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PDB_Stat_100_Lecture_04_Printable

PDB_Stat_100_Lecture_04_Printable - STA 100 Lecture 4 Paul...

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STA 100 Lecture 4 Paul Baines Department of Statistics University of California, Davis January 10th, 2011
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Admin for the Day I Homework 1 due Wednesday, Jan 12th in class I Electronic submissions are not valid: we need paper! I If you complete your homework on computer (e.g., doc, pdf) then please also submit it to Smartsite via the Assignments tab I Smartsite submission not required if you handwrite your homework solutions I Forums: Thanks and please use! I Discussion Sections start tomorrow! References for Today: Rosner, Ch 6.1-6.2, 6.4 (7th Ed.) References for Wednesday: Rosner, Ch 3.1-3.6 (7th Ed.)
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Recap: Measures of Spread I Sample Variance: Var ( X ) = 1 n - 1 n X i =1 ( X i - ¯ X ) 2 (1) I Standard Deviation: SD ( X ) = p Var ( X ) = v u u t 1 n - 1 n X i =1 ( X i - ¯ X ) 2 (2) Why n - 1? We will see (next week).
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Linear Transformations Birthweights of 20 babies born in San Diego (grams): 3265, 3260, 3245, 3484, 4146, 3323, 3649, 3200, 3031, 2069, 2581, 2841, 3609, 2838, 3541, 2759, 3248, 3314, 3101, 2834 I Mean = 3166.9g, Var = 198323.6, SD = 445.323 I Need to convert to kilograms i.e., y = x / 1000. I Need to compute new mean, var and SD. Do we need to convert each data point to kgs, and then recompute?
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Linear Transformations More generally, if y = ax + b then: 1. Mean( y ) = a * Mean( x ) + b 2. Var( y ) = a 2 * Var( x ) 3. SD( y ) = a * SD( x ) These enable us to easily compute mean, SD and variance after a linear transformation – without converting each data point and recomputing.
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Example Birthweights of 20 babies born in San Diego (grams): 3265, 3260, 3245, 3484, 4146, 3323, 3649, 3200, 3031, 2069, 2581, 2841, 3609, 2838, 3541, 2759, 3248, 3314, 3101, 2834 I Mean = 3166.9g, Var = 198323.6, SD = 445.323 I Need to convert to kilograms i.e., y = x / 1000. I What are a and b ? I Compute the mean, variance, SD of the new data in kilograms: I Mean = ? Variance = ? SD = ?
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Producing Useful Graphs Plotting Principles: I Choose axes/scaling so that the data is not overly ‘clumped’ in one part of the graph I Always label axes and the plot itself I Select informative color schemes (more later) I Do not overclutter I Message should be rapidly discernible Tufte’s Principles: web link.
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