Parameter Standard Estimate D F 45 103 19 2 Error t Value Pr 10.76487 511 1.21 2
ID: 3172239 • Letter: P
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Parameter Standard Estimate D F 45 103 19 2 Error t Value Pr 10.76487 511 1.21 227 15 0.0003 4.190 0.3238, 1922 9.9455 68 0.0008 3.745 2.65 605 655 8 59 24 449 0.0008 3.744 4.498, 68, 122 0.0664 1.910 Square d Squared Parti a Parti a L Corr Type I D F Corr Type II 0.600 941 36 0.33373458 0.32 291 131 0.3336 6.934 0.1 1526997 0.1 15 26 997 An to performing a partial F test for the nificance of adding a new ble to a model while controlling for variables already in the model is to perform attest using the appropriate partial correlation coefficient. If the dependent the inde endent variable of interest is variable is Y, the t test for Ho: pr z zo 0 and the controlling variables are Z1, Z2 Z then versus HA: pyxlzi,z,..... z. 0 is given by the test statistic YX Z, Z. which has a t distribution under Ho with n p 2 degrees of freedom. The critical region for this test is therefore given by n-p-2, 1-a/2. 88 North Carolina counties, the following partial correlations were obtained 124 and r x 121 where X1 Distance from county seat to main hospital center X2 Population per physician X3 Water hardness index for county Test separately the following null hypotheses: 0 and prxixi, x An alternative way to form the ANOVA table associated with a regression analysis is use partial correlation coefficients. For example, if three independent variables XI, and X3 are used, the ANOVA table is as shown next.Explanation / Answer
Here we have to test the hypothesis that,
H0 : YX3/X1 = 0 Vs H1 : YX3/X2 not= 0
Assume alpha level of significance = 0.05
The test statistic is,
t = rYX3/X1 * sqrt[n-p-2] / sqrt[1 - rYX3/X1^2]
where n=88
p = number of predictors = 3
rYX3/X1 = 0.124
t = 0.124 * sqrt(88-3-2) / sqrt(1-0.124^2)
= 1.138
Now we have to find P-value for test statistic.
The P-value we can find by uisng EXCEL.
syntax :
=TDIST(x, deg_freedom, tails)
where x is test statistic
deg_freedom = n-p-2
tails = 2
P-value = 0.2582
P-value > alpha
Accept H0 at 5% level of significance.
The population partial correlation of Y on X1 and X2 may be 0.
And H0 : YX3/X1,X2 = 0 Vs H1 : YX3/X1,X2 not= 0
t = 0.121 * sqrt(88-3-2) / sqrt(1-0.121^2)
= 1.1105
P-value = 0.2700
P-value > alpha
Accept H0 at 5% level of significance.
The population partial correlation of Y on X1, X2 and X3 may be 0.
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