Question

6. Find the least squares line associated with the following data. Show all work for any credit. X 12 2.1 3.2 6.3

Answer 1

6

x	y	xy	x2
12	2.1	25.2	144
10	3.2	32	100
6	6.3	37.8	36
2	9.1	18.2	4

To find the least squares line, the following three formulas are required

m= [n($\sum$xy)-($\sum$x)($\sum$y)]/ [n($\sum$x²)-($\sum$x)²

b= ($\sum$y)-m($\sum$x)/n

y=mx+b(formula for equation of a line: slope-intercept form)

m: slope of line

b: y-intercept

n=4

m=[4(113.2)-30(20.7)]/[4(284)-(30)²]

=- 168.2/236=0.7127

Substituting the value of m in the equation for b we get

b=[ 20.7-(-168.2/236*30)]/4

=10.520

Substituting the above values in the equation y=mx+b

y= 0.7127x+10.520 is the least squares line associated with the given data