Microsoft Word - Assignment_Econ6034_Final.docx Econometrics and Business Statistics tal Marks 80 The assignment relates to the following learning outcomes: • Apply basic statistical techniques to...

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Answered Same DayMay 30, 2021ECON6034Macquaire University

Answer To: Microsoft Word - Assignment_Econ6034_Final.docx Econometrics and Business Statistics tal Marks 80...

Komalavalli answered on May 31 2021
145 Votes
Question 1:
Model 1:
(a)
yi = ?0 + ?1 x1i+ ?2 x2i + ?3 x3di + ?i
yi - Weekly expenditure on food (excluding restaurants) in dollars
x1i - Log of weekly household income in dollars
x2i - Number of dependent children living in the household
x3di = 1 If head of the household is retired
    0 If head of the household is not retired
Log linear Regression equation: Foodexp = 174.09+ 0.0432*log(Income) + 22.8*Children - 13.8*Retired.
Summary of Income variable; t statistics-7.406, s
tandard error-0.005, p-value -0.00
Summary of Children variable; t statistics-4.541, standard error-5.028.005, p-value -0.00
Summary of Retired dummy variable; t statistics is -0.947, standard error-14.569, p-value -0.3445
Summary of overall Model:
Prob (F-statistics) is 0.000; value of F statistic is 34.342, Adjusted R-squared is 0.33, R squared value is 0.34.Sample size of the model is 1200.
(b)
Expect the variable retired rest of all 2 variables, income and children are significant at 5 % level of significance.
Interpretation of coefficient:
By holding retired and children variable constant for a one percent increase in weekly household income on an average increases the weekly expenditure on food by $0.04 retired. Increase in one dependent children living in the household on an average increases the weekly expenditure on food by $22.82 by holding other variables constant. We can’t interpret the coefficient value of Retired variable, because it is insignificant at 1%, 5%, and 10% level of significance. Insignificant variable does not have influence on the regression model
(c)
From the model we can observe that there is a positive relationship between food expenditure and income, food expenditure and dependent children. When we look in real life relation between these variable, it will also have a positive relationship between these variable. It indicating the food expenditure increases when dependent children in the household and weekly income of the household increases. Therefore the sign of the model coefficients is similar to what I have expected.
(d)
Predicted change in food expenditure when income increases by 10 % by holding other things constant. Log linear Regression equation:
Log linear Regression Model y = 174 + 0.0432x1i + 22.8 x2i - 13.8 x3di.
For 10% increase in income: y = 174 + 0.0432(10) + 22.8 (0) - 13.8 (0).
y = 174 + 0.432
y = 174.432
The model predicted that when income increases by 10 % on an average expenditure on food is $174.432 by holding other variable constant.
(e)
Hypothesis of this model is H0 null hypothesis: β0= β1= β2= β3=0,by indicating all the coefficient variable equal to zero we assume that none of the variable in this model has influence on food expenditure.H1 β0≠β1≠β2≠β3≠0, we assume that all variables has influence on the food expenditure .
Unrestricted or full model is y = β0+ β1 x1+ β2 x2 + β3 x3d and restricted model is y = 0.If null hypothesis is true we use restricted model and we use unrestricted model when alternate hypothesis is true
Here the critical value of F stasticts (3,196) is 2.7 .The value of F statistics is 34.342 which is greater than the value critical value of F test .Therefore we reject null hypothesis and accept alternate hypothesis H1.Furthure we will use unrestricted model.
(f)
Variable log income of 95% confidence interval is (0.031719, 0.054742) stating that the population mean lies between the 0.031719 and 0.054742
(g)
Above analysis show that the population mean is does not include the value of null hypothesis .So we reject the null hypothesis ?0: ?2 = 100 and accept the alternate hypothesis ?1: ?2 ≠ 100, which indicates the variable log (income) has influence on the model.
(h)
Residual plot against log(income)
The above plot shows an upward line pattern, indicating the presence of heteroscedasticity indicates that there is no evidence for constant variance of residuals.
(i)
    Heteroskedasticity Test: Breusch-Pagan-Godfrey
    Null hypothesis: Homoskedasticity
    
    
    
    
    
    
    
    
    
    
    F-statistic
    21.74638
        Prob. F(3,196)
    0.0000
    Obs*R-squared
    49.94591
        Prob. Chi-Square(3)
    0.0000
    Scaled explained SS
    46.42366
        Prob. Chi-Square(3)
    0.0000
    
    
    
    
    
    
    
    
    
    
    
    Test Equation:
    
    
    
    Dependent Variable: RESID^2
    
    
    Method: Least Squares
    
    
    Sample: 1 200
    
    
    
    Included observations: 200
    
    
    
    
    
    
    
    
    
    
    
    
    Variable
    Coefficient
    Std. Error
    t-Statistic
    Prob.
    
    
    
    
    
    
    
    
    
    
    C
    1833.589
    1041.575
    1.760401
    0.0799
    INCOME
    4.092107
    0.528356
    7.744979
    0.0000
    CHILDREN
    -1618.538
    454.8451
    -3.558437
    0.0005
    RETIRED
    -539.9479
    1318.818
    -0.409418
    0.6827
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    
    R-squared
    0.249730
        Mean dependent var
    5642.232
    Adjusted R-squared
    0.238246
        S.D....
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