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ECON241 Assignment

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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. 

 ECON241 Assignment 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

Part II log-log model

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.

 R: t-ratio = -1.62 , p-value: 0.11. At 5% significance level, null hypothesis of zero slope coefficient is not rejected. R is not 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)

 The point prediction is 

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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