For the error's degrees of freedom in this case, it is indicated by df_{error}=N-k-1=24. Knowing k allows us to ascertain N.

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

The total degrees of freedom would be df=N-1=27 -1 =26

This leads us to conclude that the correct answer is N=27 participants.

</passuming>
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