Lec18p4 - JUST THE MATHS UNIT NUMBER 18.4 STATISTICS 4(The...

Info iconThis preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon
“JUST THE MATHS” UNIT NUMBER 18.4 STATISTICS 4 (The principle of least squares) by A.J.Hobson 18.4.1 The normal equations 18.4.2 Simplified calculation of regression lines 18.4.3 Exercises 18.4.4 Answers to exercises
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
UNIT 18.4 - STATISTICS 4 THE PRINCIPLE OF LEAST SQUARES 18.4.1 THE NORMAL EQUATIONS Suppose two variables, x and y , are known to obey a “straight line law” of the form y = a + bx , where a and b are constants to be found. Suppose also that, in an experiment to test this law, we obtain n pairs of values, ( x i , y i ), where i = 1,2,3,. .., n . If the values x i are assigned values, they are likely to be free from error, whereas the observed values, y i will be subject to experimental error. The principle underlying the straight line of “best fit” is that, in its most likely position, the sum of the squares of the y -deviations, from the line, of all observed points is a minimum. Using partial differentiation, it may be shown that n X i =1 y i = na + b n X i =1 x i --- (1) and n X i =1 x i y i = a n X i =1 x i + b n X i =1 x 2 i --- (2) . The statements (1) and (2) are two simultaneous equations which may be solved for a and b . They are called the “normal equations” .
Background image of page 2
Image of page 3
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

Page1 / 7

Lec18p4 - JUST THE MATHS UNIT NUMBER 18.4 STATISTICS 4(The...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online