Given:
(-5,14), (1,-16)
The linear regression formula is
[tex]y=mx+b[/tex]Substitute x=1 and y=-16 in the formula, we get
[tex]-16=m(1)+b[/tex][tex]-16=m+b[/tex]Subtracting m from both sides of the equation, we get
[tex]-16-m=m+b-m[/tex][tex]-16-m=b[/tex]We get
[tex]b=-16-m[/tex]Substitute x=-5 and y=14 in the formula, we get
[tex]14=m(-5)+b[/tex][tex]14=-5m+b[/tex]Substitute b=-16-m in this equation to find the value of m.
[tex]14=-5m-16-m[/tex][tex]14=-6m-16[/tex]Adding 16 to both sides of the equation, we get
[tex]14+16=-6m-16+16_{}[/tex][tex]30=-6m[/tex]Dividing both sides by (-6), we get
[tex]\frac{30}{-6}=-\frac{6m}{-6}[/tex][tex]m=-5[/tex]Substitue m=-5 in b=-16-m to find the value of b.
[tex]b=-16-(-5)[/tex][tex]b=-16+5[/tex][tex]b=-11[/tex]Substitute b= -11 and m= -5 in the line equation, we get
[tex]y=-5x-11[/tex]Hence linear regression is
[tex]y=-5x-11[/tex]