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Exam1Key - STAT 512 MidTerm I Section(circle Spring 2012...

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1 STAT 512 MidTerm I (2/15/2012) Spring 2012 Section (circle): 12:30 pm 1:30 pm Name: ___ KEY ______________________________________ INSTRUCTIONS 1. This exam is open book/open notes. All papers (but no electronic devices except for calculators) are allowed. 2. There are 4 pages in addition to the cover sheet. If you need more room for a problem, use the back of the sheets; clearly indicate where the location of the answer is. 3. Work is required to receive credit. Partial credit will be given for work that is partially correct. Points will be deducted for incorrect work even if the final answer is correct. 4. If I cannot read your answer, it will be marked wrong. 5. Good Luck! Question Possible Score 1 45 2 21 3 40 Total 107
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2 (45 pts.) 1. The Tri-City Office Equipment Corporation sells and performs maintenance on imported copiers via a franchise business. They want to know if there is a relationship between the number copiers serviced (X = number) and the total number of minutes spend by the service person (Y = time). The following data is based on 42 recent calls for routine preventive maintenance. Parameter Standard Variable DF Estimate Error t Value Pr > |t| Intercept 1 -0.58016 2.80394 ? 0.8371 number 1 15.03525 0.48309 ? <.0001 a) Write down the simple linear regression model and the assumed distribution of the errors. Y i = 0 + 1 X i + i with i ??? ~ N (0, 2 ) where Y i is the time in minutes, X i is the number of copiers b) Write down the estimated regression line. i = -0.58016 + 15.03525 X i c) Explain the difference between parts a) and b). a) refers to the model with the true parameters and b) refers to a calculation from the data. a) refers to the actual points (the error term) and b) refers to only the best fit line Note: you did not need to include all of these points to get full credit. d) What is the fitted value of Y for X = 6? If the actual value of Y is 96, what is the residual? 6 = -0.58016 + 15.03525 (6) = 89.63134 e 6 = 96 - 89.63134 = 6.36866 e) Calculate the missing t values for the intercept and slope.
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