Analytical Methods in Finance and Economics

This document provides a detailed analysis of analytical methods used in finance and economics. It includes descriptive statistics, regression models, and their interpretations. The document also discusses the significance of variables and overall model in relation to weekly recreational expenses.

Running head: ANALYTICAL METHODS IN FINANCE AND ECONOMICS
Analytical Methods in Finance and Economics
Name of the Student
Name of the University
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1ANALYTICAL METHODS IN FINANCE AND ECONOMICS
Table of Contents
Question i.........................................................................................................................................2
Question ii........................................................................................................................................3
Question iii.......................................................................................................................................4
Question iv.......................................................................................................................................5
Question v........................................................................................................................................6
Question vi.......................................................................................................................................8
Question vii......................................................................................................................................8
Question viii.....................................................................................................................................9
Question ix.....................................................................................................................................10
Question x......................................................................................................................................11

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Question i
Table 1: Descriptive statistics of recexp, inc and chd
As shown from the descriptive statistics, average weekly recreational expense of the
household is 130.14. The standard deviation for weekly recreational expense is 187.14. As the
standard deviation exceeds the mean expenses, it means recreational expenses are highly volatile.
The maximum and minimum weekly recreational expenses are 7700.86 and 5 respectively.
For the income series, the mean income of the household is 977.39. The obtained
standard deviation for the series is 642.07. As the standard deviation is smaller than mean
income, it can be said that household incomes are not much dispersed. The recorded household
income is as high as 8484.47 and as low as 185.03.
The descriptive statistics for number of children shows household on an average has 2
children. The standard deviation is 1.43. The smaller value of standard deviation of the series

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means that values are not highly dispersed around mean. The maximum and minimum number of
children that the sample household have are 5 and 0 respectively.
Question ii
The regression model of weekly recreational expense on income to be estimated is
recexp=β0+ β1 inc+u
Table 2: Regression Result
From the regression result, the obtained regression equation is
recexp=30.4485+0.1020 inc
The regression coefficient of income is 0.1020. The positive value of coefficient indicates
a positive relation between income and weekly recreational expenses. That is as income
increases, weekly expense on recreational activities increases and vice versa. From the
coefficient estimate, it can be said that a 10 percent increase in household income increases

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recreational expense by 1 percent. The p value for the coefficient us 0.0000. As the obtained p
value is lower than 5% significance level, the null hypothesis of no significant relation between
income and weekly recreational activities are rejected implying income is a statistically
significant determinant of weekly recreational expenses.
Question iii
The weekly recreational activities can be modelled with log-log specification as follows
log (recexp)=β0 + β1 log (inc)+ u
Table 3: Regression result with log-log specification
Using the above regression result, the estimated regression equation is obtained as
log ( recexp )=−1.4798+0.8610 log (inc)

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The estimated coefficient for log(inc) is 0.8610. The positive regression coefficient
indicates that log (inc) has a positive influence on log (recexp). More specifically, the co-
efficient value implies that for 10 percent increase in log (inc), log(recexp) increases almost by 9
percent. The associated p value for the coefficient is 0.0000. The p value is less than 5% level of
significance indicating that rejection of null hypothesis of no significant relation between
log(recexp) and log (inc). The log(inc) thus has a positive significant association with
log(recexp). Higher income implies a higher purchasing power of people. With increase in
income, people are able to purchase more of everything. Apart from purchasing necessary goods,
people then tend to increase their spending on recreational activities. This justifies the positive
association between income and recreational expenses. The estimated coefficient thus has
expected sign.
Question iv
The regression model that relates recreational expense to household income and number
of children is gives as
recexp=β0+ β1 inc+β2 chd +u
Table 4: Regression model relating recreational expenditure to income and number of
children

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Using the result of the regression the estimated regression equation is
recexp=28.5883+0.1020 inc+0.8869 chd
In a regression model, goodness of fit of the model is examined from the estimated R
square value. R square in the regression model is also termed as coefficient of determination.
Value of R square signifies proportion of variation in the dependent variables that is explained
by the independent variables. Regression mode estimated in part ii), has R square value of 0.12.
This implies household income can explain only 12 percent variation in weekly recreational
expense. The new regression model has two independent variables. To compared goodness of fit
of the multiple regression model to that of the previous model, adjusted R square value is used.
The obtained value of adjusted R square is 0.12. This means income and number of children
together explain again only 12 percent variation in recreational expense. Goodness of fit thus
remain same for the two models.
Question v
The regression model with log log specification is given as
log (ℜc exp)=β0+ β1 log (inc)+ β2 chd +u

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Table 5: Regression result of log(recexp) on log(inc) and chd
From thee regression result, the estimated regression equation is
log ( ℜc exp )=−1.4764+0.8611 log ( inc )−0.0018 chd
In part (iv), estimated coefficient for number of children is 0.8869. The model shows a
positive influence of number of children on recreational expenses. That is with increase in
number of children, recreational expense increases. The coefficient for number of children in the
new model is -0.0018. This model shows an adverse effect of number of children on weekly
recreational expenses. This indicates weekly recreational expenses fall with increase in number
of children. The two model thus show a contradictory effect of number of children on
recreational expenses.
Statistical significance of the model can be determined by examining either the t statistics
or the p values. Computed t statistic for the coefficient is (-0.0018/0.0087) = -0.2090. The critical

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t value at 1% level of significance and 6227 degrees of freedom is 2.5766. Computed t value is
less than the critical t value implying acceptance of null hypothesis of no significant relation
between number of children and weekly recreational expenses. The variable thus is not
statistically significant at 1% level of significance.
Question vi
Estimated regression equation in part (v) is obtained as
log ( ℜc exp ) =−1.4764+0.8611 log ( inc ) −0.0018 chd
Given that weekly income is $400 and number of children is 3, the estimated recreational
expense is
log ( recexp )=−1.4764+ 0.8611 log ( 400 )− ( 0.0018 ×3 )
¿−1.4764+5.1593−0.0054
¿ 3.6775
recexp=39.55
The predicted fortnightly recreational expense of an Australian household with weekly
income of $400 and 3 children under age of 15 is obtained as
recexp= ( $ 39.55× 2 )
¿ $ 79.1
Question vii

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In model v, the coefficient of inc is 0.8611. The positive coefficient indicates that income
is likely to have a positive influence on weekly. Whether the relation is statistically valid or not
that is to be determined from testing the significance of the coefficient at the chosen level of
significance. The computed t statistics for inc is (0.8611/0.0200) = 43.1304. The critical t value
at 1% level of significance and 6227 degrees of freedom is 2.5766. The computed t value is
greater than the critical t value indicating rejection of null hypothesis of no significant
association between income and recreational expenses. The variable inc thus a positive
significant effect on recexp. The result is also supported by the associated p value of the
coefficient. The p value of inc is 0.0000. As the value is less than the significant value of 0.01,
this implies rejection of null hypothesis of no significant association between the variables. The
variable thus is statistically significant at 1% level of significance.
Question viii
The regression model to be estimated is
log ( recexp )=β0+ β1 log ( inc ) +β2 chd+ β3 male+ β4 cob+u
Table 6: Regression model with variables male and cob

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From the regression result, the obtained regression equation is as follows
log ( recexp )=−1.5528+0.8466 log ( inc ) −0.0002 chd+0.0309male +0.2027 cob+ u
The coefficient of male is 0.0309. The positive coefficient implies primary family earner
has a positive influence on recreational expenses. That is weekly recreational expense tends to be
higher if primary income earner is male. Recreational expense is likely to be lower if the primary
income earner is female.
The variable cob stands Country of Birth of household. The variable takes the value 1 if
country of birth is Australia and vice-versa. The estimated coefficient for cob is 0.2027. The
positive coefficient implies household with country of birth being Australia has a tendency to
spend more on recreational activities compared to others.
Question ix
The computed t value for male and cob is
male :t= 0.0309
0.0264 =1.1703

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cob :t= 0.2027
0.0287 =7.0558
The critical t value at 1% level of significance and 6225 degrees of freedom is 2.5766.
For the variable male, the computed t value is less than the critical t. The null hypothesis that
primary income earners has no statistically significant association with weekly recreational
expenses is accepted. This shows the variable ‘male’ is not statistically significant.
For the variable cob, the computed t value exceeds the critical t implying rejection of null
hypothesis of no significant association between weekly recreational expenses and country of
birth of household. That means the variable ‘cob’ is statistically insignificant.
The joint significance of the two variables “male” and “cob” can be tested using the F
statistics. The significance value of the F statistics is obtained as 0.000. The significance value is
less than the 5% significance level. This implies rejection of null hypothesis stating both the
coefficient are equals to zero. This in turn means that at least one of the two variables is
statistically significant. It can therefore be concluded that the two variables are jointly significant
at 5% level of significance.
Question x
For testing overall significance of the model, F test is used.
The null and alternative hypotheses of the test are
Null hypothesis (H0): β1=β2=β3=β4 =0
Alternative hypothesis (H1): at least one of βs is not zero.

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F=
RSS
K
SSE
[n− ( k +1 )]
= Mean regrssion∑ of square
Meansquared error = MSR
MSE F4,6225
Using the regression result, the F value can be computed as
F=
1865.847
4
6031.932
6225
= 466.462
0.969 =481.392
The critical value of F at 1 percent level of significance and (4, 6225) degrees of freedom
is 3.3222. The computed F value exceeds the critical F value implying rejection of the null
hypothesis stating all the coefficients are zero. Therefore, a least one of the coefficient is
significantly different from zero implying the model has overall significance at 1 percent level of
significance. The associated p value for significant F is 0.000. As the p value is less than the 1%
level of significance indicating rejection of null hypothesis of no overall significance of the
model.