Mathematics, 12.12.2019 05:31 kira96

Ga sample of 10 observations collected in a regression study on three variables, x_1(independent variable), x_2(independent variable and y(dependent variable). the sample resulted in the following data. ssr=26, sst=47 using a 0.01 level of significance, we conclude that the regression model is significant overall. (enter 1 if the conclusion is correct. enter 0 if the conclusion is wrong.)

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Answer from: hailey5campbelp7d1c0

$p_v = P(F_{2,7} 4.3333)=0.0596$

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 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 independent variables.

The degrees of freedom for the error on this case is given by $df_{error}=N-k-1=10-2-1=7$ . Since for this case N=10 and k=2

And the total degrees of freedom would be df=N-1=10 -1 =9

SSE=SST-SSR=47-26=21

Now we can find the mean squares for the regression and the error, given by:

$MSR=\frac{SSR}{df_{regression}}=\frac{26}{2}=13$

$MSE=\frac{SSE}{df_{error}}=\frac{21}{7}=3$

And now we can find the F statistic given by:

$F=\frac{SSR}{SSE}=\frac{13}{3}=4.333$

Now we can find the p value given by:

$p_v = P(F_{2,7} 4.333)=0.0596$

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.

Answer from: Quest

828. all there is to it!

here, if you ever need with rounding (or other forms of arithmetic/math) again, use this:

thats the rounding one, but if you just click the top left, it shows you all the calculators you may need!

Answer from: Quest

If you make it a little more clear i can answer it

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