ECON241 Assignment
Part I
a)
^P = 5.50 - 1.72*R + 0.00143*Y
(11.4) (0.911) (0.000102)
T = 54, R-squared = 0.834
(standard errors in parentheses)
Interpretation of R: when interest rate is increased by 1% , the value of the housing index is decreased by 1.72
Interpretation of Y: when real GDP is increased by 1 million, the value of housing index is increased by 0.00143.
Signs of both coefficients agree with intuition. It is expected that interest rate should go inversely with housing price . Higher output should lead to higher housing prices.
b) The scatter plot is shown as below
It is found that P and Y have positive relationship, but the relationship is not entirely linear.
c)
Decision rule: reject the null hypothesis is |t| >tc = 1.675
Distribution of test statistic under null: t-distribution with 51 degrees of freedom. The critical value is calculated in GRETL and is shown as below.
Y: t-test statistic: |t| = 14.00> 1.675. At 5% significance level, null hypothesis of zero slope coefficient is rejected. Log(Y) is a significant regressor.
R: t-ratio = |t| = 1.89 > 1.675. At 5% significance level, null hypothesis of zero slope coefficient is not rejected. R is a significant regressor.
d)
The confidence interval is (-3.5526,0.1036). It shows that there are 95% confidence that when the interest rate is increased by 1%, the value of housing index should change between -3.55 and 0.104
e)
The point prediction is shown as below
P = 5.50424 – 1.72448 ( 7 ) + 0.00143249 ( 80000 ) = 108.03
a)
the regression equation is reported as below
logP = -7.84 + 1.12*log(Y) - 0.0143*R
(0.778) (0.0676) (0.00884)
T = 54, R-squared = 0.868
(standard errors in parentheses)
Interpretation of log(Y): when real output is increased by 1% , the housing index will increase by 1.12%
Interpretation of R: when interest rate is increased by 1% , the housing index will decrease by 1.43%.
Signs of both coefficients agree with intuition. It is expected that interest rate should go inversely with housing price . Higher output should lead to higher housing prices.
b)
Comments:
logP and logY appear to be linearly associated. When real output is high, the linear relationship does not appear as strong as other parts.
c)
Decision rule: p-value obtained from test statistic is less than 5%
Distribution of test statistic under null: t-distribution with 51 degrees of freedom
log(Y): t-test statistic: 16.55 , p-value < 0.0001 . At 5% significance level, null hypothesis of zero slope coefficient is rejected. Log(Y) is a significant regressor.
d)
H0: alpha3 = 1
H1: alpha3 > 1
Test statistic: (1.118 – 1)/0.0675 = 1.781
Using the critical value obtained from above, the value at 1% level is 2.402
The test statistic is less than critical value . The null hypothesis is not rejected.
Therefore, alpha3 is not greater than 1 at 1% level of significance.
Part e)
The confidence interval is (0.983, 1.254)
The confidence interval is (0.983, 1.254). It shows that there are 95% confidence that when the real output Y is increased by 1%, the value of housing index should increase between 0.983% and 1.254%
Part f)
Log(P) = -7.84196 – 0.0142931 (7 ) + 1.10615* log(80000) = 4.5462
P= exp(4.5462 ) = 94.272
The value calculated in part is lower than the value calculated in Part I.
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