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REv. Test 3 Regr., Categ.

# REv. Test 3 Regr., Categ. - Review for Test 3 STA-3123 I...

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Unformatted text preview: Review for Test 3 STA-3123 I. Operations managers often use work sampling to estimate how much time workers spend on each operation. Work sampling, which involves observing workers at random points in time, was applied to the staff of the catalog sales department of a clothing manufacturer. The department applied regression to the following data collected for 40 consecutive working days: TIME: y = Time spent (in hours) taking telephone orders during the day ORDERS: x = Number of telephone orders received during the day Initially, the simple linear model E ( y ) = β + β 1 x was fit to the data. PREDICTOR VARIABLES COEFFICIENT STD ERROR STUDENT'S T P --------- ----------- --------- ----------- ------ CONSTANT 10.1639 1.77844 5.72 0.0000 ORDERS 0.05836 0.00586 9.96 0.0000 R-SQUARED 0.7229 RESID. MEAN SQUARE (MSE) 11.6175 ADJUSTED R-SQUARED 0.7156 STANDARD DEVIATION 3.40844 SOURCE DF SS MS F P ---------- --- ---------- ---------- ----- ------ REGRESSION 1 1151.55 1151.55 99.12 0.0000 RESIDUAL 38 441.464 11.6175 TOTAL 39 1593.01 1. Conduct a test of hypothesis to determine if time spent (in hours) taking telephone orders during the day and the number of telephone orders received during the day are positively linearly related. 2. Give a practical interpretation of the correlation coefficient for the above output. 3. Give a practical interpretation of the coefficient of determination, R 2 . 4. Give a practical interpretation of the estimated slope of the least squares line. 5. Find a 90% confidence interval for β 1 . Give a practical interpretation. 6. Give a practical interpretation of the model standard deviation, s . 7. Interpret the 95% Prediction interval (17.753, 31.755) shown on the printout. 8. Interpret the 95% Confidence interval (23.568, 25.940) shown on the printout. PREDICTED/FITTED VALUES OF TIME LOWER PREDICTED BOUND 17.753 LOWER FITTED BOUND 23.568 PREDICTED VALUE 24.754 FITTED VALUE 24.754 UPPER PREDICTED BOUND 31.755 UPPER FITTED BOUND 25.940 SE (PREDICTED VALUE) 3.4584 SE (FITTED VALUE) 0.5857 Predictor values: orders = 250 Answers: [The mean total order time for all days with 250 telephone orders falls between 23.568 and 25.94 hours. The total order time for a day with 250 telephone orders falls between 17.7 and 31.7 hours.] 9. Give a practical interpretation of the estimate of the y-intercept of the least squares line. 10. Based on the value of the test statistic given in the problem, make the proper conclusion. II. Example 13.2 on page 747 (page 788 for the 10ed.). H o : _______________ H a : ___________________ D.F. = _____ α = .05 RR: _________________ Test Statistic: _____________, χ 2 = ________ Decision: ___________________________________________ E( n 1 ) = ________, E( n 2 ) = ________, E( n 3 ) = ________, E( n 4 ) = ________....
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REv. Test 3 Regr., Categ. - Review for Test 3 STA-3123 I...

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