Question

Psychopaths tend to be cold and calculated, often not worrying about others or consequences so they are typically not anxious. You are curious whether anxiety scores for people are associated with psychopathy scores. To test this you survey 12 undergraduate students on their anxiety level (0 to 100, higher mean more anxious) and their score on a standard psychopathy measure (0 to 40, higher score indicated a higher level of psychopathy). The data is as follows:

person	Anxiety	Psychopathy
1	75	5
2	50	15
3	27	20
4	60	10
5	5	19
6	5	21
7	6	15
8	71	3
9	2	30
10	9	17
11	3	12
12	10	18

2) How much variability in psychopathy is accounted for by anxiety (r^2)?

Answer 1

The output is generatred by using R-software to get the answer of question. The r-codes are given along with output.

> Anxienty=c(75,50,27,60,5,5,6,71,2,9,3,10)
> Psychopathy=c(5,15,20,10,19,21,15,3,30,17,12,18)
> model=lm(Psychopathy~Anxienty)
> summary(model)

Call:
lm(formula = Psychopathy ~ Anxienty)

Residuals:
Min 1Q Median 3Q Max
-8.1115 -2.3911 -0.7282 1.9895 9.6922

Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 20.70041 1.98269 10.44 1.07e-06 ***
Anxienty -0.19630 0.05152 -3.81 0.00343 **
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 4.909 on 10 degrees of freedom
Multiple R-squared: 0.5922,   Adjusted R-squared: 0.5514
F-statistic: 14.52 on 1 and 10 DF, p-value: 0.003426

Conclusion: Here the r^2 = 0.5922. i.e., 59.22 % variablity in Psychopathy is accountedby the variable Anxienty.