a. Explanation The data sample of 26 weeks of a broadcasting operations for a television station is given. Here, standby hours is the dependent variable and the total staff and number of engineering hours employed at location away from the central plant are the independent variables. The steps to test the independent variable; total staff. Total staff : Step 1: Null and alternative hypothesis are given below. H 0 : The variable Total staff does not signifcanlty improve the model after remote hours is included H 1 : The variable Total staff signifcanlty improve the model after remote hours is included Step 2: The level of significance is 5 % . Step 3: The general formula to calculate the contribution of variable X 1 given that X 2 has been included is given below. S S R X 1 | X 2 = S S R X 1 a n d X 2 − S S R X 2 Software procedure: Open the â€œStandby hours â€� workbook. Select the Stat > Regression > Regression > Fit regression model. Double click on column C1 to add â€œStandbys â€� column to Reponses box. Double click on column C2 â€œTotal staffâ€� and C3 â€œRemote â€� to Continuous predictors box. In the regression, results dialog box selects the Expanded tables from Display of results from drop down list. Back in the regression dialog box, click options. In the regression: options dialog box: enter 95 in the confidence level for all intervals box. Verify that the type of confidence interval is two-sided and that the Sum of square for tests is adjusted (Type 111). Click Ok. Back in the regression dialog box, click Ok. From the Minitab output, the value of S S R X 1 a n d X 2 = 27663 Now, run the regression by using only â€œremote hoursâ€� as an independent variable. Software procedure: Select the Stat > Regression > Regression > Fit regression model. Double click on column C1 to add â€œStandbys â€� column to Reponses box. Double click on column C3 â€œRemoteâ€� to Continuous predictors box. Back in the regression dialog box, click Results. In the regression, results dialog box selects the Expanded tables from Display of results from drop down list. Check all the check boxes except Durbin-Watson statistic. Back in the regression dialog box, click options. In the regression: options dialog box: enter 95 in the confidence level for all intervals box. Verify that the type of confidence interval is two-sided and that the Sum of square for tests is adjusted (Type 111). Click Ok. Back in the regression dialog box, click Ok. From the Minitab output, the value of S S R X 2 = 513.3 Therefore, S S R X 1 | X 2 can be calculated as shown below. S S R X 1 | X 2 = S S R X 1 a n d X 2 − S S R X 2 = 27663 − 513.3 = 27149.7 Similarly, the mean square error can be calculated as shown below. M S E = S S E D F = 28802 23 = 1252 The general formula to calculate the F S T A T is given below. F S T A T = S S R X j | A l l X s e x c e p t j M S E Therefore, the F S T A T for the regression model with â€˜total staffâ€™ as an independent variable is calculated below. F S T A T = S S R X 1 | A l l X s e x c e p t 1 M S E = 27149.7 1252 = 21 b. To determine Compute and interpret the coefficients of partial determination r 2 Y 1 , 2 and r 2 Y 2 , 1 .

Basic Business Statistics, Student Value Edition (13th Edition)

13th Edition

ISBN: 9780321946393

Author: Mark L. Berenson, David M. Levine, Kathryn A. Szabat

Publisher: PEARSON

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Chapter 14, Problem 35PS

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Determine whether each independent variable makes a significant contribution to the regression model at a 5% level of significance.

To determine

Compute and interpret the coefficients of partial determination r2Y1,2 and r2Y2,1 .

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Chapter 14, Problem 34PS

Chapter 14, Problem 36PS

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Basic Business Statistics, Student Value Edition (13th Edition)

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Determine whether each independent variable makes a significant contribution to the regression model at a 5 % level of significance.

Solution Summary: The author explains the steps to test the independent variable, total staff, and number of engineering hours employed at location away from the central plant.