A researcher wants to determine the causal relationship among number of family members who are at least high school graduate (W), number of working family members (X), monthly gross income (Y), monthly expenditure (Z), and average monthly bank deposits (A). A random sample of 20 families was selected and the data on the variables were collected: Consider the following path diagram Consider the R outputs from the conducted path analysis. c.    Identify the factors affecting the endogenous variables. Leave blank if variable is exogenous. W:       X:       Y:       Z:       A:       d.    Illustrate the output path diagram including the estimated path coefficients

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A researcher wants to determine the causal relationship among number of family members who are at least high school graduate (W), number of working family members (X), monthly gross income (Y), monthly expenditure (Z), and average monthly bank deposits (A). A random sample of 20 families was selected and the data on the variables were collected: Consider the following path diagram

Consider the R outputs from the conducted path analysis.

c.    Identify the factors affecting the endogenous variables. Leave blank if variable is exogenous.

W:      
X:      
Y:      
Z:      
A:      

d.    Illustrate the output path diagram including the estimated path coefficients. 

Dependent variable: Y
Coefficients:
(Intercept)
W
Estimate Std. Error t value Pr(>ltl)
0.963
2152.0 9.465 2.07e-08 ***
7088.7 0.047
335.7
20368.8
Signif. codes: 0 ***** 0.001 *** 0.01 *** 0.05 '.' 0.1' 1
Residual standard error: 17450 on 18 degrees of freedom
Multiple R-squared: 0.8327,
F-statistic: 89. 58 on 1 and 18 DF, p-value: 2.068e-08
Adjusted R-squared: 0.8234
> Im.beta(fit.Y)
W
0.9125181
Dependent variable: Z
Coefficients:
Estimate Std. Error t value Pr(>|t|)
|(Intercept) 6.757e+03 3.605e+03 1.874 0.0782 .
-1.719e+03 1.328e+03 -1.294 0.2129
8.035e-01 4.934e-02 16.285 8.34e-12 ***
Y
Signif. codes: 0 ***** 0.001 *** 0.01 **' 0.05 '.' 0.1'1
Residual standard error: 5627 on 17 degrees of freedom
Multiple R-squared: 0.972, Adjusted R-squared: 0.9687
F-statistic: 294.9 on 2 and 17 DF, p-value: 6.357e-14
> Im.beta(fit.Z)
Y
|-0.08338779 1.04924122
Dependent variable: A
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) -1833.0488 1878.3151 -0.976 0.34459
-1575.6756 1095.0959 -1.439 0.17073
703.7910 -0.396 0.69753
3.032 0.00841 **
0.1395 -1.699 0.10999
-278.8482
0.4128
-0.2370
Y
0.1361
signif. codes: 0 *** 0.001 **** 0.01 ** 0.05 '.' 0.1 '1
Residual standard error: 2656 on 15 degrees of freedom
Multiple R-squared: 0.8928,
F-statistic: 31.24 on 4 and 15 DF, p-value: 4.088e-07
Adjusted R-squared: 0.8643
> Im.beta(fit.A)
Y
-0.40652867 -0.05965043 2.37732884 -1.04538544
Transcribed Image Text:Dependent variable: Y Coefficients: (Intercept) W Estimate Std. Error t value Pr(>ltl) 0.963 2152.0 9.465 2.07e-08 *** 7088.7 0.047 335.7 20368.8 Signif. codes: 0 ***** 0.001 *** 0.01 *** 0.05 '.' 0.1' 1 Residual standard error: 17450 on 18 degrees of freedom Multiple R-squared: 0.8327, F-statistic: 89. 58 on 1 and 18 DF, p-value: 2.068e-08 Adjusted R-squared: 0.8234 > Im.beta(fit.Y) W 0.9125181 Dependent variable: Z Coefficients: Estimate Std. Error t value Pr(>|t|) |(Intercept) 6.757e+03 3.605e+03 1.874 0.0782 . -1.719e+03 1.328e+03 -1.294 0.2129 8.035e-01 4.934e-02 16.285 8.34e-12 *** Y Signif. codes: 0 ***** 0.001 *** 0.01 **' 0.05 '.' 0.1'1 Residual standard error: 5627 on 17 degrees of freedom Multiple R-squared: 0.972, Adjusted R-squared: 0.9687 F-statistic: 294.9 on 2 and 17 DF, p-value: 6.357e-14 > Im.beta(fit.Z) Y |-0.08338779 1.04924122 Dependent variable: A Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) -1833.0488 1878.3151 -0.976 0.34459 -1575.6756 1095.0959 -1.439 0.17073 703.7910 -0.396 0.69753 3.032 0.00841 ** 0.1395 -1.699 0.10999 -278.8482 0.4128 -0.2370 Y 0.1361 signif. codes: 0 *** 0.001 **** 0.01 ** 0.05 '.' 0.1 '1 Residual standard error: 2656 on 15 degrees of freedom Multiple R-squared: 0.8928, F-statistic: 31.24 on 4 and 15 DF, p-value: 4.088e-07 Adjusted R-squared: 0.8643 > Im.beta(fit.A) Y -0.40652867 -0.05965043 2.37732884 -1.04538544
EY
Y
W
A
Z
EA
Ez
Transcribed Image Text:EY Y W A Z EA Ez
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