Consider the following set of ordered pairs. x 33 55 33 11 y 77 66 66 22 Calcula
ID: 3243682 • Letter: C
Question
Consider the following set of ordered pairs.
x
33
55
33
11
y
77
66
66
22
Calculate the coefficient of determination and test its significance using =0.05.
1 Click the icon to view a partial ANOVA table.
2 Click the icon to view a partial table of critical F-scores with 0.05 in the right tail of the distribution.
Calculate the coefficient of determination.
R^2 = ________________
(Round to three decimal places as needed.)
Determine the null and alternative hypotheses. Choose the correct answer below.
Determine the critical F-score,
F = ____________
(Round to three decimal places as needed.)
Calculate the F-score for this test.
F = _________
(Round to three decimal places as needed.)
Determine the correct conclusion. Choose the correct answer below.
Reject H0 There does not appear to bea relationship between x and y
Do not reject H0. There appears to be a relationship between x and y
Reject H0. Ther appears to be a relationship between x and y
Do not reject H0. There does not appear to be a relationship between x and y
------------------------------
1: Partial ANOVA
ANOVA
d.f.
SS
MS
F
Regression
1
8.0008.000
Error
2
6.7506.750
Total
3
14.75014.750
x
33
55
33
11
y
77
66
66
22
Explanation / Answer
To comple the anova table, its necessary to calculate the mean square.
For the model mean square (MSM) the formula is =SSM/DFM, SSM refers to sum of squares of the model = 8; and DFM is the model degrees of freedom =1 then the result is 8
Then mean square of the error (MSE) is calculated by SSE/DFE, SSE represents sum of squares of the error = 6.750, and DFE, degrees of freedom of the error (n-2) = 2, the result is 6.250/2=3.375
And finally the sample variance SST/DFT, SST stands for the total sum of squares and DFT the total degrees of freedom, 14.75/3=4.9166
F is then calculated with MSM/MSE = 8/3.375 = 2.370
The final ANOVA is:
r^2 coefficient is claculated as SSM/SST (sum of squares of the model divided by total sum of squares) according to the previuos tables they are 8 and 14.750=0.542
The nullhypothesis is that there is relationship between X and y
and alternative hypothesis is that there is no relationship between X and Y
F critical score is determined by (DFM, DFE) dor this example is F(1,2)=18.513
The F-score of the test is 2.370. 18,513>2.370
Then the conslusion is
Do not reject H0. There appears to be a relationship between x and y
d.f. SS MS F Regression 1 8 8 2.370 ERROR 2 6.75 3.375 Total 3 14.75 4.91666667