A major health care organization conducted a study relating the risk of heart at
ID: 2909701 • Letter: A
Question
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 + ?1X1 + ?2X2 + ?3X3
where Y is heart attack risk, Xl is patient's age, X2 is blood pressure, and X3 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 t-Stat P-Value
Intercept -101.92 - - -
X1 1.1400 0.2554 4.463 .0004
X2 0.3521 0.0744 4.367 .0005
X3 -0.0935 0.3108 - 0.301 .7674
The result of conducting the hypothesis test described in the previous question at the 5% level of significance is??????????
The value of the sample multiple coefficient of determination is????????????????
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????????
Based on your answers to the last few questions, you may make which of the following statements about the regression relationship
Explanation / Answer
null hypothesis H0 :model is not significant
alternative hypothesis H1: model is significant
Decision rule :-
i) if F calculated < Fcritical then accept null hypothesis H0 at level of significance 0.05
ii) if F calculated > Fcritical then reject null hypothesis H0 at level of significance 0.05
a) The result of conducting the hypothesis test described in the previous question at the 5% level of significance is
from the anova table ,Fcalculated(11.66) > Fsignificant( .0003) so reject the null hypothesis
so the model is significant
b) The value of the sample multiple coefficient of determination is 0.828 (from table Multiple R )
c) we can say that 9.57 percent of the variation in heart attack risk, y, is explained by the regression relationship.
=> because for finding variation in the model we use standard error.it useful to calculate the vatiation in the response variable so it is 9.57
d) 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
=>Decision rule :-
i) if p value > 0.05 l.o.s then accept null hypothesis H0 at level of significance 0.05
ii) if p value < 0.05 l.o.s if then reject null hypothesis H0 at level of significance 0.05
here pvalue( 0.7674) > 0.05 level of significance so accept null hypothesis that there is no effect of HDLcholesterol level on heart attack
conclusion :- from the above model regression relationship we can say that the model is good and there is significant effect of patients age and blood pressure but not of HDL level