Question

An analyst for the World Health Organization, WHO, is working with the United Nations to predict Country GDP. Regression used a .05 level of significance. Variable definitions, a partial data set, and regression output are provided below.

LifeExp = 1992 Life expectancy at birth

TV = Televisions per 100 people

PopDoc = Population per doctor

GDP = real Gross Domestic Product, (GDP) per capita

LifeEx	TV	PopDoc	GDP
65.6	7.4	2330	2870
71.1	22.2	330	5120
76.7	49	440	16680
75.7	47	230	17690
71	41.4	930	11536
52.2	0.5	6670	1160
75.3	26.5	1120	9667
71	27	250	6850

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.880215946
R Square	0.774780112
Adjusted R Square	0.768904811
Standard Error	2959.734047
Observations	119
ANOVA
	df	SS	MS	F	Significance F
Regression	3	3465572145	1.16E+09	131.8707004	4.5254E-37
Residual	115	1007402947	8760026
Total	118	4472975093
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	-9996.823294	2829.983569	-3.53247	0.000593683	-15602.47609	-4391.17
LifeEx	192.8743017	45.24570105	4.26282	4.15558E-05	103.2512758	282.4973
TV	213.575929	21.61514899	9.880845	4.86389E-17	170.7604789	256.3914
PopDoc	0.027765841	0.026000413	1.0679	0.287802219	-0.023735973	0.079268

a. State the predicted regression equation.

b. Is the coefficient on PopDoc statistically significant? On what basis did you make your decision?

c. Find predicted GDP for a country if LifeExp = 64 , TV = 17, and PopDoc = 8000.

d. The regression results show that the variable TV is statistically significant.  Discuss why the variable TV was included in this model. You must provide justification beyond that the coefficient is statistically significant. In other words, provide a justification why TV would have been included in a model to predict GDP.

Answer 1

a. GDP = -9996.823 + 192.874*Life Exp + 213.576*TV + 0.028*PopDoc

b. H₀: β₃ = 0, Coefficient on PopDoc is not statistically significant

H₁: β₃ ≠ 0, Coefficient on PopDoc is statistically significant

p-value = 0.288

Level of significance = 0.05

Since p-value is more than 0.05, we do not reject the null hypothesis and conclude that β₃ = 0.

So, coefficient on PopDoc is not statistically significant.

c. LifeExp = 64 , TV = 17, and PopDoc = 8000

GDP = -9996.823 + 192.874*64 + 213.576*17 + 0.028*8000

= -9996.823+12343.94+3630.792+224

= 6201.909

d. It can be seen that there is a positive relationship between Televisions per 100 people and GDP. For one unit increase in televisions per 100 people, GDP increases by 213.576 units. This can be explained in relation to disposable income. With increase in disposable income of people, the number of TVs per 100 people would increase. Increase in disposable income or prchasing power is directly linked to increase in GDP. Hence, TV was included in the model.