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, X_l 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

Answer 1

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