Respuesta :
Answer:
[tex]p_v = P(F_{2,7} >4.3333)=0.0596[/tex]
Since our p value it's higher than the significance level provided we can conclude that at 1% of significance we FAIL to reject the null hypothesis that the slopes for the inpendent variables are equal. So we don't have a significant effect on this case.
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 independent variables.
The degrees of freedom for the error on this case is given by [tex]df_{error}=N-k-1=10-2-1=7[/tex]. Since for this case N=10 and k=2
And the total degrees of freedom would be [tex]df=N-1=10 -1 =9[/tex]
[tex]SSE=SST-SSR=47-26=21[/tex]
Now we can find the mean squares for the regression and the error, given by:
[tex]MSR=\frac{SSR}{df_{regression}}=\frac{26}{2}=13[/tex]
[tex]MSE=\frac{SSE}{df_{error}}=\frac{21}{7}=3[/tex]
And now we can find the F statistic given by:
[tex]F=\frac{SSR}{SSE}=\frac{13}{3}=4.333[/tex]
Now we can find the p value given by:
[tex]p_v = P(F_{2,7} >4.333)=0.0596[/tex]
We can use the following excel code to verify the operation:"=1-F.DIST(4.3333,2,7,TRUE)"
Since our p value it's higher than the significance level provided we can conclude that at 1% of significance we FAIL to reject the null hypothesis that the slopes for the independent variables are equal. So we don't have a significant effect on this case.
