In: Statistics and Probability
Use Excel to develop a regression model for the Hospital Database (using the “Excel Databases.xls” file on Blackboard) to predict the number of Personnel by the number of Births. Perform a test of the overall model, what is the value of the test statistic? Write your answer as a number, round your answer to 2 decimal places.
SUMMARY OUTPUT | ||||||||
Regression Statistics | ||||||||
Multiple R | 0.697463374 | |||||||
R Square | 0.486455158 | |||||||
Adjusted R Square | 0.483861497 | |||||||
Standard Error | 590.2581194 | |||||||
Observations | 200 | |||||||
ANOVA | ||||||||
df | SS | MS | F | Significance F | ||||
Regression | 1 | 65345181.8 | 65345181.8 | 187.5554252 | 1.79694E-30 | |||
Residual | 198 | 68984120.2 | 348404.6475 | |||||
Total | 199 | 134329302 | ||||||
Coefficients | Standard Error | t Stat | P-value | Lower 95% | Upper 95% | Lower 95.0% | Upper 95.0% | |
Intercept | 390.6214398 | 54.07601821 | 7.223561437 | 1.06764E-11 | 283.9825868 | 497.2602928 | 283.9825868 | 497.2602928 |
Births | 0.538734917 | 0.039337822 | 13.69508763 | 1.79694E-30 | 0.461160045 | 0.616309789 | 0.461160045 | 0.616309789 |
The model that we want to estimate is
from this
The estimated regression equation is
The hypotheses to Perform a test of the overall model, is
The test statistic is given in the ANOVA output
ans: The test statistic is F=187.56
The p-value is 0.0000 (rounded to 4 decimals) (from the significance F)
We will reject the null hypothesis if the p-value is less than the significance level.
Assuming a significance level of , we can say that the p-value is less than the significance level. Hence we reject the null hypothesis
ans: We conclude that the overall model is significant.