Question

One economic development strategy suggests that some economies benefit from having government policies that promote growth in manufacturing and growth in exports. A regression analysis is undertaken (using the following data) from a sample of countries that operate these types of policies.

Country	Growth GDP (Y)	Growth Manufacturing (X1)	GrowthExports (X2)
China	11.0	7.3	14.4
Hong Kong	7.1	10.2	6.2
Japan	10.5	6.0	14.0
Korea	9.7	13.1	13.8
Malaysia	4.9	8.0	9.8
Singapore	6.1	5.9	8.1
Thailand	7.0	8.1	12.8
Mean	8.0	8.4	11.3

A summary of the multiple regression analysis undertaken in Excel is reported below.

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.746
R Square	0.556
Adjusted R Square	0.334
Standard Error	1.918
Observations	7
ANOVA
	df	SS	MS	F	Significance F
Regression	2	18.439	9.220	2.506	0.197
Residual	4	14.718	3.679
Total	6	33.157
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	1.389	3.781	0.367	0.732	-9.109	11.886
X1	0.075	0.308	0.245	0.819	-0.780	0.931
X2	0.533	0.240	2.221	0.091	-0.133	1.199

State the multiple regression model for this data and interpret all the slope coefficients.

Question 11

Using the Excel output from Question 10, at a 0.05 level of significance test the significance of the individual independent variables and the overall regression model.  

Question 12

Using the Excel output from Question 10, comment on the goodness of fit of the model.

Answer 1

Given data:

Country	Growth GDP (Y)	Growth Manufacturing (X1)	Growth Exports (X2)
China	11.0	7.3	14.4
Hong Kong	7.1	10.2	6.2
Japan	10.5	6.0	14.0
Korea	9.7	13.1	13.8
Malaysia	4.9	8.0	9.8
Singapore	6.1	5.9	8.1
Thailand	7.0	8.1	12.8
Mean	8.0	8.4	11.3

Multiple regression equation

y^ = 1.389+0.075X1+0.533*2

Or

Growth GDP = 1.389+0.075(Growth Manufacturing) + 0.533(Growth Exports)

Slope coefficient of growth manufacturing = 0.075

That means if we increase per unit growth manufacturing the growth GDP increase by 0.075, keeping growth exports constant.

Slope coefficient of growth exports = 0.533

That means if we increase per unit growth exports the growth GDP increase by 0.533, keeping growth manufacturing constant.

Intercept = 1.389

The estimated mean value of growth GDP is 1.389.