## ECON241 Solution Linear Model

**ECON241 Solution Linear Model**

Based on the above OLS model

**The regression equation is:**

P = -109.210 – 1.05514*R + 0.002462*Y

T = 54, R-squared = 0.965

** Interpretation of R:** When Interest Rate is increased by 1%, the value of the housing index is decreased by 1.055

** Interpretation of Y:** When real GDP is increased by 1 million, the value of housing index is increased by 0.00246.

The cause of Interest rate & State final demand on House price can be interpreted from the OLS model equation. It can be interpreted that Interest rate goes inversely with housing price. And higher State demand causes House price to go up.

Interpretation: It can be found that P and Y have positive relationship, but the relationship is not entirely linear.

c)

Degree of freedom = number of data points – number of variables – 1

= 54 -2 -1 =51

**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-ratio__: |t| = 30.85 > 1.675.

At 5% significance level, null hypothesis of zero slope coefficient is rejected. Y is a significant regressor.

__R: t-ratio__: |t| = 1.615 < 1.675.

At 5% significance level, null hypothesis of zero slope coefficient is not rejected. R is not a significant regressor.

NOTE: t-ratio for Y & R are calculated in section “a”

- d) 95% Confidence Interval for the coefficient of R:

The confidence interval is (-2.3668,0.2565).

**Interpretation:** A 95% confidence for example says that the population mean is likely to be within the specified range for 95 out of 100 times.

e)

Point prediction for the Melbourne housing price index when *R *= 7% and *Y *= $100000 millions:

Based on the above OLS model (as discussed in “a” section of this question)

P = – 109.210 – 1.05514*R + 0.002462*Y

=> – 109.210 – 1.05514*7 + 0.002462*100000

=> P = 129.60

Based on the above OLS model

**The regression equation is:**

log(P) = – 22.157 – 0.0038*R + 2.352*log(Y)

T = 54, R-squared = 0.964

** Interpretation of R:** When Interest Rate is increased by 1% , the value of the housing index is decreased by 0.0038.

** Interpretation of log(Y):** When log(Y) is increased by 1 million, the value of housing index is increased by 2.352.

The cause of Interest rate & State final demand on House price can be interpreted from the OLS model equation. It can be interpreted that Interest rate goes inversely with housing price. And higher State demand causes House price to go up.