Question

05) (Numerical Analyses). For all items, round the results for four decimal digits: A-Using the method of least square , fit a straight line to the points (1,1),(3,2),(4,4), (6,4), (8,5), (9,7), (11,8) and (14,9). (12 marks)

Answer 1

Answer:

To fit the straight line to the given points, there are the steps which need to be followed for least square method and the steps are given as

1. For each point given,calculate the $x^{2}$ and xy
2. After this sum all the x, y, $x^{2}$ and xy which gives the summation of all these
3. Calculate the slope
4. Calculate the intercept
5. After all these, assemble the equation of line as

$y=mx+b$

Where m is slope and b is intercept

Solution is given below step by step

Points given." (11), (3, 2) (4,4) (6,4), (8,5) ( 9,7)(11,83(14,9) So are Now we can prepa a table for easy understanding and for calculating x² and ny y xy 22 2x IL I 1 I 3 2 6 9 16 4 4 4 6 16 24 40 8 9 5 7 36 64 81 121 196 3 63 8 9 la 88 126 Ex: 56 Ey = 40 {x²=524 Eny = 364 Number of data N=8 valiers M Now slope = m = Nery - Exey NEX² - {x)² (8x 364)-(56x40) 8 x 524-(56) (29 12 - 2 240) (4192-3136) 1056 m- 672.6363

intercept b can be ginen as b= sy- mex Non Love 81 40-606363X 54) o dol rore 8 dinh NOM nuste 40-35.6328 TOM blou 4.3672 co b= 5459 Cound ou a so ya = math. A - from here YA 6363x4.5459 y = = .6363x + 5459 Ang OM