To help schedule staffing and equipment needs, a large hospital uses a multiple

Question

To help schedule staffing and equipment needs, a large hospital uses a multiple regression model to predict its 'bed census' y, the number of beds occupied at the end of each day. Using hospital records from the most recent 23 days, a total of 2 independent variables are used to find the estimated regression model. Let ?1 and ?2 denote the coefficients of the 2 variables in this model. A computer printout indicates that the total sum of squares (SST) associated with the model is 670.99 and the corresponding regression sum of squares (SSR) is 151.25. Using a significance level of 0.05, can you conclude that at least one of the independent variables in the model provides useful (i.e., statistically significant) information for predicting daily bed census?

Perform a one-tailed test. Then fill in the table below.

Carry your intermediate computations to at least three decimal places and round your answers as specified in the table.

1. The null hypothesis: H0:

2. The alternative hypothesis: H1: at least one of the independent variables is useful

3. The type of test statistic is: z; t; chi square; F and degrees of freedom

4.The value of the test statistic: (Round to at least two decimal places.)

5. The critical value at the 0.05 level of significance: (Round to at least three decimal places.)

6. Can you conclude that at least one of the independent variables in the model provides useful information for predicting daily bed census? Yes or No

Explanation / Answer

Null Hypothesis : H0 : The regresssion model is significant.

ALternative Hypothesis : Ha : at least one of the independent variables is useful.

Here type of test statistic is F.

Here value of test statistic

MSR = SSR/dF(Regession) = 151.25/2 = 75.625

MSE = SSE/dF(Error) = 670.99/20 = 33.5495

Here

F = 75.625/33.5495 = 2.2541

5. Here F(critical) = 3.493

6. Here F < F(critical) so here we can conclude that none of the independent variables in the model provides useful information for predicting daily bed census. The answer is no.

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