Question

X1	X2	Y
11	4	9
6	8	4
8	4	6
8	5	5
10	7	9

Conduct an ANOVA test. Is the model significant? If so, at what level? Please show work

Answer 1

		9				X1	X2
		4			1	11	4
	Y=	6		X=	1	6	8
		5			1	8	4
		9			1	8	5
					1	10	7
	1	1	1	1	1
X'=	11	6	8	8	10
	4	8	4	5	7
	5	43	28
X'X=	43	385	234
	28	234	170
	13.85233	-0.98187	-0.93005
(X'X)-1=	-0.98187	0.085492	0.044041
	-0.93005	0.044041	0.098446
	33
X'Y=	301
	180
	-5.82383
B^=(X'X)-1X'Y=	1.259067
	0.284974
	9.165803
Fitted (Y^)=	4.010363
	5.388601
	5.673575
	8.761658
	-0.1658
	-0.01036
Residual ( r)=Y-Y^=	0.611399
	-0.67358
	0.238342
SS Residual=r'r=	0.912
SS Total=(Y-M)'(Y-M)=	21.2		, M= mean of the Y variable=6.6

Hypothesis:

Ho: Both the slopes parameters are equal to zero.

H1: At least one slope parameter does not equal to zero.

Conclusion: The p-value is 0.043 and less than 0.05 level of significance. Hence, reject the null hypothesis and so the model is significant. The level is 0.05.