Question

Id	x	z	y
A	6	7	3
B	4	4	7
C	10	10	8
D	3	1	4
E	2	3	2

given

Ryx= 0.6719

Ryz=0.5190

ssy=26.8

1. what is the variation in y that is redundantly explained by x and z
2. What is the proportion of variation in y that is redundantly explained by x and z

Answer 1

using excel>data>data analysis>Regression

we have

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.951247
R Square	0.904871
Adjusted R Square	0.809741
Standard Error	1.542152
Observations	5
ANOVA
	df	SS	MS	F	ignificance F
Regression	2	45.24354	22.62177	9.512014	0.095129
Residual	2	4.756463	2.378231
Total	4	50
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	0.321769	1.625405	0.197962	0.861371	-6.67178	7.31532
z	-0.27891	0.402224	-0.69342	0.55975	-2.00954	1.45172
x	1.203401	0.329235	3.655146	0.067373	-0.21318	2.619985

1. 90.48% variation in y that is redundantly explained by x and z
2. 0.9048 proportion of variation in y that is redundantly explained by x and z