A major health care organization conducted a study relating the risk of heart at

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 p-value for conducting the test of the overall usefullness of the model is:

If we decide to use the F statistic to conduct the test of overall usefullness, the correct critical value of the F statistic for alpha=0.05 drawn from the table is:

Based on the Excel output above and your answers above, your hypothesis test decision is ________________ H0.

The result of conducting the hypothesis test described in the previous question at the 5% level of significance is?: (Reject/Accept, significant or not?)

Explanation / Answer

From the above excel output we see that the value of F-test statistic is 11.66 and corresponding p-value is 0.0003 and given level of significance is alpha = 0.05. Since p-value is less than alpha we shall reject the null hypothesis H0. The conclusion would be that the regression coefficients are significant and the model is useful.

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