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final_06s - MATH202 Spring 2006 Final Exam a Instructions 1...

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MATH202 Spring 2006 Final Exam a Instructions: 1. Do not start until instructed to do so. 2. If you brought a cell phone by mistake, turn it off and place it under your seat. You may NOT use it as a calculator. 3. You may use a calculator (NOT a cell phone calculator) and three 3x5 cards (front and back) with notes, but nothing else. 4. Code your UDelNet ID in the Last Name space on your scansheet and fill in the bubbles. 5. Write your name in the white space below the name box on your scansheet. 6. DO NOT put any part of your Social Security Number on your scansheet. 7. Choose the best answer to each question. 8. Use α = .05.
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Questions 1 – 7 : The table at the left shows quarterly retail sales figures for JCPenney (in millions of dollars). Some data analyses are shown below including regression output for the following models: y = retail sales (millions of dollars) Time = time index (1, 2, ..., 24) 1 Q = 1 if quarter 1, 0 otherwise 2 Q = 1 if quarter 2, 0 otherwise 3 Q = 1 if quarter 3, 0 otherwise Model 1: ε β β + + = Time y 1 0 Model 2: ε β β β β β + + + + + = 3 2 1 4 3 2 1 0 Q Q Q Time y Model 1: Regression Analysis: Sales versus Time The regression equation is Sales = 5903 + 119 Time Predictor Coef SE Coef T P Constant 5903.2 492.9 11.98 0.000 Time 118.75 34.49 3.44 0.002 S = 1169.71 R-Sq = 35.0% R-Sq(adj) = 32.1% Analysis of Variance Source DF SS MS F P Regression 1 16217509 16217509 11.85 0.002 Residual Error 22 30100626 1368210 Total 23 46318136 Model 2: Regression Analysis: Sales versus Time, Q1, Q2, Q3 The regression equation is Sales = 7859 + 99.5 Time - 2274 Q1 - 2565 Q2 - 2023 Q3 2 Year Quarter Sales 1996 1 4452 1996 2 4507 1996 3 5537 1996 4 8157 1997 1 6481 1997 2 6420 1997 3 7208 1997 4 9509 1998 1 6755 1998 2 6483 1998 3 7129 1998 4 9072 1999 1 7339 1999 2 7104 1999 3 7639 1999 4 9661 2000 1 7528 2000 2 7207 2000 3 7538 2000 4 9573 2001 1 7522 2001 2 7211 2001 3 7729 2001 4 9542 Index Sales 24 22 20 18 16 14 12 10 8 6 4 2 10000 9000 8000 7000 6000 5000 4000 Moving Average Length 3 Accuracy Measures MAPE 14 MAD 1141 MSD 2165531 Variable Actual Smoothed Moving Average Plot for Sales Index Sales 24 22 20 18 16 14 12 10 8 6 4 2 10000 9000 8000 7000 6000 5000 4000 Smoothing Constant Alpha 0.6 Accuracy Measures MAPE 13 MAD 1056 MSD 1834078 Variable Actual Smoothed Single Exponential Smoothing Plot for Sales Time Y- Data 25 20 15 10 5 0 10000 9000 8000 7000 6000 5000 4000 Variable Sales FITS_T Scatterplot of Sales, FI TS_T vs Time (from Model 1) Time Y-Data 25 20 15 10 5 0 11000 10000 9000 8000 7000 6000 5000 4000 Variable Sales FITS_TS Scatterplot of Sales, FI TS_TS vs Time (from Model 2)
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Predictor Coef SE Coef T P Constant 7858.8 331.3 23.72 0.000 Time 99.54 16.93 5.88 0.000 Q1 -2274.2 331.1 -6.87 0.000 Q2 -2564.6 328.9 -7.80 0.000 Q3 -2022.8 327.6 -6.17 0.000 S = 566.720 R-Sq = 86.8% R-Sq(adj) = 84.1% Analysis of Variance Source DF SS MS F P Regression 4 40215885 10053971 31.30 0.000 Residual Error 19 6102250 321171 Total 23 46318136 1. Use single exponential smoothing with w = .6 to find the smoothed value for 1996 quarter 2. a. 4474 b. 4832 c. 4480 d. 4485 e. 4507
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