Deakin University MAE256: Analytical Methods Assignment Solution

This document presents a comprehensive solution to an economics assignment centered on analytical methods, specifically regression analysis and its application to household recreational expenses. The solution begins with the analysis of a multiple regression model, evaluating the fit of the model using R-squared and assessing the significance of the coefficients. It then explores a second regression model with a transformed dependent variable, comparing the results and interpreting the coefficients. The assignment continues with a practical application, calculating recreational expenditure based on given input values. Finally, the solution tests the significance of the income slope coefficient. The assignment brief provided data on household weekly recreational expenses, income, number of children, and other demographic variables, requiring the student to apply econometric techniques to analyze the factors influencing recreational spending. The analysis includes hypothesis testing, interpretation of coefficients, and assessment of model fit.

ANALYTICAL METHODS IN ECONOMICS AND FINANCE
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ANALYTICAL METHODS
Question 1
The requisite multiple regression model has been run using Excel and the data provided. The
following output has been obtained.
The regression equation is listed below.
Recexp = 28.59 + 0.10Inc(x) + 0.89chd + 175.33
The fit of the given model can be estimated by referring to R2 whose value is a dismal 0.1225.
This implies that only 12.25% of the variation in dependent variable (recexp) can be explained
with regards to variation of the independent variables (inc & chd) jointly. This implies a very
low predictive power for the model with a high majority of the variation not being explained by
the given model. Also, referring to the slopes of the two coefficients included, it is apparent that
the slope of chd variable is not significant considering that the p value is quite high at 0.57. If
the given model is compared with model in part (ii), then there is a deterioration of goodness of
fit as a non-significant variable in the form of chd has been added to the regression model.

ANALYTICAL METHODS
Question 2
The requisite multiple regression model has been run using Excel and the data provided. The
following output has been obtained.
The regression equation is listed below.
Log(recexp) = -0.64 + 0.86log(Inc(x)) -0.0008chd + 0.4292
In comparison to the multiple regression model estimated for question 1, the coefficient of chd is
negative and lower in magnitude when compared to the corresponding coefficient of chd in the
model worked out in question1. Clearly as per model 1, the increase in number of children
would lead to higher recreation expenses while in model 2, the nature of relationship is opposite
owing to the slope coefficient being negative. With regards to the significance of the slope, the
relevant hypotheses are stated below.
Null Hypothesis: βCHD = 0 i.e. slope is insignificant since it can be assumed to be zero.
Alternative Hypothesis: βCHD ≠ 0 i.e. slope is significant since it cannot be assumed to be zero

ANALYTICAL METHODS
The relevant t statistic is -0.21 and the corresponding p value is 0.83 as stated in the regression
output shown above. Assuming a 1% significance level, it is evident that the null hypothesis
would not be rejected since p value is greater than the level of significance. Hence, it can be
concluded that the underlying slope efficient of variable corresponding to number of children is
insignificant.
Question 3
In the given case, the input values are given as inc = $400, chd = 3
Hence, Log(recexp) = -0.64 + 0.86log(400) -0.0008*3 + 0.4292
Solving the above, we get recreational expenditure per week (or recexp) = $ 105.82
Fortnightly expenditure on recreational expenditure for the given input data = (105.82)*(15/7) =
$226.76
Question 4
The significance of the inc slope coefficient based on model 2 has been tested as shown below.
Null Hypothesis: βINC = 0 i.e. slope is insignificant since it can be assumed to be zero.
Alternative Hypothesis: βINC ≠ 0 i.e. slope is significant since it cannot be assumed to be zero
The relevant t statistic is 43.13 and the corresponding p value is 0.00 as stated in the regression
output shown above. Assuming a 1% significance level, it is evident that the null hypothesis
would be rejected since p value is lower than the level of significance. Hence, it can be
concluded that the underlying slope efficient of variable corresponding to weekly income is
significant. Also, considering that the coefficient is positive, it would imply that the effect of this
variable would be positive.