Econometrics coursework

Econometrics Coursework



Econometrics Coursework

Question 1

P [ - 1.96 SE () = = + 1.96 SE ()] = 0.95

i.e. [3.24 - 1.96(1.634) = = + 1.96 (1.634)]

= [0.037= = 6.442]

Above is the 95% confidence interval for .

The null hypothesis will be rejected, since the 95% confidence interval does not include 0. However, if H0 were that the true slope coefficient> 0, we would not reject the null hypothesis as the 95% confidence interval includes this value.

Using the Following Hypothesis:

H0: = 0.

H1: 0.

Using the t - value

t = = = 1.982

tcal = 1.982

ttab= 2.145

Hence, tcal < ttab , therefore we cannot reject the null hypothesis and conclude that statistically has no impact on the model. This can be practically implemented as the real disposable income (billions of 1972 dollars) has no statistical impact on the retail sales of passenger cars. Thus the inclusion of the variable will not provide a reliable and significant result.

The econometric technique used to determine the significance of the parameters is known as Wald Test. In this technique, the parameters are used for significance i.e. whether their inclusion is sufficient in the model and that it can provide with the reliable highly significant results. For this purpose, we assume the hypothesis that = 0 i.e. it has no impact on the dependent variable.

R - Square is an important while considering any econometric model i.e. the greater the R - Square of the model, it is found to be highly significant. Its value is ranged from 0 to 1 i.e. more the value is towards 1, more significant and strong relationship exists between the variables. In our model, the value of R - square is 0.22 which shows that it represents only 22% variation in the model which is certainly very low. While running a significant regression, R - Square greater than 0.8 is considered as a significant relationship between the variables.

Question 2

Explanation

It is an old economic theory that the growth of a country highly depends on its savings. This theory has also been checked by using the Sample Regression Function (SRF) i.e. a sample has been taken from UK and applied a regression function. For this purpose, growth has been taken in terms of GDP (Dependent Variable) and savings has been taken as an independent variable. The following model has been assumed:

The results of our analysis also supports the theory of PRF i.e. there is an 85.5% relationship between the variables which is highly significant. The regression results show that people almost save 30% of their income because the slope coefficient is 0.302 which is a normal amount that the people of UK save. Following are the statistical results:

SUMMARY OUTPUT

 

 

Regression Statistics

 

Multiple R

0.855338199

 

R Square

0.731603435

 

Adjusted R Square

0.725361655

 

Standard Error

1.1106E+11

 

Observations

45

 

 

 

ANOVA

 

 

 

 

 

 

 

df

SS

MS

F

Significance F

 

Regression

1

1.44572E+24

1.44572E+24

117.2106944

7.3413E-14

 

Residual

43

5.30379E+23

1.23344E+22

 

 

 

Total

44

1.9761E+24

 

 

 

 

 

 

 

Coefficients

Standard Error

t Stat

P-value

Lower 95%

Upper 95%

Intercept

4.05548E+11

19901402784

20.37784066

1.02052E-23

3.65413E+11

4.45683E+11

GDP

0.302878573

0.003960561

10.8263888

7.3413E-14

0.034891341

0.000865806

Question 3

The intercept and slope in the investment model shows interesting results. It shows that 0.7264 are the risk free rates or Treasury bill rates. The investor can easily expect 0.7264 returns on the investment portfolio without any risk but the ...