2011fall-exam1-practiceproblems-solutions.pdf

2011fall-exam1-practiceproblems-solutions.pdf - ISyE4031...

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Group A 1 ISyE4031 Regression and Forecasting Practice Problems 1 Solutions Fall 2011 1. Short answers 1.1. b 1.2. c 1.3. b 1.4. c Q2. Short answers 2.1. d 2.2. a 2.3. b 2.4. a Q3. y x x y x x n y n n x x y n n x n n x n y n i i i i n i i = + - = + - = + - = + = + = = 1 1 1 1 1 1 0 1 0 1 ˆ ˆ ) ˆ ˆ ( 1 ) ˆ ) ˆ ( ( 1 ) ˆ ˆ ( 1 ) ˆ ˆ ( 1 ˆ 1 β β β β β β β β β β Q4. a. Since t value from the output=11.77> 2.024 which is the critical t value at α =0.025, d.f=38 (it’s ok to use 2.021), we reject H 0 : β 1 =0; and conclude that there is a significant relationship between Price and Carat. b. For every 1 unit increase in carat, there will be a corresponding increase of $9,349 in the mean diamond price. c. 1 ˆ β ± t 0.025,38 1 ˆ β S 9349 ± *2.021*794.1 9349 ± 1604.88 or (7744.12,10953.9). I used 2.021 instead of 2.024. With 95% confidence, the mean price will increase between $7744.12 and $10953.9 for every 1 unit increase in diamond carat. d. Let’s look at 95% PI and CI: 2 1576.1 54.8 (1465.2, 1687.0) ( 895.1, 2257.1) Even though the price of the diamond, $1,675 is greater than the predicted value, y ˆ =1576.1, it’s enclosed in the prediction interval (also CI). So, I would buy it.
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