Question

Foreign Direct Investment and Economic Growth

Economic theory suggests that foreign direct investment affect the economic growth (the growth of the Gross DomesticProduct (GDP)) in developing countries. The objective of this project is to carry out a simple linear regression analysisto examine this theory. Your independent and dependent variables are the growth of the foreign direct investment andthe economic growth (the growth of the Gross Domestic Product (GDP)) respectively.

Required Tasks:

1. State the regression model and determine the least squares regression line.

Consider the GDP (Y), and foreign direct investment (X), the simple linear model is given by:

Where:  is the y-intercept

               is the line slope

               is the error variable

And the least squares regression line is :      

Where:  are estimated parameters.

2. What sign did you expect the estimated parameter to have? Explain.

The estimated parameter of +ve sign, because the relation between GDP, and foreign direct investment is direct relation.

3. Use the scatter diagram presented in figure 1 to comment on whether it appears that a linear model might beappropriate.

Yes it appears that a linear model is appropriate to represent a direct relation

Figure 1. Scatter diagram

4. Complete the table

Variable	Coefficient	Std. Error	t-Statistic	Prob.
C	0.825323	0.025088	32.89712	0.0000
FDI	0.395143	0.004999	79.13680	0.0000
R-squared	0.997928	Mean dependent var		2.799762
Adjusted R-squared	0.997769	S.D. dependent var		0.215471
S.E. of regression	0.010177	Akaike info criterion		-6.213784
Sum squared resid	0.001346	Schwarz criterion		-6.119377
Log likelihood	48.60338	Hannan-Quinn criter.		-6.214790
F-statistic	6262.633	Durbin-Watson stat		2.011334
Prob(F-statistic)	0.000000

Table 1. Estimation results

5. Write the regression line.

6. Conduct a test of the coefficient of correlation to determine at the 5% significance level whether FDI isrelated to the GDP, as the theory suggests.

H₁: ρ≠ 0     (i.e. there is a linear relationship)

H₀: ρ = 0    (i.e. there is no linear relationship when ρ = 0)

The test statistic : t =  =

Since R-squared = 0.997928

So : r =  = 0.998963

t =  = 98.159

so we accept the null hypothesis i.e. there is a linear relationship.

7. Conduct a test of the regression slope to determine at the 5% significance level whether a positive and significant linear relationship exists between the two variables.

H₀: β₁ = 0.

H₁: β₁ >0   (testing for a positive slope)

Test statistic t = 79.13680, and p-value = 0.000

There is overwhelming evidence to infer that a positive and significant linear relationship between FDI, and GDP at the 5% significance level.

8. Does it appear that the error variable is normally distributed? Explain. (Refer to the Histogram of theresiduals presented in figure 2.

It appears that the error variable is normally distributed, because it seems as bell shaped histogram and the mean is close to zero.

Figure 2. Histogram of the residuals

Answer 1

the regressi on model is

the y-intercept is 0.825323 and the slope is 0.395143

are estimated parameters. b0=0.825323 and b1=0.395143

The estimated parameter of +ve sign, because the relation between GDP, and foreign direct investment is direct relation.

test of the coefficient of correlation suggest that there is a linear relationship.since the p value is > 0.05 we fail to reject the null hypothesis

a test of the regression slope  infer that a positive and significant linear relationship p value <0.05 , we reject the null hypothesis

R-squared

0.997928

which means that 99.79% of the total variation in the independent variable can be explained by the regression model

GDP = 0.825323 + 0.395143 * FDI