Question

1. GDP Population Inflation interest rate 78 14 111 0.09 88 15 112 0.1 45 25 113 0.12 65 32 114 0.14 98 25 112 0.06 88 45 112.5 0.05 85 47 114 0.111 68 85 107.5 0.124 92 66 107 0.123 81 63 106 0.147 79 54 105.5 0.159 77 87 105 0.25 73 25 104 0.16 76 45 110 0.12 66 30 102 0.08 80 50 100 0.09 Considering GDP as dependent variable and other variables as independent variables 1) Apply multiple regression for the above data and copy the Excel output 2) Indicate intercept, and all slope coefficients 3) interpret coefficients 4) State coefficients are significant or not at 5%? 5) Write the coefficient of determination 6) State overall model is fit or not considering the F-test 7) Copy first five residuals and predicted GDP values

Answer 1

Answers :

1. Multiple Regressin and Excel ouput

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.3535
R Square	0.1250
Adjusted R Square	-0.0938
Standard Error	13.1901
Observations	16
ANOVA
	df	SS	MS	F	Significance F
Regression	3	298.1812	99.3937	0.5713	0.6446
Residual	12	2087.7563	173.9797
Total	15	2385.9375
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	73.9639	93.7334	0.7891	0.4454	-130.2638	278.1915
Population	0.1710	0.1849	0.9250	0.3732	-0.2318	0.5739
Inflation	0.0816	0.8293	0.0984	0.9233	-1.7254	1.8886
interest rate	-107.6273	85.8834	-1.2532	0.2340	-294.7511	79.4965

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2.

Intercept = 73.9639

Slope coefficient for Population = 0.1710

Slope coefficient for Inflation = 0.0816

Slope coefficient for interest rate = -107.6273

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3.

Coefficient interpretation :

i) For every one unit increase in Population, GDP will increase by 0.1710 units

ii) For every one unit increase in Inflation , GDP will increase by 0.0816 units

iii) For every one unit increase in interest rate, GDP will decrease by 107.6273 units

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4. None of the coefficients are significant at 5% because p-ualues of all coefficients are

greater than 0.05.

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5.

Coefficient of determination = 0.1250 ( 12.50 % ) [ R square value in Summary output 1st table ]

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6.

Since F value = 0.5713 and p-value = 0.6446 which is greater than 0.05, Model is NOT significant

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7.

RESIDUAL OUTPUT
Observation	Predicted GDP	Residuals	Standard Residuals
1	75.7263	2.2737	0.1927
2	74.9026	13.0974	1.1102
3	74.5418	-29.5418	-2.5041
4	73.6680	-8.6680	-0.7347
5	80.9179	17.0821	1.4479

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