Question

We would like to analyze expenditures on research and development and use regression analysis. We assume that total expenditures would be closely related to the income , GDP, investments and inflation rate. Please describe results and quality of regression model.

Formulate inferences about the regression model parameters. Test usefulness of the model. Are parameter statistically significant? Please set up correct hypothesis and formulate your conclusions.

SUMMARY OUTPUT
Regression Statistics
Multiple R	0,9499
R Square	0,9023
Adjusted R Square	0,8878
Standard error	1294,9574
Observations	32
ANOVA
	df	SS	MS	F	Significance F
Regression	4	4,18E+08	1,05E+08	6,23E+01	3,06E-13
Residual	27	4,53E+07	1,68E+01
Total	31	4,63E+08
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	-1754,829	7818,344	-0,2245	0,8241	-17796,7451	14287,09
Income	3,0913	1,6497	1,8738	0,0718	-0,2936	6,4762
GDP	0,0719	0,4915	0,1463	0,8848	-0,9367	1,0805
Investments	0,81	0,3471	2,3337	0,0273	0,0978	1,5221
Inflation	-24,6261	37,5128	-0,6565	0,5171	-101,596	52,3438

Answer 1

Soln

Regression Equation

Expenditure = -1754.829 + 30913 * Income + 0.0719 * GDP + 0.81 * Investments – 246261 * Inflation

Hypothesis Test for Overall Model

Alpha = 0.05

Null and Alternate Hypothesis

H0: Model is insignificant

Ha: Model is significant

Test Statistic

From the Regression Output

F = 6.23E+01

P-value = 3.06E-13

Result

Since the p-value is less than 0.05, we reject the null hypothesis ie the model is significant

Hypothesis Test for Independent Variables

i)

alpha = 0.05

Independent Variable = Income

Null and Alternate Hypothesis

H₀: β₁ = 0

H_a: β₁ <> 0

Test Statistic

t = 1.8738

p-value = 0.0718

Result

Since the p-value is greater than 0.05, we fail to reject the null hypothesis ie the independent variable is not significant

ii)

alpha = 0.05

Independent Variable = GDP

Null and Alternate Hypothesis

H₀: β₂ = 0

H_a: β₂ <> 0

Test Statistic

t = 0.1463

p-value = 0.8848

Result

Since the p-value is greater than 0.05, we fail to reject the null hypothesis ie the independent variable is not significant

iii)

alpha = 0.05

Independent Variable = Investments

Null and Alternate Hypothesis

H₀: β₃ = 0

H_a: β₃ <> 0

Test Statistic

t = 2.33

p-value = 0.0273

Result

Since the p-value is less than 0.05, we reject the null hypothesis ie the independent variable is significant

iv)

alpha = 0.05

Independent Variable = Inflation

Null and Alternate Hypothesis

H₀: β₁ = 0

H_a: β₁ <> 0

Test Statistic

t = -0.66

p-value = 0.51

Result

Since the p-value is greater than 0.05, we fail to reject the null hypothesis ie the independent variable is not significant