2DS00

1
2DS00

• Statistics 1 for Chemical Engineering
• Lecture 2

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Week schedule

• Week 1 Measurement and statistics
• Week 2 Introduction to regression analysis
• Week 3 Simple linear regression analysis
• Week 4 Multiple linear regression analysis
• Week 5 Nonlinear regression analysis

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Detailed contents of week 2

• error propagation
• significant numbers
• Least Squares Method
• basic notions of regression analysis

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Error propagation

• measurements usually consist of submeasurements
• examples
• titration (begin reading and end reading)
• concentration is function of mass and volume
• ...
• how to compute precision and accuracy of
  composite measurements?

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Expectation and variance

• X is random variable with density f

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Linear combinations

• random variables Xi with mean ?i and variance
• linear combination
• Rule 1
• Rule 2 (independent random variables)

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Example titration

• Begin reading burette 3.51 ml with ?0.02 ml
• End reading burette 15.67 ml with ?0.03 ml
• Questions
• What is ? of used titrate?
• The ? of used titrate should not exceed 0.03.
  What ? should both readings have, assuming that
  they have equal ?s?

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Error propagation law

• Zf(X1,X2) with E(Xi ) µi and Var(Xi ) ?i 2

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Roots
10
Logarithms
11
Products
12
Quotients
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Example pH

• z pH 3.0 H 1,010-3 M. ?z 0.1
• Calculate the coefficient of variation in H

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Significance

• Basic rules
• Addition and subtraction as many digits behind
  the decimal point as the measurement with the
  least digits behind the decimal point0.03 0.12
  0.4576 0.61
• Multiplication and division as many significant
  digits as the measurement with the least
  significant digits0.12 9.678234 1.2 Note
  12.40 has 4 significant digits