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 ...