A major health care organization conducted a study relating the risk of heart at
ID: 2909681 • 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 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.