Data were collected from a random sample of eight patients currently undergoing

Question

Data were collected from a random sample of eight patients currently undergoing treatment for hypertension. Each subject reported the average number of cigarettes smoked per day and each was average a numerical value reflecting their risk of cardiovascular disease (CVD). The risk assessments were computed by physicians and based on blood pressure, cholesterol level, and exercise status. The risk assessments ranged from 0 to 100, with higher values indicating increased risk. a. Compute the correlation between number of cigarettes and risk of CVD. b. Based on this sample, is there evidence of a significant correlation between number of cigarettes and risk of CVD? c. compute the equation of the line that best fits the data to predict risk of CVD from the number of cigarettes (i.e.risk of CVD - dependent variable).

Explanation / Answer

a)

Using technology, we get the correlation,              
              
r =    0.910641548   [ANSWER]

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b)      

Thus, the coefficient of determination is          
          
r^2 =    0.829268029      
          
          
As t = r sqrt [(n - 2) / (1 - r^2)], then          
          
t =    5.398407429      
          
As alpha =    0.05      

df =    6      
          
Then by table/technology,          
          
tcrit =    2.446911851      
          
As t > 2.447, there is significant correlation between number of cigarettes and risk of CVD.   [CONCLUSION]      

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c)
Using technology, we get
              
slope =    4.080265096          
intercept =    14.87334315          
              
Thus, the regression line is              
              
Risk of CVD =    4.080265096*(Number of cigarettes)   +   14.87334315 [ANSWER]
              

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