Factors Influencing Housing Prices in Gold Coast, Queensland - Assignment Example

We intend to test the null hypothesis = 0 against the alternative of  0.

From table 1 we find that the computed t-statistic is 0.275, and the p-value is 0.78. Recall that the critical t-value at the 5% level is 1.96. Therefore, we fail to reject the null hypothesis. Thus, we fail to reject that the coefficient of D2 is statistically significantly not different from zero.

Thus, we do not have any evidence to support that if the distance of the property from the coast is between 2 and 5 KMs there is no impact on the price of the property.

Part (f)
We intend to test whether inclusion of the dummies improved the fit of the basic model.

Model (2): Y = β0 + β1X1 + β2X2 + β3X3 + β4X4 + ε

Model (3): Y = β 0 + β 1X1 +β2X2 +β3X3 +β4X4 + γA + δ1D1 + δ2D2 + ε

Recall that the test statistic is formed according to the rule:

which translates to:

F(3, 1716) = 111.99 F crtical(5%)(3, v2 =2.68

Thus, including the dummy variables improves the fit significantly. Therefore, we reject the null.

Part (g)
Yes, there is evidence to support that inclusion of central air conditioning leads to higher prices. This is evident from the fact that the estimated coefficient on the variable “central air” is positive and significant.

The significance is visible from the t-stat of 6.487819 which is greater than the critical value of 1.96 and the p-value is 0<0.05. Thus, the null hypothesis that the coefficient is zero ( 

My advice would be to charge higher prices on properties that include central air conditioning.

Part (h)
The dummy variables for coastal proximity are D1 and D2. If the coefficients of these turn out to be significantly different from zero, we can conclude that coastal proximity does indeed lead to differences in prices. We have already tested for the significance of the coefficient on D2 in part (e). Using the same methodology of a t-test of = 0 against the alternative of  0, we find that the calculated t-value is 1.714 which is significant only at the 10% level but not at the 5% level (p-value = 0.09). Thus we conclude the coefficient is statistically insignificant as well at the 5% level.

Thus, since neither coefficient turns out to be significant, we conclude that we do not have any evidence to suggest that proximity to the coast makes any differences to the prices with 95% or higher confidence.

Part (i)
Using our estimate of model 3, we have:
-64900.2+6.515929*900+2176.247*180+0.969664*140000+3724.135*7+50415.54+2387.41 = 547313.5

Thus, the forecasted price is: 547313.5