2DS00 Statistics 1 for Chemical Engineering Lecture 2

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

Detailed contents of week 2 error propagation significant numbers Least Squares Method basic notions of regression analysis

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?

Expectation and variance X is random variable with density f

Linear combinations random variables X i with mean  i and variance linear combination Rule 1 Rule 2 (independent random variables):

Example: titration Begin reading burette: 3.51 ml with  =0.02 ml End reading burette: ml with  =0.03 ml Questions: 1.What is  of used titrate? 2.The  of used titrate should not exceed What  should both readings have, assuming that they have equal  ’s?

Error propagation law Z=f(X 1,X 2 ) with E(X i )= µ i and Var(X i )=  i 2

Roots

Logarithms

Products

Quotients

Example: pH z = pH = 3.0 [H + ] = 1,0∙10 -3 M.;  z = 0.1 Calculate the coefficient of variation in [H + ]

Significance Basic rules: 1.Addition and subtraction: as many digits behind the decimal point as the measurement with the least digits behind the decimal point = Multiplication and division: as many significant digits as the measurement with the least significant digits 0.12 * = 1.2 Note: has 4 significant digits