Question

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.727076179
R Square	0.528639771
Adjusted R Square	0.525504337
Standard Error	3.573206748
Observations	455
ANOVA
	df	SS	MS	F	Significance F
Regression	3	6458.025113	2152.67504	168.601791	2.7119E-73
Residual	451	5758.280717	12.7678065
Total	454	12216.30583
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%	Lower 99.0%	Upper 99.0%
Intercept	-0.250148858	0.359211364	-0.6963835	0.48654745	-0.9560846	0.45578693	-1.1793476	0.67904987
RBUK	0.025079378	0.023812698	1.05319345	0.29281626	-0.0217182	0.07187699	-0.0365187	0.08667745
RSUS	0.713727515	0.042328316	16.8617037	8.0578E-50	0.6305423	0.79691273	0.60423372	0.82322131
RSJA	0.222104292	0.029996288	7.40439254	6.5208E-13	0.16315445	0.28105414	0.14451066	0.29969792

1) Conduct a test for the overall significance of the regression equation at the 1% level of significance. (Test for the significance of the regression relationship as a whole) 2) Present the R-Square (Coefficient of Determination) and its interpretation.

Answer 1

the regression equation that is being estimated is

where Y is the dependent variable (mention the name of the dependent variable)

is the intercept

are the slope coefficients for independent variables, RBUK, RSUS, RSJA respectively.

is a random disturbance

The estimated values of the parameters are

The estimated model is

1) To a test for the overall significance of the regression equation at the 1% level of significance we test the following hypotheses

The test statistics is the F value and the p-value is the signiifcance

The tets statistics is

F=168.60 and the p-value=0.0000 (rounding to 4 decimal places)

We will reject the null hypothesis if the p-value is less than the significance level .

Here, the p-value is 0.0000 and it is less than the significance level . Hence we reject the null hypothesis.

We conclude that the overall significance of the regression equation is significant.

2) The R-Square value from the output is

This indicates that 52.86% of the variation in the dependent variable (place the name of the dependent variable) can be explained by the regression model (or the independent variables)