Question

Multiple R	0.800223
R Square	0.640357
Adjusted R Square	0.610387
Standard Error	5.793039
Observations	40
ANOVA
	df	SS	MS	F	Significance F
Regression	3	2151.13	717.0433	21.36645	4.02E-08
Residual	36	1208.135	33.5593
Total	39	3359.265
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%	Lower 95.0%	Upper 95.0%
Intercept	6.702471	7.166119	0.9353	0.355866	-7.83109	21.23603	-7.83109	21.23603
Price Discount (in %)	0.341666	0.068923	4.957206	1.71E-05	0.201884	0.481449	0.201884	0.481449
Radio Exp (in $1,000)	6.062389	1.626002	3.728403	0.000661	2.764705	9.360073	2.764705	9.360073
Newspaper Exp (in $1,000)	9.396795	2.201828	4.267723	0.000137	4.93128	13.86231	4.93128	13.86231

(1) Ho and Ha (in notation and words)

(2) Identify F-stat

(3) Specify the decision criteria (use the CV approach). Be sure to identify the critical value

(4) State your conclusion. Explain what it means in one sentence

Answer 1

1. It is a multiple regression model as the number of independent variables is more than one. The given information shows that the ANOVA method is used to determine the significance of the overall model. Hence, hypothesis testing would be as follows;

$Ho: R^2=0 Ha:R^2\neq 0$

2. The computed F value from ANOVA table is determined by dividing the mean sum of squares of the explained sum of squares and residual sum of squares implies 21.36645

3. The critical value of F statistic is determined from the F table given numerator degree of freedom is 3 and denominator degrees of freedom is 36 and the level of significance is 5% is 2.9223.

4. Since computed F value is greater than F critical implies that the regression is statistically significant at 5% level of significance and the p-value of computed F value is very small affirms the same results.