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Fit a straight line to the following data with x-as independent variable. | X : | 1965 | 1966 | 1967 | 1968 | 1969 || Y : | 125 | 140 | 165 | 195 | 200 |

written 4.6 years ago by teamques10 ★ 70k

modified 4.1 years ago by pg1118329 • 0

engineering mathematics

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written 4.6 years ago by teamques10 ★ 70k

Equation of a straight line: y=mx+c

Let x=X-1967, Y-y, N=number of points =5

x	1965	1966	1967	1968	1969
Y=y	125	140	165	195	200	825
x	-2	-1	0	1	2	0
x2	4	1	0	1	4	10
xy	-250	-140	0	195	400	205

$y=mx+c $

$\sum y=m \sum x+ cN $

$825=m(0)+5c $

$c=165 $

$xy=mx^2+cx $

$\sum xy = m \sum x^2 +c \sum x $

$205 = m (10)+c(0) $

$m=20.5 $

$y=20.5x+165 \ or \ 2y-41x=330$

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