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 (see household.xslx). Consider the following path diagram: 1. Set-up the structural equations. Consider the R outputs from the conducted path analysis.
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 (see household.xslx). Consider the following path diagram: 1. Set-up the structural equations. Consider the R outputs from the conducted path analysis.
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Question
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 (see household.xslx). Consider the following path diagram:
1. Set-up the structural equations. Consider the R outputs from the conducted path analysis.
2. Identify the factors affecting the endogenous variables. Leave blank if variable is exogenous.
W: ____________
X: ____________
Y: ____________
Z: ____________
A: ____________
3. Illustrate the output path diagram including the estimated path coefficients.
Transcribed Image Text:Y
A
4
5.
80000
70000
5000
3
74000
60000
3000
8000
8000
1
15000
15000
2
2
45000
34000
2000
4
4
60000
45000
3000
5
5
65000
40000
3000
2
4
22500
21000
3
30000
26000
2
18000
17500
5000
5000
2
2
20000
16000
2000
3
4
50000
43000
5000
4
88000
69000
10000
4
85000
71000
10000
4
4
120000
103000
15000
5
130000
107500
20000
7
7
145000
98000
25000
1
3
26500
25000
2
2
40000
36000
2000
n53 4
Transcribed Image Text:Dependent variable: Y
Coefficients:
Ey
Estimate Std, Error t value Pr(>it|)
7088.7
2152.0
335.7
20368.8
0.963
(Intercept)
0.047
9.465 2.07e-08 ***
Y
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
A
> Im. beta(fit.Y)
0.9125181
En
1 Dependent variable: Z
Coefficients:
Estimate Std. Error t value Pr(>it|)
(Intercept) 6.757e+03 3.605e-03 1.874 0.0782.
-1.294 0.2129
8.035e-01 4.934e-02 16.285 8.34e-12 ***
Instructions: Use the variable notations in writing your answers. Conduct all tests at
5%% level of significance.
-1.719e+03 1.328e+03
Signif. codes: 0 ** 0.001 ** o.01 0.05 . 0.1 1
Residual standard error: 5627 on 17 degrees of freedom
Multiple R-squared: 0.972.
F-statistic: 294.9 on 2 and 17 DF. p-value: 6.357e-14
Adjusted R-squared: 0.9687
> Im. beta(fit.z)
-0.08338779 1.04924122
Dependent variable:A
Coefficients:
Estimate Std. Error t value Pr(ltl)
(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 *
-1.699 0.10999
-278.8482
0.4128
-0.2370
0.1361
0.1395
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.
Adjusted R-squared: 0.8643
, p-value: 4.088e-07
Activate Window
> Im.beta(fit.A)
Go to Settings to acti
-0.40652867 -0.05965043 2.37732884 -1.04538544
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