Question

1. Calculate the correlation coefficient r value using the Z scores for the two variables. (Round the answer to 2 decimal places)

2. What is the proportion of variance shared by anxiety level and externalizing behavior? In other words, how much of the variance in externalizing behavior can be predicted by the variance in anxiety level, or vice versa? (Round the answer to 2 decimal places)

3. What is the effect size in this hypothesis test? (Round the answer to 2 decimal places)

Subject ID #	Externalizing	Anxiety
1	9	37
2	7	23
3	7	26
4	3	21
5	11	42
6	6	33
7	2	26
8	6	35
9	6	23
10	9	28

Answer 1

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.64824
R Square	0.420215
Adjusted R Square	0.347742
Standard Error	5.636685
Observations	10
ANOVA
	df	SS	MS	F	Significance F
Regression	1	184.2223	184.2223	5.79822	0.042644
Residual	8	254.1777	31.77221
Total	9	438.4
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	18.40663	4.901077	3.755629	0.005579	7.104722	29.70853
Externalizing	1.665663	0.691735	2.407949	0.042644	0.070519	3.260806

Regression equation is

Anxiety=18.40663+1.665663(Externalizing)

r=0.648

r²=r*r=0.648*0.648=0.420215

that is 0.4202*100=42.02% variation in shared by anxiety level and externalizing behavior.