A major health care organization conducted a study relating the risk of heart attack to a patient's age, blood pressure, and HDL cholesterol. They have hypothesized the following relationship:
Y = ?_{0} + ?_{1}X_{1} + ?_{2}X_{2} + ?_{3}X_{3}
where Y is heart attack risk, X_{l} is patient's age, X_{2} is blood pressure, and X_{3} is HDL level. Data are collected and a regression relationship is determined through the use of the computer. The following Excel output is obtained:
Regression
Statistics ANOVA df SS MS F Significance
F
Multiple
R .828 Regression 3 3201.82
1067.27
11.66 .0003
R
Square .686 Residual
(Error) 16 1464.98 91.56
Standard
Error 9.57 Total 19 4666.80
Observations 20
Coefficients Standard
Error tStat PValue
Intercept 101.92  

X_{1 }1.1400 0.2554 4.463 .0004
X_{2 }0.3521 0.0744 4.367 .0005
X_{3 }
0.0935 0.3108 
0.301 .7674
The value of the sample multiple coefficient of determination is:
Based on your answer to the previous question, we can say that ______________ percent of the variation in heart attack risk, y, is explained by the regression relationship.
The result of conducting a hypothesis to determine if the relationship between heart attack risk and HDL Level is significant at the alpha=0.05 level is (Accept/Reject, Significant or not).
Based on your answers, you may make which of the following statements about the regression relationship:
A. 
The regression relationship is strong and can be used to predict risk. 

B. 
The regression relationship is moderately strong. 

C. 
It is possible that the regression relationship may be improved by dropping HDL Level from the relationship. 

D. 
B and C above are both true. 

E. 
None of the above are true. 
The value of the sample multiple coefficient of determination is:0.828.
Which represents that we can say that 82.8 percent of the variation in heart attack risk, y, is explained by the regression relationship.
we want to determine if the relationship between heart attack risk and HDL Level is significant at the alpha=0.05 level.
The hypothesis testing problem is:
against
Here test statistics is t=  0.301
and corrosponding Pvalue is=0 .7674
Therefore we are unable to reject the null hypothesis at 5%level of significance.
It is possible that the regression relationship may be improved by dropping HDL Level from the relationship.
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