Question 144763
 A 10-year study conducted by the American Heart Association provided data on how age related to the risk of strokes.  Suppose that the following data was obtained in a follow-up study. Risk is interpreted as the probability that the patient will have a stroke over the next 10-year,

 

Patient Risk       Age
 
1       
 12
 57
 
2
 24
 67
 
3
 13
 58
 
4
 56
 86
 
5
 28
 59
 
6
 51
 76
 
7
 31
 78
 
8
 18
 56
 
9
 37
 80
 
10
 15
 78
 
11
 22
 71
 
12
 36
 70
 
13
 15
 67
 
14
 48
 77
 
15
 15
 60
 
16
 36
 82
 
17
 8
 66
 
18
 34
 80
 
19
 3
 62
 
20
 37
 59
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I ran a Linear Regression function on a TI calculator to find
the following: 

a)     Develop an estimated regression equation that can be used to relate the risk of a stroke to the person’s age.
Ans: age = 58.103 + (0.4210)(risk)

b)     Is the relationship between risk and age significant at the 95% confidence level?
Critical value for n=20 and alpha = 5% is 0.444
Since r=0.65.. > 0.444, reject Ho, which claimed there was no linear
relation, and conclude there is a significant linear relation between
age and risk.


c)      Compute the correlation coefficient and interpret the result.
r = 0.6502...
r is a measure of the linear correlation between age and risk.
r^2 is the proportion of the variation in age that is explained
by the linear relationship between risk and age.
==============
cheers,
Stan H.